Time-lapse Acoustic Imaging of
Oceanic Fronts and Eddies
Kathryn Louise Gunn
A dissertation submitted for the degree of
Doctor of Philosophy
at the University of Cambridge
St Edmund’s College
July 2018
How inappropriate to call this planet Earth when it is clearly Ocean.
Arthur C. Clarke
Declaration
This dissertation describes my original work except where acknowledgement is made in the text.
It does not exceed the page limit and is not substantially the same as any work that has been, or
is being submitted to any other university for any degree, diploma or any other qualification.
Kathryn Louise Gunn
July 2018
Acknowledgements
First, I would like to thank my supervisor Nicky White for giving me this opportunity and for
his guidance throughout my time in the Drum Building. Secondly, I would like to thank Rob
Larter for his calm leadership onboard the RRS James Clark Ross and for the decision to land
in Rothera Research Station for a wonderful 8 hours. Thanks also to the crew and scientists
onboard the JR298 who made the cruise an unforgettable experience. Finally, Colm Caulfield
for his support in all things, especially those fluid dynamical. Special thanks to the office mates
that have graced my time in and out of the Drum Building: Paddy Ball, Laurence Cowton, Alex
Dickinson, Marthe Klo¨cking, Fergus McNab, Conor O’Malley, Fred Richards, Vero´nica Rodr´ıguez
Tribaldos and Charlie Schoonman (not forgetting Simon Stephenson). In the wider Bullard Labs
and downtown community, I would like to thank Katy Relph, Ophelia Crawford, Thomasina Ball
and Camilla Penney whose various dinners, yoga and general meet-ups have proven to be invaluable.
I would like to thank Tanya Blacic and Alex Dickinson for sharing their scripts with me, which
has been greatly appreciated and released me from endless hours of coding. I would also like to
thank Sophie Fielding and Jules Hummon for taking the time to teach me about echo-sounding
and acoustic doppler current profiling. Thanks to Alex Brearly, Hugh Venables and Mike Meredith
for many questions and discussion about physical oceanography.
Special thanks go to my housemates and friends scattered around Cambridge, Leeds, London and
Australia who have kept me sane throughout my Ph.D. Special mention for the lovely Carlie Ng
and John Hamp, who have been by my side for close to a decade. I wish to thank Tom for his
love and support, which I would have been lost without. Finally, all my love and gratitude to my
parents as ever. Thank you.
Kathy
Publications Arising from this Work
Chapter 3 is based on work published in:
Gunn, K. L., White, N. J., Larter, R. D., & Caulfield, C. P. 2018. Calibrated Seismic Imaging of
Eddy-Dominated Warm-Water Transport across the Bellingshausen Sea, Southern Ocean. Journal
of Geophysical Research. 123, 3072–3099.
Time-lapse Acoustic Imaging of Oceanic Fronts and Eddies
Kathryn Louise Gunn
Seismic reflection surveying is used to generate acoustic images of the water column. This tech-
nique employs conventional multi-channel equipment which is used to image the solid Earth. In
the water column, acoustic impedance contrasts are produced by variations in temperature and,
to some extent, salinity. Acoustic impulses generated by an array of airguns suspended behind
a vessel are reflected from these contrasts and recorded on long cables of hydrophones that are
towed below the sea-surface. In this way, two- and three-dimensional images of thermohaline cir-
culation can be generated. Critically, these images have equal vertical and horizontal resolutions
of O(10) m. Here, I describe, process, and analyse a calibrated two-dimensional seismic survey
from the Bellingshausen Sea of the Southern Ocean and a three-dimensional seismic survey from
the Brazil-Falkland Confluence located offshore Uruguay. First, the Bellingshausen survey was de-
signed to image the thermohaline structure across the west Antarctic shelf where warm-core eddies
are reported. Processed and calibrated seismic images reveal the detailed thermohaline structure of
Circumpolar Deep Water. Many warm-core eddies are observed, which have diameters of 1–12 km
and thicknesses of 100–200 m. Pre-stack analysis demonstrates that this eddy field is being ad-
vected onto the shelf at speeds of O(0.1) m s−1. An iterative inverse modelling procedure is used to
convert reflectivity into temperature and salinity, which confirms that the eddies have anomalously
warm centres (i.e. ∼1◦C). These results have significant implications for ice shelf melting. Sec-
ondly, the Uruguay survey is used to investigate a large-scale frontal system. Although this system
has been studied using hydrographic methods, these studies either have limited spatial resolution
or have restricted depth penetration. The three-dimensional seismic survey, which was acquired
in a ‘racetrack’ pattern, permits the volume to be interrogated. Since the frontal system migrates
southwestwards at a speed of O(10) km day−1, this survey is time-lapse in nature. Processed images
reveal a band of dipping reflections that extend to depths of ∼2000 m. These reflections represent
the frontal interface between the Brazil and Falkland currents. Physical oceanographic properties
are calculated for images that cross this front. On the warm side of the front, the water mass is
characterised by flat and continuous reflectivity. On the cold side of the front, the water mass is
characterised by deformed reflectivity on all scales. Pre-stack analysis suggests that near-surface
flow at the frontal interface is convergent. Between 0.5 and 1 km depth, a substantial eddy that
is 30 km long and 250 m thick is visible on the cold side of the front. Detailed mapping suggests
that this eddy grew and decayed over a period of 6 days. Its observed scale and duration are
inconsistent with analytical and numerical studies of intra-thermocline eddies. Nevertheless, its
duration is consistent with scaling arguments of frictional spin-down. Spatial and temporal distri-
butions of mixing rates (i.e. diapycnal diffusivities) are estimated by spectrally analysing vertical
displacements of automatically tracked reflections. Both internal wave and turbulent regimes are
identifiable. Recovered diapycnal diffusivities are of O(10−6–10−2.2) m2 s−1, consistent with hydro-
graphically determined estimates. Mixing is suppressed and enhanced on the warm and cold sides
of the front, respectively. Seismic Oceanography has considerable potential to quantify aspects of
thermohaline circulation on multiple scales.
Contents
List of Figures viii
List of Tables ix
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Seismic Reflection Profiling of the Water Column . . . . . . . . . . . . . . . . . . . . 3
1.3 Dissertation Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Seismic Acquisition and Processing 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Two-dimensional Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Acoustic Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Convolution Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Common Midpoint Gathers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.5 JR298 Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.6 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Three-dimensional Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.1 Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
i
2.3.2 Acoustic Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3.3 CMP Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.4 Uruguay Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.5 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4 Water Column Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.1 Temperature and Salinity Contributions . . . . . . . . . . . . . . . . . . . . . 50
2.4.2 Vertical and Horizontal Resolution . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Warm-Water Transport across West Antarctic Shelf 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Oceanographic Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Seismic Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3.1 Acquisition and Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4 Temperature Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Development of Adapted Sound Speed Model . . . . . . . . . . . . . . . . . . 66
3.5 Additional Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.1 High Frequency Acoustic Data . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.2 Acoustic Doppler Current Profiler . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 Seismic Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.1 Large-scale Patterns of Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.2 Small Mesoscale to Sub-Mesoscale Structures . . . . . . . . . . . . . . . . . . 74
3.6.3 Eddy Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.7.1 On-shelf transport of warm-water . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.7.2 Frequency and Duration of Eddies . . . . . . . . . . . . . . . . . . . . . . . . 88
3.7.3 Off-Shelf Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
ii
4 Time-lapse Imaging of the Brazil-Falkland Confluence 99
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2 Oceanographic Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3 Seismic Acquisition and Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.4 Seismic Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.4.1 Patterns of Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4.2 Spatial and Temporal Variation of Reflectivity . . . . . . . . . . . . . . . . . 116
4.4.3 T , S, ρθ, N
2, and ugy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.4.4 Current Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5.1 Slope of Frontal Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.5.2 Frontogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.5.3 Time-lapse Imaging of Deep Eddy . . . . . . . . . . . . . . . . . . . . . . . . 142
4.5.4 Generation Mechanisms of Deep Eddy . . . . . . . . . . . . . . . . . . . . . . 148
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5 Estimating Diapycnal Diffusivity from Seismic Images 153
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.2 Energy Density Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.3 Seismic Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.3.1 Assessing Suitability for Spectral Analysis . . . . . . . . . . . . . . . . . . . . 159
5.3.2 Power Spectra of Horizontal Gradient of Vertical Displacements . . . . . . . . 163
5.3.3 Diapycnal Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.3.4 Comparing Internal Wave and Turbulent Estimates of K . . . . . . . . . . . 168
5.3.5 Spatial and Temporal Variation of Diapycnal Diffusivity . . . . . . . . . . . . 173
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.4.1 Mixing Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
iii
6 Conclusions and Further Work 185
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
A Seismic Processing Flow 203
B JR298 Seismic Survey 205
C Uruguay Seismic Survey 215
iv
List of Figures
1.1 Instruments that measure physical properties of the ocean . . . . . . . . . . . . . . . 3
1.2 Global map showing location of marine seismic reflection datasets used in this dis-
sertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Set of cartoons that show evolving geometry of seismic reflection experiment. . . . . 13
2.2 Schematic of two-dimensional marine seismic acquisition . . . . . . . . . . . . . . . . 14
2.3 Schematic showing airgun operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Comparison of ideal versus typical source wavelet convolved with reflectivity series . 17
2.5 Amplitude, frequency and phase of common source wavelets . . . . . . . . . . . . . . 18
2.6 JR298 near-field source wavelet recorded during acquisition . . . . . . . . . . . . . . 19
2.7 Example shot gathers showing common noise types encountered during marine ac-
quisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.8 Example shot gathers showing effect of bandpass frequency filtering . . . . . . . . . 24
2.9 Direct wave removal using linear filtering . . . . . . . . . . . . . . . . . . . . . . . . 26
2.10 Variable rates of decay for three bandwidths in a seismic trace . . . . . . . . . . . . 30
2.11 Cartoon showing normal move-out correction . . . . . . . . . . . . . . . . . . . . . . 31
2.12 Sound speed analysis of two example CMP gathers . . . . . . . . . . . . . . . . . . . 33
2.13 Effect of carefully choosing vrms for Profile 52 from JR298 survey . . . . . . . . . . . 34
2.14 Effect of carefully choosing vrms for Profile 2 from Uruguay survey . . . . . . . . . . 35
2.15 Effect of deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
v
2.16 Schematic of three-dimensional marine seismic acquisition . . . . . . . . . . . . . . . 39
2.17 Two statistical estimation methods used to reconstruct source wavelet . . . . . . . . 41
2.18 Binning three-dimensional seismic reflection data . . . . . . . . . . . . . . . . . . . . 43
2.19 Schematic showing two-dimensional Fourier Transform of t-x data into f -k domain . 46
2.20 Spatial aliasing of direct wave in t-x space . . . . . . . . . . . . . . . . . . . . . . . . 47
2.21 Filtering in f -k space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.22 Attenuating anomalously high amplitudes using time-frequency filtering . . . . . . . 49
2.23 Diagrams of physical properties and their T and S partial derivatives of v and ρ . . 52
2.24 Stacked seismic images that show each stage of processing flow applied to water
column reflection records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.1 Bellingshausen Sea regional context . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Physical oceanographic context of west Antarctic marginal seas. . . . . . . . . . . . . 61
3.3 Seismic reflection profiles 52, 61 and 62. . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Sound speed analysis of two different CMP gathers from Profile 52 . . . . . . . . . . 67
3.5 Sound speed model development for adapted inversion procedure . . . . . . . . . . . 69
3.6 Converted temperature distributions for Profile 52, 61 and 62. . . . . . . . . . . . . . 71
3.7 Comparison of converted temperature profiles obtained from adapted inversion pro-
cedure with coeval measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.8 Zoom of seismic and calculated temperature anomalies for Profile 52 . . . . . . . . . 75
3.9 Zoom of seismic and calculated temperature anomalies for Profile 61 . . . . . . . . . 77
3.10 Zoom of seismic, echo-sounder and calculated temperature anomalies for Profile 62 . 79
3.11 Interecting seismic, ADCP and calculated temperature anomaly measurments for
Profiles 55 and 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.12 Measuring current speed using pre-stack seismic records . . . . . . . . . . . . . . . . 83
3.13 Interpretation of warm-core eddies along Profile 52 . . . . . . . . . . . . . . . . . . . 90
3.14 Cartoon showing assumption of constant U and constant Q . . . . . . . . . . . . . . 93
4.1 Regional map of southwest Atlantic Ocean showing confluence of water masses . . . 101
vi
4.2 Physical oceanographic properties of southwest Atlantic Ocean . . . . . . . . . . . . 106
4.3 Three-dimensional seismic survey configuration and setting . . . . . . . . . . . . . . 108
4.4 Intersecting perpendicular seismic images from Profile 2 showing three-dimensional
thermohaline structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.5 Zoomed portions of central cross-section from Profile 2 . . . . . . . . . . . . . . . . . 112
4.6 7 synthetic seismograms generated from hydrographic casts and projected onto Pro-
file 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.7 Seismic reflection profiles from Set A shown with coeval sea-surface temperature
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.8 Seismic reflection profiles from Set B shown with coeval sea-surface temperature
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.9 Regional sea-surface temperature variation during seismic surveying . . . . . . . . . 119
4.10 Zoomed portions of Profiles 5, 6 and 7 with line-drawing interpretation of thermo-
haline structure evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.11 Seismic reflection profiles 9 and 10 from Set C . . . . . . . . . . . . . . . . . . . . . . 124
4.12 Seismic reflection profiles 13, 14 and 15 from Set D . . . . . . . . . . . . . . . . . . . 125
4.13 Seismic reflection profile 18 and 19 from Set E . . . . . . . . . . . . . . . . . . . . . 127
4.14 Seismic reflection profiles 2 and 4 converted into temperature . . . . . . . . . . . . . 129
4.15 Seismic reflection Profile 2 converted into salinity, potential density, buoyancy fre-
quency, and geostrophic current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.16 Internal wave speed measurements across Profile 2 . . . . . . . . . . . . . . . . . . . 136
4.17 Measuring internal wave speed from pre-stack seismic data . . . . . . . . . . . . . . 137
4.18 Temporal evolution of frontal interface and deep eddy . . . . . . . . . . . . . . . . . 144
4.19 Three hypotheses for cross-sectional area change of eddy . . . . . . . . . . . . . . . . 146
4.20 Idealised sketch of deep reaching front at Brazil-Falkland Confluence . . . . . . . . . 151
5.1 Estimating diapycnal diffusivity from seismic images . . . . . . . . . . . . . . . . . . 158
5.2 Assessing suitability of seismic images for spectral analysis . . . . . . . . . . . . . . . 161
5.3 Suite of 20 horizontal gradient spectra calculated from tracked seismic reflections . . 164
5.4 Distribution of K estimated from seismic imagery . . . . . . . . . . . . . . . . . . . . 167
vii
5.5 Spatial pattern of K estimated using internal wave and turbulent spectral sub-regions169
5.6 Correlation of diapycnal diffusivity estimated from internal wave and turbulent sub-
ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
5.7 Comparison of vigorous mixing rates estimated from internal wave and turbulent
sub-ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.8 Seismic reflection profiles from Set A overlain with spatial pattern of K . . . . . . . 176
5.9 Relationship between K and depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.10 Spatial and temporal variation of diapycnal diffusivity across front . . . . . . . . . . 181
A.1 Processing flow applied to two- and three-dimensional seismic datasets discussed in
this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
B.1 Biscoe Trough seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . . . . . 207
B.2 Thurston Island Drift seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . 208
B.3 Belgica Trough seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . . . . . 209
B.4 Alexander Island Drift seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . 210
B.5 Alexander Island Drift seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . 211
B.6 Marguerite Trough seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . . . 212
B.7 Marguerite Trough seismic reflection profiles . . . . . . . . . . . . . . . . . . . . . . . 213
C.1 Seismic reflection profiles from Set C . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
C.2 Seismic reflection profiles from Set D . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
C.3 Seismic reflection profiles from Set E . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
C.4 Seismic reflection profiles from Set A converted into temperature using iterative
inversion procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
C.5 Seismic reflection profiles from Set B converted into temperature using iterative
inversion procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
C.6 Zoom of seismic imagery around frontal interface and deep eddy highlighting tem-
poral variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
viii
List of Tables
2.1 Comparison between two- and three-dimensional seismic survey acquisition parameters. 56
3.1 Coeval hydrographic measurements from cruise JR298 used to calibrate seismic profiles. 60
3.2 Constants and variables used in scaling analysis . . . . . . . . . . . . . . . . . . . . . 87
4.1 Near-coeval hydrographic measurements acquired during seismic surveying . . . . . . 104
4.2 Seismic reflection profile acquisition information. . . . . . . . . . . . . . . . . . . . . 109
5.1 Constants and variables used in mixing analysis. GM = Garrett-Munk. . . . . . . . 157
B.1 Seismic reflection profiles acquired during cruise JR298 . . . . . . . . . . . . . . . . . 206
ix
Chapter 1
Introduction
1.1 Background
Oceanic circulation and stratification is forced by fluxes of mass, heat, salt, and nutrients across
scales that range from millimetres to tens of thousands of kilometres. Since oceans cover ∼70%
of the Earth’s surface, these interactions are a key control on our climate. Despite this extensive
coverage, the National Oceanic and Atmospheric Administration (NOAA) estimate that 95% of the
ocean floor remains unexplored. Large-scale fluxes play the largest role in controlling the climate.
However, equilibrium is necessarily achieved through a balancing of kinetic energy dissipation at
centimetre scales (McWilliams, 2016). Diapycnal mixing, which is driven by intermittent patches
of small-scale turbulence across a few metres, drives basin-scale meridional overturning circulation
of the ocean. Thus, there is a dynamic route of energy distribution that traverses all intervening
scales. This relationship between large-scale circulation and small-scale mixing is a consequence of
the turbulent nature of oceanic flows and ensures that energy is continuously exchanged at all scales
of motion. Not only are these flows broad in the spatial domain, their temporal range extends from
minutes to years. For these reasons, large-scale structures should not be analysed in isolation from
smaller-scale swirls and billows (Ferrari & Wunsch, 2009). However, measuring and understanding
interactions that span this wide range of scales presents a significant challenge.
K.L. Gunn, Ph.D. Dissertation
Introduction 2
The most widely used oceanographic observational tool, the Conductivity Temperature Depth
probe (CTD), collects single vertical profiles of physical properties with millimetre to centimetre
resolution (Figure 1.1a). The primary function of a CTD is to detect conductivity and tempera-
ture changes relative to depth. Since conductivity is directly related to salinity and temperature,
these measurements can be used to determine density which is a primary driving force of ocean
circulation. The Hydrographic Programme of the World Ocean Circulation Experiment (WOCE)
was a comprehensive global hydrographic survey of physical and chemical properties during the
1990s (e.g. Koltermann et al., 2011). These data represent the state of the oceans during this time
and provide valuable atlases of basic physical properties. Several hours are often required to collect
each CTD cast, during which the acquisition vessel is stationary. Although it is possible to space
CTD casts as closely as required, practically, the time needed for each deployment leads to large
lateral spacing of O(10) km between each vertical profile. For example, nominal horizontal spacing
between WOCE CTD profiles is 50 km (Koltermann et al., 2011). This spatial separation translates
to large temporal spacing on the order of hours to days. The discrete, one-dimensional nature of
CTD transects leads to inherent limitations in observing the lower end of horizontal spatial and
temporal scales (i.e. less than kilometres and hours). Nevertheless, CTDs remain one of the most
popular oceanographic tools, and, as a result, these data are widely available.
The advent of new technologies has improved sampling limitations imposed by point or averaged
measurements. Underwater gliders provide vertical profiles with lateral spacing of ∼1 km, whilst
moored arrays provide temporally continuous profiles (Figure 1.1b). Argo floats are a global array
of 3,800 free-drifting profiling floats that measure temperature and salinity of the upper 2000 m
of the ocean (e.g. Argo, 2000). Furthermore, satellite observations have revolutionised spatial
coverage of surface ocean measurements (Figure 1.1c). Satellites provide global physical property
databases with samples every few kilometres (e.g. https : //www.nasa.gov/). These methodologies
provide a detailed picture of the ocean yet have observational limitations. For example, gliders,
moored arrays, and Argo floats are one-dimensional whilst satellites observe surface properties.
Acoustic reflection methods are able to provide high resolution two-dimensional profiles of the
ocean. These profiles can span a broad range of spatial and temporal scales thereby complementing
standard hydrographic methods and bridging the observational gap between large- and small-scales.
Sound energy generated beneath the sea-surface propagates downwards, echoes at reflectors, and
is recorded at an array of receivers. Recorded data provide a profile of the ocean as a function
of depth and horizontal distance (i.e. vertical cross-sections of the oceanic volume). At high
frequencies (18–200 kHz), acoustic methods record suspended particulates, zooplankton and larger
Introduction 3
biological matter, such as fish. These instruments are broadly referred to as echo-sounders. Within
this high frequency range are Acoustic Doppler Current Profilers (ADCP) which measure current
velocity. At low frequencies (10–150 Hz), acoustic methods record fine-scale thermohaline contrasts
that have vertical length scales of metres. Acoustic records obtained using low frequency sources
are commonly known as seismic records, and the method as seismic reflection profiling (Figure
1.1d).
Figure 1.1: Instruments that measure physical properties of the ocean. (a) Conductivity Temper-
ature Depth probe (CTD). (b) Underwater glider. (c) Geostationary Operational Environmental
Satellite Two (GOES-2) before its launch in 1975. (d) Seismic vessel during acquisition. Sources:
(a-c) NOAA and (d) Polarcus.
1.2 Seismic Reflection Profiling of the Water Column
For decades, marine seismic reflection profiling has been used for solid Earth hydrocarbon explo-
ration (Sheriff, 1991). The technique employs a towed array of airguns that generate periodic pulses
of acoustic energy. When fired, the airguns release compressed air into the water column which
is transmitted at and reflected from thermohaline fine-structure (Holbrook et al., 2003). Reflected
K.L. Gunn, Ph.D. Dissertation
Introduction 4
energy is recorded on a receiver array that is towed behind the vessel in water depths of 5–10 m.
A typical seismic survey extends >100 km horizontally, and records reflections at depths of several
kilometres. A seismic survey of this size can be acquired in several hours and typically samples the
water column every 6.25 m horizontally. Seismic data have been acquired in marine settings for
decades through the joint efforts of the hydrocarbon industry and academic institutions. The qual-
ity and abundance of these records has created an extensive archive of high resolution, O(10) m,
remote sensing data. This relatively untapped archive can be used to complement both traditional
(CTD) and emerging (Glider and Argo) hydrographic techniques.
Although reflections in the water column have often been observed, the ocean has largely been
considered a murky lens that obscures target hydrocarbons (e.g. Gonella & Michon, 1988). For
this reason, the water column component of seismic data is usually removed during the first stages
of processing (Yilmaz, 2001). In 2003, water column reflections observed by the seismic reflection
technique were linked to oceanic phenomena in the North Atlantic Current (Holbrook et al., 2003).
In their seminal paper, Holbrook et al. (2003) showed the correspondence between water column re-
flections and vertical temperature gradient and they are credited with launching the cross-discipline
of seismic reflection profiling and physical oceanography, namely ‘seismic oceanography’. Oceanic
impedance contrasts, that occur over metre length scales, are caused by sound speed and density
variations that are in turn controlled by temperature and salinity (Ruddick et al., 2009; Sallare`s
et al., 2009). This conclusion underpins interpretation of water column seismic imagery. Over
the past decade these images have provided new insights into a variety of oceanographic phenom-
ena such as fronts, eddies, internal waves and thermohaline staircases (e.g. Holbrook et al., 2003;
Nakamura et al., 2006; Biescas et al., 2008; Krahmann et al., 2009; Holbrook et al., 2013; Fortin
et al., 2017). Inverse modelling of seismic data to obtain quantitative physical properties, such as
salinity and temperature, has emerged as a key challenge facing the seismic oceanography commu-
nity. Papenberg et al. (2010) have shown that sections of high resolution thermohaline properties
can be obtained from seismic inversion of reflection data that are constrained by coincident CTD
casts. Spectral analysis of tracked seismic reflections has demonstrated that seismic imaging can
identify the internal wave and turbulent regimes of energy spectra. These sub-ranges can be used
to measure diapycnal diffusivity (e.g. Holbrook & Fer, 2005; Sheen et al., 2009). Seismic imagery
of the water column yields vertical and lateral resolutions of up to 10 m, and therefore improves
our ability to map the world’s ocean and address long-standing problems.
In this dissertation, specialised and adapted processing techniques are used to produce seismic im-
Introduction 5
ages at two locations that have wider implications for global ocean circulation and climate change.
A two-dimensional seismic reflection survey acquired in the Bellingshausen Sea, off the west Antarc-
tic Peninsula, is presented and analysed. The survey was acquired during February 2015 on board
RRS James Clark Ross during academic research cruise JR298. The main purpose of JR298 was
to collect marine geological and geophysical data in support of the International Ocean Discovery
Program proposal “Sediment drifts off the Antarctic Peninsula and West Antarctica”. The resul-
tant seismic profiles traverse parts of the continental shelf in the vicinity of the Bellingshausen Sea
adjacent to the West Antarctica Peninsula (Figure 1.2). Widespread and intensifying glacial accel-
eration has been linked to on-shelf transport of warm water via an energetic eddy field (e.g. Stewart
& Thompson, 2015). Since this field is characterised by eddies with lengths of O(10) km it is dif-
ficult to quantity the properties and numbers of these lenses using sparsely spaced hydrographic
casts. Using the JR298 survey, the first aim of this dissertation is to constrain warm-water intrusion
mechanisms that contribute to increasing ice-shelf basal melt rates. Coeval oceanographic, current
speed and echo-sounder data were acquired and have been processed and interpreted to calibrate
the seismic images obtained from this cruise.
In the latter part of this study, a three-dimensional industry-standard seismic reflection survey
is presented and analysed. The survey was acquired between December 2012 and April 2013 by
Polarcus, and is owned by Royal Dutch Shell and Administracio´n Nacional de Combustibles, Alcoholes y
Portland (ANCAP). The resultant seismic profiles run parallel to the continental shelf edge 220 km
east of the R´ıo de la Plata estuary, offshore Uruguay (Figure 1.2). This region is characterised
by a complex frontal system that is generated by the meeting of the cold Falkland and warm
Brazil Currents. Fronts are ubiquitous and occur on virtually all space and time scales. They may
be permanent, transient, shallow or deep, and therefore most technologies do not have both the
spatial coverage and resolution to fully resolve their properties. The high resolution and ability
to simultaneously image large portions of the oceans provided by seismic reflection profiles means
resultant images of the water column are well-suited to investigate the mesoscale to sub-mesoscale
dynamics of the Brazil-Falkland Confluence. Using the Uruguay survey, the second aim of this
dissertation is to demonstrate that seismic surveying can be used to constrain the nature of a front
at the spatial resolution and coverage required. This dataset is spectrally analysed with a view
to investigating four-dimensional patterns of diapycnal diffusivity at the confluence. These images
are calibrated and interpreted with the aid of coeval satellite observations and a small number of
in situ measurements.
K.L. Gunn, Ph.D. Dissertation
Introduction 6
Figure 1.2: Global map showing location of marine seismic reflection datasets used in this disser-
tation. Black labelled boxes = location and name of seismic survey.
The inversion method of Papenberg et al. (2010) is adapted so that full temperature and salinity
profiles can be derived without the need for coeval oceanographic data. In this way, temperature
conversion can be performed without the restricting requirement of coincident and densely sampled
hydrographic measurements. This adapted methodology is applied to the datasets presented in this
dissertation. Furthermore, this adaptation can be applied to any uncalibrated seismic survey, which
means that substantial archives of legacy surveys can be exploited. A technique that measures
movement of internal waves from pre-stack seismic records is described and automated. These
measurements can be used to constrain the two-dimensional ocean current field. Finally, the internal
wave and turbulent sub-ranges of the ocean’s energy spectrum are probed to investigate spatial
and temporal patterns of diapycnal diffusivity in the southwestern Atlantic Ocean.
In this study, spatial and temporal patterns of thermohaline circulation are investigated in the
Bellingshausen Sea and southwestern Atlantic Ocean using acoustic reflectivity. These seismic
datasets have been used to further constrain an eddy field and frontal system. These regions
require sampling of the ocean that simultaneously achieves high spatial resolution and coverage
Introduction 7
due to the mesoscale to sub-mesoscale nature of the processes occurring in the water column. This
dissertation demonstrates that calibrated seismic surveying can be used to constrain a mesoscale
to sub-mesoscale eddy field and front system and to quantify their physical properties. In this
way, our understanding of shelf-slope exchange processes and their contribution to ice mass loss
plus frontal dynamics and its effect on the surrounding water masses is improved. Moreover, the
high resolution images of oceanic processes provide new and important insights into the quantity
of eddies in the Bellingshausen Sea and spatial patterns of mixing associated with a frontal system.
1.3 Dissertation Structure
Chapter 2: Seismic Acquisition and Processing. Chapter 2 is an overview of the history,
acquisition and processing of seismic reflection data. Seismic acquisition and processing tech-
niques for a two-dimensional survey are described in the context of the JR298 survey. The
Uruguay survey is used to demonstrate three-dimensional seismic acquisition and specialised
processing techniques. This chapter provides a detailed description of the main principles
of acquisition and processing that constitute a seismic oceanographic study. The signal pro-
cessing strategy has been developed to produce optimal seismic images of the water column.
Temperature and sound speed variations are shown to be the major contribution to reflections
that are observed in water column seismic imagery. Finally, estimates for vertical and lateral
resolution of the final images are described.
Chapter 3: Warm-Water Transport across West Antarctic Shelf. A set of processed seis-
mic images from the JR298 survey are presented. These profiles traverse the continental shelf
of the Bellingshausen Sea, Southern Ocean, and are interpreted and calibrated with the aid of
coeval and regional oceanographic measurements. An adapted inversion procedure is devel-
oped that converts seismic imagery into maps of temperature. This adapted scheme follows
the method of Papenberg et al. (2010) yet does not require coeval hydrographic data. Temper-
ature distributions are used to describe thermohaline properties of observed eddies. Internal
wave speeds are measured and used to infer the direction of eddy propagation. Reflectivity,
temperature distributions, and current measurements are used to constrain a mesoscale to
sub-mesoscale eddy field and to quantify its physical properties. The results are compared
to published estimates of eddy frequency, temperature anomalies and current velocities. The
contribution of warm-core eddies to increased ice-shelf basal melt rates is discussed. A set
K.L. Gunn, Ph.D. Dissertation
Introduction 8
of sloping reflections and a bowl-like structure are interpreted as a front and Taylor Column,
respectively.
Chapter 4: Time-lapse Imaging of the Brazil-Falkland Confluence. Chapter 4 presents an
industry-standard three-dimensional seismic survey acquired 220 km west of the Rio de la
Plata estuary, Uruguay. These profiles traverse the Brazil-Falkland Confluence. In this chap-
ter mesoscale to sub-mesoscale seismic and oceanographic observations are analysed and in-
terpreted. Seismic imagery reveal a narrow band of dipping reflections that are interpreted as
a deep-reaching front between the Brazil and Falkland Currents. Thermohaline frontal struc-
ture is found to be consistent in the cross-front direction but highly variable in the along-front
direction. The entire frontal zone translates southwestward at a speed of O(10) km day−1,
which is consistent with semi-annual variability of the confluence location. Seismic images
are converted into profiles of temperature and salinity from which potential density, buoyancy
frequency and geostrophic currents are calculated. The results are compared to hydrographic
measurements. Internal wave speeds are measured from pre-stack gathers, revealing confluent
flow at the frontal interface. Rapidly evolving lens-shaped reflectivity is observed on the dense
flank of the front with lengths and thicknesses of up to 30 km and 500 m, respectively. These
observations are compared with hydrographic observations and numerical model in order to
isolate the dynamics at the front.
Chapter 5: Estimating Diapycnal Diffusivity from Seismic Images. Sub-mesoscale seismic
and hydrographic observations of the Brazil-Falkland Confluence are analysed. At these
scales, seismic imagery is used to extract information about the oceanic internal wavefield.
Over 20,000 automatically tracked reflections are spectrally analysed. Power spectra of the
horizontal gradient of isopycnal displacement are calculated from tracked reflections. Diapyc-
nal diffusivity is then estimated from the internal wave and turbulent sub-ranges. Seismically
inferred diapycnal diffusivity varies over four orders of magnitude (10−6–10−2 m2 s−1) with a
mean value of ∼10−3 m2 s−1. These two types of measurments are compared and discussed.
Estimated mixing rates are compared to published values and diffusivity calculated from
near-coeval hydrographic data. The spatial and temporal variation of diapycnal diffusivity
is analysed, revealing a clear pattern of diapycnal diffusivity that is strongly correlated with
the structure of the front. Likely mixing mechanisms are discussed and compared with other
frontal regions.
Chapter 6: Conclusions and Further Work
Chapter 2
Seismic Acquisition and Processing
2.1 Introduction
Exploration geophysics is an applied branch of geophysics that measures physical properties of the
Earth. Seismic reflection profiling is a principal method of imaging the solid Earth and employs
a controlled acoustic source of energy and a series of recording devices. This technique utilises
the principals of seismology, whereby timing and amplitude of reflected acoustic energy contains
information about reflection depth and physical properties. In this way, information about the
subsurface is extracted using surface experiments. In 1921, a small team of physicists and geolo-
gists used dynamite and a seismograph to record seismic (i.e. acoustic) waves reflected from the
subsurface beneath Vines Branch, Oklahoma. The experiment revealed reflections from a boundary
between two rock layers that agreed with a known geological feature. This experiment is widely
regarded as the first seismic survey that proved the technique’s imaging capability (Dragoset, 2007).
Although the Vines Branch experiment stimulated a boom in seismic development, the first marine
sonic sounder experiment was performed prior to 1921. Reginald Fessenden, motivated by the
sinking of the Titanic in 1912, used sound waves to detect icebergs (Roden, 2005). During World
War I, the first portable seismic detection equipment was developed to locate Allied artillery for
the German Imperial Army. Post-war advancement of seismic reflection profiling has largely been
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 10
driven by the hydrocarbon industry, and arguably the most important developments have been
related to the acoustic source. Dynamite requires small explosive charges to be ignited in shallow
holes on land, or beneath the sea-surface in marine settings. The obvious safety concerns and high
cost of transporting, storing and using dynamite led to rapid development of alternative sources.
In the early 1950s a seismic vibrator mounted on a truck was developed by Conoco. The ‘Vibroseis’
technique is capable of injecting low-frequency vibrations into the earth. By the late 1960s, airguns
had become the preferred method for marine exploration. Airguns create an explosive-like sound
impulse by sudden mechanical releases of highly compressed air beneath the sea-surface.
The first 30 years of geophysical exploration was limited by the processing power of computers
at the time. The advent of digital computers in the 1960s revolutionised seismic reflection pro-
cessing. TIAC 827 was the first digital computer dedicated to seismic processing, and had a core
memory of 1 kilobyte (Dragoset, 2007). Faster central processing units, increased memory and
parallel applications mean that today seismic datasets are commonly terabytes in size. The next
major innovation occurred in the 1980s as seismic survey design moved towards three dimensions.
Previously, seismic surveys were limited to single lines that provided two-dimensional cross-sections
of target hydrocarbon fields. During this time, so called ‘three-dimensional’ acquisition was simply
a series of closely spaced parallel lines collected in series. Today, three-dimensional surveys collect
multiple parallel lines simultaneously, thereby providing a swath of acoustic information. Strictly
speaking, three-dimensional surveying is not truly so. Along the direction of acquisition, sampling
can be as small as 6.25 m yet, in the perpendicular direction sampling is an order of magnitude
greater (typically 31.25 m). Therefore, the third dimension is an interpolation across tens of metres
that separates each simultaneously collected two-dimensional cross-section. IsoMetrix represents the
latest in three-dimensional seismic imaging and is the result of a ten year research and development
programme by Schlumberger. The technology uses broadband receivers that allow reconstruction
of the acoustically generated three-dimensional pressure wavefield at each receiver. This recon-
struction effectively removes large measurement gaps between parallel lines providing fine spatial
sampling in all directions (Robertsson et al., 2008).
Seismic reflection profiling also has applications in non-commercial avenues. Academic research
has utilised seismic reflection profiling to investigate deep Earth structure, tectonic processes that
have shaped geological structures and the structure of ice-shelves in Antarctica. For example, the
British Institutions Reflection Profiling Syndicate (BIRPS) Atlas collates 12,000 km of deep seismic
reflection data collected around the British Isles by the BIRPS Group (Klemperer & Hobbs, 1992).
Seismic Acquisition and Processing 11
The collection provides a detailed image of deep continental crust and mantle of northwest Europe.
Claerbout (1986a,b) made significant contributions to time series analysis and wave propagation
of seismic data, that are contained within ‘Fundamentals of Geophysical Data Processing’ and
‘Imaging the Earth’s Interior’. Sheriff (1991) gives a history of seismic profiling and introduces
processing techniques. ‘Seismic Data Processing’ by Yilmaz (2001) describes processing techniques
up to the 1980s and provides abundant clear examples. It is considered a classic reference volume
for seismic processing due to its detailed explanations.
In the past decade, it has been shown that oceanic reflectivity provides information about water
mass structure, thermohaline properties, and mixing rates (e.g. Sheen et al., 2009; Papenberg et al.,
2010; Holbrook et al., 2013). Seismic reflection profiles of the ocean display laterally coherent
reflectivity attributed to fine-scale changes in acoustic impedance or, in other words, fine-scale
oceanic layering (Holbrook et al., 2003). Seismic reflectivity is generated by changes in acoustic
impedance, I, which is the product of sound speed, v, and density, ρ,
I = ρv. (2.1)
Seismic Oceanography adheres to the same principles as seismology and water column information
is collected as a by-product of standard solid Earth imaging. Since most seismic oceanography
studies are based on data collected to investigate the subsurface, acquisition parameters remain
unchanged. A limited number of dedicated water column studies have quantified the effect of seismic
acquisition equipment on the quality of oceanic reflections (e.g. Pie´te´ et al., 2013). Although
conventional seismic acquisition systems are not designed with water column imaging in mind,
seismic oceanography has revealed a variety of ocean phenomena involved in ocean circulation and
mixing. Standard processing techniques are applied that have been adapted from those used to
build seismic images of the solid Earth (Yilmaz, 2001). Several modifications to this processing
flow are necessary to allow for the differences between subsurface and water column reflectivity.
For example, reflected waves from the ocean have amplitudes that are 100–1000 times weaker than
those from the solid Earth (Ruddick et al., 2009). A significant portion of processing is dedicated
to the careful separation of signal and noise in order to enhance the quality of the final image.
Resulting seismic imagery can be considered maps of the vertical temperature gradient that have
resolution of up to 10 m (Sallare`s et al., 2009).
The aim of this chapter is to provide an outline of core principles and techniques of acquisition
and processing that underpin seismic oceanography studies. First, techniques of seismic acquisition
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 12
and processing for two-dimensional surveying are described. Secondly, three-dimensional seismic
acquisition and specialised processing techniques are described. These techniques are demonstrated
with the aid of two seismic reflection surveys that form the basis of this dissertation. The first
dataset is a two-dimensional academic seismic survey acquired in the Bellingshausen Sea, Southern
Ocean. The second dataset is three-dimensional survey of industry standard that was acquired
220 km east of the R´ıo de la Plata estuary, southwest Atlantic Ocean (Chapter 1). Since each
seismic dataset is exposed to different types of noise, processing must be carefully tailored to
produce the highest quality seismic image. Nevertheless, several necessary key steps should be
applied to all seismic oceanographic datasets. Finally, the causes of water column reflectivity and
their effects on seismic imagery are discussed.
2.2 Two-dimensional Imaging
2.2.1 Acquisition
During seismic acquisition, a pulse of acoustic energy with frequencies of 10–100 Hz is generated
every 10–20 s (Figure 2.1). The origin of acoustic energy, simply referred to as the source, is
towed beneath the sea-surface at depths of 3–10 m by a seismic vessel (Figure 2.1a). This vessel
steams in straight lines at speeds of ∼2.5 m s−1. The source is tuned to generate an acoustic
pulse of short duration with directivity characteristics that concentrate energy downwards. Energy
propagates downward until it encounters changes in acoustic impedance. At these boundaries,
energy is partitioned so that some proportion is reflected upward and the rest is transmitted to
greater depths (Figure 2.1b). An array of receivers along a cable, that is towed at depths of 5–
10 m beneath the sea-surface, records reflected energy. The energy is recorded as a function of
time elapsed between generation and detection of the acoustic pulse, known as two-way travel time
(TWTT). The streamer (i.e. cable) is of 1–12 km length and contains a few hundred hydrophones
(Figure 2.1a). Time series are collected from each shot (i.e. a single acoustic impulse) at each
receiver along the streamer. These time series, also called traces, carry information about the
vertical acoustic impedance contrasts in the water column at the midpoint between source and
receiver (Figure 2.1c). The separation between recorded traces is half of the receiver spacing along
the streamer. Shots are fired every ∼25 m. In this way, hundreds of thousands of traces are acquired
during seismic surveying providing two-dimensional information about the acoustic properties of
the water column (Figure 2.1d). During two-dimensional seismic surveying a single streamer and
Seismic Acquisition and Processing 13
F
ig
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2
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K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 14
airgun array are towed behind the seismic vessel (Figure 2.2a) and a single vertical slice of the
water column is acquired (Figure 2.2b).
Figure 2.2: Schematic of two-dimensional marine seismic acquisition. (a) Acquisition plan.
Hatched polygon = seismic vessel towing equipment; thin grey line = connecting cables; grey
circle = source; thick black line = streamer. (b) Seismic profile collected using configuration shown
in (a). Thick black line = recorded profile; green/red square = start/end of sail-line; arrow =
direction of acquisition. Not to scale.
2.2.2 Acoustic Source
Due to their reliability and repeatability, airguns are the most widely used source for marine seismic
surveys (Figure 2.3). Air is pumped into a gun chamber until a desired volume and pressure is
reached, typically 5–70 L and O(1) MPa (Figure 2.3a). On command from the seismic recording
system, the acoustic signal is produced by an explosive release of high pressure air directly into the
surrounding water (Figure 2.3b). Upon exiting the chamber, air forms a bubble in the surrounding
water. Initially, bubble pressure is greater than that of the surrounding water so the bubble expands,
causing its pressure to fall. Once bubble pressure falls below the outside hydrostatic pressure, the
bubble begins to collapse, reducing its volume until pressure within the bubble is greater than the
surrounding water once again. This oscillation continues until the bubble breaks the sea-surface.
To avoid degrading the quality of the final seismic image, the bubble pulse can be attenuated using a
Generator-Injector (GI) airgun. A GI airgun uses two chambers to suppress the bubble oscillation.
The gun is configured to work in ‘harmonic mode’ whereby the first chamber (generator) produces
a primary pulse. When the primary pulse approaches its maximum size it encompasses the second
chamber. The second chamber (injector) injects a secondary pulse of air directly inside the bubble.
The volume of air within the bubble is increased by the injection. In this way, bubble collapse is
mitigated.
An important consideration when acquiring seismic data is source and receiver depth. Destructive
interference of propagating acoustic energy creates notches in the frequency spectrum (Yilmaz,
Seismic Acquisition and Processing 15
Figure 2.3: Schematic showing airgun operation. (a) Armed. High pressure air pumped into
lower chamber; white arrows = path of high pressure air. (b) Fired. Piston explosively released to
expel air into surrounding water; black arrow = direction of piston.
2001). Airgun arrays are tuned such that the greater proportion of energy travels downwards.
Nevertheless, a portion travels toward the sea-surface. This ghost energy is reflected at the sea-
surface and propagates downwards with a polarity switch and time delay. The time delay, td, of
this energy is given as
td =
2d cos θ
vavg
, (2.2)
where d is either the source or receiver depth, ds or dr, and vavg is the average speed of sound in
seawater near the surface. Ghost energy is generated at both the source and receiver. Interference
of ghost and primary energy will be destructive at specific frequencies, depending on the time delay.
As a consequence, notches in the frequency spectrum are created at fn,
fn =
n
td
, (2.3)
where n is a positive integer. Useful energy occurs between 0 ≤ n ≤ 1. Due to the proximity of
source and sea-surface, θ ≈ 0. Substituting Equation (2.2) into Equation (2.3) yields fn = vavg/2d.
Another important consideration is the sampling rate, dt, which controls the highest frequencies
that can be accurately recovered. The Nyquist Theorem states that in order to avoid aliasing,
the highest reproducible signal, fN , is half the maximum signal, fs. In other words, to correctly
digitize signals, a minimum number of points are required to accurately represent its changes. fN
is related to dt, by
fN =
1
2dt
. (2.4)
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 16
2.2.3 Convolution Model
Seismic traces that are recorded as a function of time, s(t), are a convolution of the reflectivity
series, R(t), and source wavelet, w, given by
s(t) = R(t) ∗ w(t) + n, (2.5)
where n is ambient noise. Variations of sound speed, v, and density, ρ, as a function of depth
result in reflective boundaries (Figure 2.4a). Impedance, I, is the product of v and ρ. Impedance
contrasts as a function of time form R(t), given by
R =
ρ2v2 − ρ1v1
ρ2v2 + ρ1v1
(2.6)
where subscripts 1 and 2 represent the upper and lower boundaries across an interface in impedance,
respectively. An increase in I results in positive R and vice versa. Typical values of R are:
-1 from water to air, meaning that 100% of energy is reflected at the sea-surface; 0.2–0.5 for
water to sediment, meaning that up to half of energy reaching the seabed is transmitted into the
subsurface; and 0.2 from shale to sand. Reflections caused by boundaries in the water column have
R of O(10−3). These amplitudes are 100–1000 times smaller than subsurface reflections. R(t) is
proportional to the water column, yet s(t) is a convolution of R with the source wavelet and noise.
Since the primary control on s(t) is w(t), it is important to understand the effects imposed by w
in Equation (2.5).
The ideal source wavelet is characterized as having a broad, flat spectrum in the frequency domain.
This ideal wavelet corresponds to a spike or Dirac delta function, δ, in the time domain. δ is
zero everywhere except at time zero where all frequency content is contained. If s(t) were given
by s(t) = R(t) ∗ δ(t), recorded seismic traces would be representative of the vertical impedance
changes of the medium being imaged (Figure 2.4b). However, w is band-limited and does not
approach δ. The lowest emittable frequency is inversely proportional to the volume of an airgun.
Since large airguns are difficult to manoeuvre, most seismic sources are limited in volume and are
therefore incapable of producing frequencies lower than ∼3 Hz. Furthermore, low frequencies are
paired with wavelengths much larger than the size of receivers, making this information difficult
to record. Instead, band-limited source wavelets impose their own intrinsic spectral characteristics
on s(t) (Figure 2.4c). Each recorded trace contains information about R(t). Since thousands of
traces are recorded during each survey, two-dimensional profiles of water column information are
Seismic Acquisition and Processing 17
Figure 2.4: Comparison of ideal versus typical source wavelet convolved with reflectivity series. (a)
Basic model of seismic reflection. Sound speed, v, and density, ρ, variations give rise to impedance
changes, I. Impedance contrasts at each layer form reflectivity series, R, which describes depth
and properties of reflectors. (b) R shown in (a) convolved with ideal wavelet. δ = delta spike;
A = recorded amplitudes. (c) R shown in (a) convolved with typical source wavelet. w = zero-phase
source wavelet; A = recorded amplitudes. (d) Thousands of traces record depth and properties of
reflectors providing two-dimensional cross-sections of water column.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 18
acquired (Figure 2.4d).
Figure 2.5 shows the characteristic spectra of common source wavelets. Minimum-phase is of short
time duration, energy is concentrated at the start and amplitude is zero before time zero (Figure
2.5a–c). A signal that is zero before time zero is known as causal (i.e. it is a physically realizable
signal). Zero-phase signals have shorter time duration than their minimum-phase equivalent and are
symmetrical with a maximum at time zero (i.e. non-causal; Figure 2.5d–f). All other causal wavelets
that are not minimum-phase are strictly mixed-phase, whereby energy is mostly concentrated in the
middle (Figure 2.5g–i). Phase describes the starting point of the signal as an angle, which manifests
as an apparent lateral shift in the waveform (Figure 2.5c,f,i). Considering that recorded seismic
amplitudes are a complex filter of source wavelet and target impedance contrasts, this lateral
shift (i.e. time shift) has important implications for processing and subsequent interpretation.
For example, assuming w is zero-phase, each positive target impedance contrast has a doublet
amplitude response (i.e. negative side-lobes around a positive peak) which can lead to ambiguity
during interpretation (Figure 2.4c).
Figure 2.5: Amplitude, frequency and phase of common source wavelets. (a–c) Amplitude, fre-
quency and phase spectra of minimum-phase wavelet. (d–f) Amplitude, frequency and phase spec-
tra of zero-phase wavelet. (g–i) Amplitude, frequency and phase spectra of mixed-phase wavelet.
Dashed line = time zero.
An important consideration is the sign of w. Polarity of s(t) depends on the relative signs of w
and I. A simple way to determine wavelet polarity is to examine the seabed reflection (Yilmaz,
2001). The reflection recorded from the interface between water and sediments will always have a
positive impedance contrast. Therefore, if the amplitude of the seabed reflection is positive, the
wavelet is normal polarity. Furthermore, frequency filtering can change the phase of seismic data.
Seismic Acquisition and Processing 19
Figure 2.6: JR298 near-field source wavelet recorded during acquisition. Amplitudes normalised
between -1 and 1.
Consequently, unknown time shifts are introduced to each seismic trace. The most desirable source
wavelet is zero-phase since maximum amplitudes will be aligned with its corresponding impedance
contrast (Figure 2.4b). For these reasons it is important to understand the type of source wavelet
used during acquisition. Near-field receivers may provide auxiliary traces that record the airgun
signature (i.e. w). A near-field source signature was provided alongside the JR298 survey (Figure
2.6). The source signature used during the JR298 survey has energy concentrated at the start and
is causal, i.e. minimum phase (compare Figures 2.5a and 2.6).
2.2.4 Common Midpoint Gathers
Since shot spacing is much smaller than the length of the streamer, each spatial location within the
water column is sampled multiple times. A set of individual seismic traces for different shot-receiver
pairs that share the same sampling location is known as a common midpoint (CMP) gather (Figure
2.1d). The number of times each spatial location within the water column is sampled is known as
fold of cover, nf , given by
nf =
ng∆g
2∆s
, (2.7)
where ∆g and ∆s are the receiver group and shot spacing, respectively, and ng is the number of
receivers (Table 2.1). nf ranges from 20–120. To exploit the fold of a seismic experiment, temporal
and spatial locations of each trace need to be assigned, allowing collection of traces within a CMP
gather. Each recorded trace has a unique source and receiver location from which non-unique
midpoint numbers (i.e. CMPs) are determined based on the positional information collected during
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 20
seismic surveying. Absolute source locations can be calculated given information about the bearing
and position of the seismic vessel plus the distance between equipment. Typically, the source is
towed ∼100 m behind the vessel. Locating receivers is more complex due to the length of the
streamer, which is often several kilometres. The accuracy of receiver location is affected by the
number of global positioning systems (GPS) systems in use during acquisition, since feathering and
cable stretch will shift streamer position. In most cases, GPS systems are placed at the end of the
streamer in a tail buoy and spaced at equal distances along its length.
2.2.5 JR298 Survey
The two-dimensional survey presented in this dissertation was acquired during February 2015 on-
board RRS James Clark Ross during research cruise JR298. The acoustic source comprised a pair
of GI airguns, each of which had a volume of 2.46 L (i.e. 150 in3). These guns were primed with an
air pressure of 13.5 MPa (i.e. 1960 psi) and fired every 10 s in harmonic mode. Reflected acoustic
waves were recorded along a 2.4 km cable that had 192 groups of hydrophones spaced every 12.5 m.
This streamer was towed at a depth of 5 m. In portions of the surveyed area the length of this
streamer was reduced by one half to safeguard against iceberg hazard. The record sampling interval
was 1 ms. In general, the vessel steamed in straight line segments at a speed of 2.5 m s−1 and
shots were fired every 25 m, yielding a fold of cover of 60 (i.e. each discrete point along a traverse
is sampled 60 times). During the acquisition program, sea-surface conditions were variable and at
times adverse so that a proportion of the seismic records have a poor signal-to-noise ratio. The
resultant profiles traverse parts of the continental shelf in the vicinity of the Bellingshausen Sea
adjacent to the west Antarctica Peninsula. Water depth varies between 400 and 4000 m in the
surveyed area. The Nyquist frequency for JR298 is 500 Hz. The notch frequency at the source
and receiver are 181 and 161 Hz, respectively (based on source/receiver depth of 4/4.5 m). These
values act as natural guide for frequency filtering. During JR298, GPS information was collected at
the centre of the seismic vessel. Therefore, all source, receiver and subsequent CMP locations were
retraced from the known seismic vessel location. Backtracking was based on the key assumption
that acquisition equipment followed the vessel track, rather than a straight line directly behind the
vessel. This approach is suitable for short streamers as was the case for JR298. To account for time
delay between shot and the start of recording, a shift of -40 ms was applied to the JR298 seismic
data.
Seismic Acquisition and Processing 21
2.2.6 Signal Processing
The Omega2 processing package, provided by WesternGeco, was used for seismic data processing
(Appendix A). There are at least three important processing stages. First, noise is reduced to
increase signal-to-noise ratio. Typical noise mitigation techniques use amplitude or spectral analysis
to separate signal from noise with a view to removing the latter. Secondly, velocity analysis is carried
out to identify a two-dimensional sound speed model for the seismic profile. Finally, seismic records
are sorted into common midpoint gathers, corrected for the effects of offset and stacked to produce
the final image. Post-stack processing is used to reduce the effect of airguns on recorded amplitudes,
correct the location of dipping reflections, and increase horizontal continuity of reflections. Seismic
stacks that are to be used to estimate diapycnal diffusivity must not be horizontally smoothed nor
deconvolved.
Coherent and Random Noise
Noise is a term that encompasses components of recorded signals that do not represent the re-
flectivity series. Each trace, shot and seismic survey is exposed to a variety of different sources
of noise. It is the processor’s role to identify which noise can and should be removed without
damaging signal. As each sail line is exposed to different noise sources, attenuation techniques
should be tailored to suit each dataset, with a view to ensuring maximum signal-to-noise ratios.
The following sections describe noise removal methods that have been applied after careful testing.
Each process is designed to target at least one type of noise, which can be divided into two types:
coherent (spatially coherent) and random (spatially incoherent). First, several types of common
marine noise and their source are described:
ˆ Swell: 0–20 Hz, random. Swell noise dominates raw marine shot gathers and is caused by
breaking of waves at the sea-surface directly above the streamer (Figure 2.7a–f). Significant
swell appears as vertical bands of large amplitude interference of variable thickness (e.g.
Figure 2.7a).
ˆ Direct wave: coherent, linear noise that is the first arrival in a shot gather. This energy
travels directly between source and receivers at the speed of sound at the sea-surface (Figure
2.7b).
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 22
ˆ Tugging: 2–15 Hz, coherent, angled linear noise of high amplitude caused by sudden move-
ments of the acquisition gear securing streamers. Tugging will affect outer streamers most
since their lead-in cables are dragged at a high angle compared to the direction of acquisition
(Figure 2.7c, Figure 2.16b).
ˆ Strumming: 2–15 Hz, random, horizontal bands of energy at near-offsets caused by vibra-
tions of the acquisition gear holding the cables (Figure 2.7d).
ˆ Seismic interference: coherent, broadband interference from other active vessels during
acquisition. This noise is generated out of plane and can be linear or parabolic. If it is the
latter, the apex is centred at the trace location within the shot gather which is closest to the
source of seismic interference. Seismic interference may appear anywhere in the data (Figure
2.7e).
ˆ Wrap-around: coherent noise generated when signal from the previous shot is recorded
on the current shot. Wrap-around noise is usually caused by seabed multiples and can be
identified from their TWTT, which will be a multiple of the seabed TWTT.
ˆ Noise spikes/bands: random, temporary, high amplitude vertical spikes.
ˆ Ambient: random, low amplitude, ubiquitous noise that appears as speckling across the
dataset (Figure 2.7a–f).
Frequency Filtering
The most common form of filtering removes unwanted components in the frequency domain. Raw
seismic data contain a wide range of frequencies (e.g. ∼3–250 Hz). However, the low and high
end of this band is often overcome by noise. Low frequency swell noise (i.e. 0–20 Hz) dominates
unprocessed shot gathers (Figure 2.7a–f). Due to the similar frequency content of swell, tugging,
and strumming noise, they are attenuated by applying a low cut frequency filter of approximately
20 Hz (compare Figures 2.7 and 2.8). Selected filters take account of the noise, frequency, and
phase content associated with each dataset (Section 2.2.3). Notch frequencies and data above the
Nyquist frequency are attenuated by applying a high-pass filter. The low and high frequencies
are simultaneously attenuated by application of a band-pass filter. A 20–100 Hz Butterworth
minimum-phase filter with a roll-off of 24 dB/octave was applied to the JR298 survey.
Seismic Acquisition and Processing 23
Figure 2.7: Example shot gathers showing common noise types encountered during marine ac-
quisition. (a) Swell. (b) Direct wave. (c) Tugging. (d) Strumming. (e) Linear seismic interference.
(f) Parabolic seismic interference. Swell noise, direct wave and background noise evident in all shot
gathers; high amplitude curved reflections = seabed and subsurface reflections; S = example swell
noise; SI = seismic interference; DW = example direct wave; T = tugging; St = strumming; open
circles = hyperbolic reflections caused by thermohaline fine-structure.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 24
Figure 2.8: Example shot gathers showing effect of bandpass frequency filtering. Zero-phase
Butterworth bandpass filter of 20–90 Hz has been applied; compare with Figure 2.7. Note removal
of swell, strumming and tugging noise. Labels as in Figure 2.7.
Seismic Acquisition and Processing 25
Water-bottom Mute
Reflections from the seabed and below are muted (i.e. set to zero). If retained, greater amplitude
reflections found in the solid Earth may mask information in the water column. Muting is particu-
larly important for processing steps that are amplitude based. To mute these subsurface reflections
a brute stack is created for each seismic profile. This brute stack uses a constant sound speed to
correct hyperbolic move-out. The chosen sound speed, vsb, should represent the value appropriate
for the seabed and is typically between 1520 and 1550 m s−1. Since the impedance contrasts across
the water-sediment boundary are much larger than those from water column reflections, the seabed
will appear as the brightest reflection in the brute stack. It is now possible to pick the seabed
position. To avoid smear and diffractions from the seafloor reflection, picks are collected ∼10 ms
shallower than the brightest reflection. Each pick gives coordinates of common midpoint number
and two-way travel time at zero-offset, t0. These zero-offset picks must be converted into a table of
pre-stack (i.e. non-zero-offset) information that can be used to mute the seabed across shot gathers
within Omega2. Picks are sampled every n CMP. At specified offsets, x, the corresponding two-way
travel time is given by
tx =
√
x2 + t20
v2sb
, (2.8)
where tx is two-way travel time at CMP n and offset x. Offset intervals and n are chosen for each
experiment.
Direct Wave Removal
For every shot, energy travels from source to receiver directly along the sea-surface. This coherent,
linear and high amplitude wavefront is known as the direct wave. The direct wave dominates
the upper 0.5 s TWTT (∼500 m) of each shot gather (Figure 2.7a–f). When processing seismic
records to image the solid Earth it is not necessary to remove the direct wave since the entire water
column is muted. However, since most of the oceanic realm has abrupt temperature gradients in
the upper 500 m, known as the thermocline, it is important to effectively remove the direct wave
to observe the entire vertical extent of water column reflectivity. As the direct wave is a form
of coherent noise its predictability can be exploited for attenuation. The direct wave is removed
using its known linear move-out. Three filtering methods have been rigorously tested; linear,
frequency-wavenumber and radon. Each method carries its own advantages and disadvantages.
Frequency-wavenumber filtering is the least effective at isolating the direct wave but is able to
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 26
F
ig
u
re
2
.9
:
D
irect
w
av
e
rem
oval
u
sin
g
lin
ear
fi
lterin
g
(S
h
een
,
2010).
(a)
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aw
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ot
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ow
in
g
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ave.
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ata
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b
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ss.
(b
)
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in
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ap
p
lied
.
(c)
T
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m
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eren
cy
of
n
oise.
(d
)
N
oise
m
o
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in
(c)
ad
ap
tively
su
b
tracted
from
in
p
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t
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ata
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(b
).
(e)
F
in
al
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ot
gath
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verse
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ear
m
ove-ou
t.
B
lack
arrow
s
=
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ear
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ection
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Seismic Acquisition and Processing 27
isolate spatially aliased noise (Section 2.3.5). Radon filtering has a high computational cost. It was
concluded that the most appropriate method here is linear filtering. The justifications are twofold:
first, linear filtering effectively removes direct wave noise without affecting hyperbolic reflections
and, secondly, processing time is reasonable.
The linear adaptive filtering method follows the approach developed by Sheen (2010). Input records
are shot gathers to exploit the linearity of the direct wave (Figure 2.9a). First, constant linear
move-out is applied, flattening the direct arrival and smearing water column reflections (Figure
2.9b). The sound speed that optimally flattens the direct wave should be used. Moved-out shot
gathers now represent a model that contains both signal and noise. Secondly, a simple moving
average is applied. This trace mix smoothes horizontal reflections thereby enhancing horizontally
continuous features (i.e. direct wave) and reducing coherency of non-linear features (i.e. water
column reflectivity; Figure 2.9c). This smoothed gather is a model of noise. Thirdly, the smoothed
gather is subtracted from the input gather, leaving signal only (Figure 2.9d). The subtraction is
performed using a pattern-matching algorithm called adaptive subtraction. Finally, constant linear
inverse move-out is applied to this signal model, returning water column reflections to their original
hyperbolic shape (Figure 2.9e).
Amplitude Corrections
Energy reflected within the water column is recorded by an array of receivers. At each receiver, the
incoming wavefront arrives at an angle from vertical, known as the angle of incidence, θ. θ varies
with x and time. A sound wave reflected from a boundary contains information about the upper
and lower layer properties. At any boundary, the reflection and transmission coefficients vary with
the angle of θ or x, known as Amplitude Variation with Offset (AVO). This variation may also
arise from other sources, such as changing physical properties across a reflective surface, and may
be used to infer useful information (e.g. Pa´ramo & Holbrook, 2005). Zoeppritz (1919) formulated
a set of equations that describe the partitioning of energy at a reflecting interface as a function of
x, density, P-wave velocity and S-wave velocity. The Zoeppritz equations are non-linear, so it is
usually more convenient to use linear approximations (Sheriff, 1991). The Aki & Richards (1981)
linear approximation describes AVO assuming that changes in elastic properties across a layer are
small and incidence angles are within the subcritical range (θ < 90◦) suitable for the water column.
For a wavefront travelling through the Earth, the Aki & Richards (1981) approximation reduces
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 28
the Zoeppritz equations to
R(θ) =
[
1
2
(1 + tan2 θ)
]
∆α
α
−
[
4
β2
α2
sin2 θ
]
∆β
β
+
[
1
2
(1− 4β
2
α2
sin2 θ)
]
∆ρ
ρ
(2.9)
where θ is angle of incidence, α = (α1 + α2)/2 is average P-wave velocity, ∆α = α2 − α1, β =
(β1+β2)/2 is average S-wave velocity, ∆β = β2−β1, ρ = (ρ1+ρ2)/2 is average density, ∆ρ = ρ2−ρ1,
and θ is incidence angle. Subscripts 1 and 2 denote the property at layers above and below a
boundary, respectively. The Aki & Richards (1981) approximation describes AVO in terms of
P-wave reflectivity (α), S-wave reflectivity (β) and fractional change in density (ρ). In practice,
recorded seismic amplitudes do not observe these three effects. Instead, changes in reflection
amplitude as a function of θ are detected. Hence, the Aki & Richards (1981) equation is recast in
terms of successive ranges of θ. This change in philosophy was first introduced by Shuey (1985),
given as
R(θ) =
[
1
2
(
∆α
α
+
∆ρ
ρ
)]
+
[
1
2
∆α
α
− 4β
2
α2
∆β
β
− 2β
2
α2
∆ρ
ρ
]
sin2 θ +
[
1
2
∆α
α
]
(tan2 θ − sin2 θ).
(2.10)
Since S-waves do not travel through liquids, Equation (2.10) is simplified, resulting in a final
approximation of the Zoeppritz equations for the ocean
R(θ) =
∆v
2v cos2 θ
+
∆ρ
ρ
, (2.11)
where v now represents the speed of sound through water (i.e. α). Equation (2.11) shows that the
AVO response within the ocean varies as 1/ cos2 θ.
Directivity caused by the receiver array is often present but the difficulty in accounting for it during
seismic processing makes it undesirable in most cases. Receiver directivity corrections account for
AVO introduced by θ. These corrections are particularly important for seismic oceanography
because the ratio between maximum source-receiver offset and depth of target reflections is smaller
than for solid Earth imaging. Here, the AVO response predicted by the Zoeppritz equations is used
to model amplitude variation at a suite of offsets and TWTTs. The modelled response is then
corrected for by applying an inverse gain factor. It is possible to remove receiver directivity effects
by applying the following correction to seismic data
Acorr = Aobs cos
2 θ (2.12)
Seismic Acquisition and Processing 29
where Aobs is the recorded amplitude and Acorr is corrected amplitude. 1/ cos
2 θ is the theoretical
AVO response caused by receiver directivity (Equation 2.11).
Directivity caused by the source is also present in seismic surveys. The frequency content of
the acoustic pulse changes in a time-variant manner as the wavefront expands, since different
bandwidths experience variable attenuation rates. The Earth is a naturally occurring low pass
filter. High-frequency attenuation occurs through intrinsic absorption as the seismic wave partitions
energy into heat. As a seismic wave travels through a material the particles vibrate generating
heat, which attenuates higher frequencies more rapidly than lower frequencies, thereby changing
the bandwidth of the acoustic pulse. At shallow depths the source frequency spectrum is almost
white (i.e. equal intensities at different frequencies). As depth increases the wavelet undergoes
high frequency attenuation, hence the ratio of low to high frequency content increases. This effect
can be seen in data from the JR298 survey (Figure 2.10). Ideally, the signal spectrum is white
at all depths. To correct for frequency directivity it is possible to use the decay rate of different
frequency groups to apply a time variant gain function. This technique, known as time-variant
spectral whitening, applies a series of narrow band-pass filters to seismic traces (Figure 2.10b–
d). The decay rates for each frequency band are found by computing the envelope of the filtered
traces for each bandwidth. The inverse of each decay rate becomes the time-variant gain function
used to correct each frequency band. Once source directivity corrections have been applied, traces
are summed leaving a whitened frequency spectrum. The number, width and range of frequency
bands are data dependent. The overall effect is to compress the wavelet and flatten the amplitude
spectrum.
Spherical divergence describes the decay in amplitude (i.e. energy) as a wavefront travels through
a medium. The wavefront spreads the same amount of energy over a larger surface area as distance
increases. Decay of energy, E, is proportional to the wavefront radius, r, E ∝ 1/r2. Wave ampli-
tude, A, is the square root of E, therefore A decays as A ∝ 1/r = 1/vt, where t is TWTT. In the
water column, it is appropriate to assume that v is constant across spreading distances, therefore
spherical divergence can be corrected by applying a time function gain of t.
Normal Move-out Correction
Non-unique CMP numbers are assigned in the initial stages of processing based on their unique
source-receiver pairs. Each seismic trace is recorded as a function of TWTT and x between source
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 30
Figure 2.10: Variable rates of decay for three bandwidths in a seismic trace. Energy in each trace
decays faster for higher frequencies. (a) Unfiltered seismic trace. (b) Trace shown in (a) band-pass
filtered using Butterworth filter of 10 < f < 40 Hz. (c) Trace shown in (a) band-pass filtered using
Butterworth filter of 40 < f < 70 Hz. (d) Trace shown in (a) band-pass filtered using Butterworth
filter of 70 < f < 100 Hz.
and receiver. Traces within a CMP gather travel along different ray-paths due to the variation in
offset between each source-receiver pair (Figure 2.11a). The time taken, tx, for a wave to reflect off
a horizon at depth, z, increases with x, given by
tx =
√
x2 + 4z2
v2
, (2.13)
where v is sound speed of the acoustic medium. At zero-offset, x = 0, the source and receiver are
spatially coincident and Equation (2.13) simplifies to tx = 2z/v. The hyperbolic increase of tx as
a function of x is referred to as normal move-out, NMO (Figure 2.11b). Move-out, ∆t, is given by
∆t = tx − t0, (2.14)
where t0 is the zero-offset travel time and tx is given by Equation (2.13). The correction is not con-
stant along a trace. At low velocities and large offsets the correction leads to significant stretching
of the data, which reduces resolution. To mitigate this effect a stretch factor of 2 is applied. Traces
are corrected for NMO (Figure 2.11c) prior to stacking (Figure 2.11d).
Since v varies as a function of depth, a series of cumulatively increasing values of v must be chosen
as a function of TWTT to ensure that NMO is properly corrected. In practice, a root mean squared
Seismic Acquisition and Processing 31
Figure 2.11: Cartoon showing normal move-out correction. (a) During seismic acquisition every
subsurface position is sampled many times by successive shot-receiver pairs. Increasing offset leads
to longer ray-paths. (b) A CMP gather contains all traces recorded for a single subsurface position.
Reflections exhibit hyperbolic move-out due to increasing travel-time as ray-path length increases.
(c) Hyperbolic move-out is corrected for using Equation (2.14). (d) Coeval subsurface samples are
added and averaged to form a stacked trace with zero-offset.
sound speed, vrms, profile is picked using an iterative process of trial and error for each CMP gather.
This sound speed profile enables NMO to be removed as a function of TWTT (Equation 2.14).
To accurately correct NMO, vrms profiles must be extracted with care. Velocity picking, as it is
commonly known, is arguably the most important stage in processing water column reflection data.
Velocity Picking
Velocity picking is of critical importance in the water column for three reasons. First, signal-to-
noise ratios are lower than the subsurface, requiring optimal stacking. Secondly, sound speeds
are low with small variation, typically between 1440–1540 m s−1 (Vallis, 2006). Finally, reflection
depth is smaller than in the subsurface. Together this means that small changes in picked velocity
profiles at relatively shallow oceanic depths will make large differences to Equation (2.14).
Two interactive data displays are used to carefully select vrms profiles (Figure 2.12). First, un-
corrected CMP gathers are used to generate velocity spectra, commonly called semblance gathers
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 32
(Figure 2.12a,f). Semblance plots have axes of time and vrms, and are contoured by power (Figure
2.12b,g). Semblance is calculated by applying hyperbolic move-out to traces within a CMP gather
at a user-specified range of sound speed. Cross-correlation of the moved-out traces are taken pro-
viding an estimate of power at various sound speeds. Cross-correlation amplitudes are greatest
when either continuity exists over a hyperbolic move-out trajectory or trace amplitudes are large.
In this way, semblance analysis provides an indicator of the most likely sound speed value at each
depth. vrms is essentially a running mean of the vertical sound speed profile and therefore can
only be used to extract long wavelength profiles of sound speed. Cross-correlations are smoothed
over specified time gates to remove high frequency content and muting is applied to shallow and
far-offset traces since the normal move-out correction causes frequency stretching that generates
artificially low frequency content. In this way, a semblance plot displays the most likely vrms as
a function of depth. Semblance analysis is paired with CMP gathers that are corrected for NMO
upon selection of a vrms (e.g. Figure 2.12c–e). The final vrms profile is the one that corrects NMO
in such a way that reflections are completely flat (Figure 2.12d,i). When a value is chosen that is
too low or too high the reflection is over- or under-corrected (Figure 2.12c,e,h,j).
vrms profiles are picked at equally spaced locations along the seismic line. Picks must be performed
at dense horizontal intervals to capture lateral variations. If intervals are too dense, operator error
may introduce minor variations in the sound speed model that are inaccurate. The optimal spacing
was found to be every 200 CMP, which equates to 1250 m for CMP spacing of 6.25 m. Velocity
picking is a time-consuming, labour intensive task. Fortin & Holbrook (2009) recommend using an
independent, coeval sound speed profile to guide initial picking. The picking process is iterative and
should be performed until there are no detectable improvements in the stacked section. Although
automatic picking algorithms exist, it was found that these algorithms produced unrealistic vrms
profiles. The poor performance of automatic algorithms is most likely due to the smaller amplitudes
and lower signal-to-noise ratios of water column reflections compared to the subsurface for which
they were designed. Finally, seismic records are gathered according to their CMP number and
traces are corrected for normal move-out based on the final vrms model. The effect of well-chosen
vrms profiles is demonstrated by Figures 2.13 and 2.14.
Stacking
NMO-corrected traces are sorted into CMP gathers, summed, and averaged (i.e. stacked). A
stacked gather constitutes a single zero-offset trace located at x/2 (i.e. the midpoint). The final
Seismic Acquisition and Processing 33
Figure 2.12: Sound speed analysis of two example CMP gathers (a) Uncorrected CMP number
9201 plotted as function of x and TWTT. (b) Semblance plot that shows root mean square sound
speed, vrms, as function of TWTT. Warm colours = optimal values of vrms that yield correct time
delays on CMP gather; white circles = chosen vrms picks. (c) Over-corrected CMP gather where
selected vrms values are too slow. (d) Optimally corrected CMP gather using vrms picks shown in
panel (b). (e) Under-corrected CMP gather where selected vrms values are too fast. (f-j) Equivalent
panels for CMP number 12001.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 34
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Seismic Acquisition and Processing 35
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K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 36
seismic image is created by placing a series of stacked zero-offset traces side by side (Figure 2.4d).
A horizontal running average (i.e. trace mix) should be applied to the stacked image to enhance
coherent events and reduce random noise if the imagery will not be used in mixing analysis. Images
are presented as a function of distance along profile (range) in kilometres and depth in metres. CMP
numbers are converted to range using the spacing between them and two-way travel is converted
to depth assuming a constant sound speed.
Deconvolution and Migration
Deconvolution is used to increase the resolution of seismic images by removing the source wavelet
contribution. Deconvolution acts to compress the source wavelet and attenuate reverberatory en-
ergy that trails behind each reflection (Figure 2.6; Sheriff, 1991). The statistical deconvolution
method applied here simultaneously estimates the source wavelet and impedance series using a
least square method, and is based on the convolution model described in Section 2.2.3. The process
starts with an initial guess of the reflectivity and uses the seismic data to find a wavelet estimate.
In the next step, the algorithm assumes the wavelet to be correct and estimates a new reflectivity
series thereby improving upon the initial guess. The procedure iterates until convergence. This
algorithm makes three key assumptions; impedance contrasts are well-spaced vertically, the source
wavelet is consistent over time and space, and reflections are horizontally continuous. The last two
assumptions are valid for the water column since reflections tend to be horizontally continuous due
to smooth variations of sound speed and shallow depths. Since impedance changes in the water col-
umn are often gradational, it is possible that the series is are not well-spaced vertically. To overcome
this limitation it is possible to feed the algorithm an estimate of the source wavelet (Figure 2.6).
Deconvolved data now represent a section of reflection coefficients (Oldenburg et al., 1983). After
deconvolution, the wavelet associated with significant reflections is compressed and reverberatory
energy is largely attenuated (Figure 2.15). Since deconvolution whitens the frequency spectrum,
it may also enhance high frequency noise, and a filter should thus be applied post-deconvolution.
Papenberg et al. (2010) use statistical post-stack deconvolution to compute reflection coefficients.
Using Equation (2.6), reflection coefficients are converted into a model of interval sound speed.
They invert this sound speed model for the first two-dimensional profiles of temperature and salin-
ity estimated from a seismic image of the water column. An adapted procedure, following the
method of Papenberg et al. (2010), is applied to seismic datasets presented in this dissertation
(Chapter 3). Due to the low amplitudes of reflectivity in the water column, the effect of post-stack
Seismic Acquisition and Processing 37
statistical deconvolution is difficult to quantify, and this would be a viable piece of future work.
Figure 2.15: Effect of deconvolution. (a) Example stacked seismic panel. (b) Same panel as in
(a) with post-stack statistical deconvolution applied.
Migration is the process by which reflected signals are moved to their correct position in the
spatial domain (Sheriff, 1991). Migration moves dipping reflections up-dip and collapses diffraction
hyperbolae. The technique adjusts dipping interfaces because energy reflected from these interfaces
does not arrive at the same time as energy reflected from horizontal interfaces. Seismic migration
will also increase lateral resolution by reducing the size of the Fresnel zone. Migration requires
a sound speed model that is derived from independent measurements. However, such a model
is not usually available and is instead derived from iterative velocity picking. Since sound speed
variations in the water column are smooth compared with the subsurface, a true-amplitude post-
stack frequency-wavenumber migration has been used here (Stolt, 1978). Frequency-wavenumber
migration is applied in f -k space after application of a two-dimensional Fourier Transform to a
stacked image. This migration is a deterministic approach that solves for dips in f -k space using the
wave equation and sound speed model. Apparent dips in f -k caused by sloping reflectors are shifted
to their correct position based on the values estimated from the wave equation. The application in
f -k space is computationally efficient. Migration is particularly effective at repositioning dipping
reflections, however there is some debate about its relevance for seismic oceanographic studies.
Holbrook et al. (2013) stress the importance of migration. However, Pinheiro et al. (2010) have
shown that, due to near-horizontal reflections (i.e. maximum dip of ∼5◦), shallow depths and
small sound speed variations, migration does not significantly improve seismic images of the water
column. In this study, migration was found to have a minimal effect on the final stacked image.
Nevertheless, post-stack seismic images have been migrated using the Stolt (1978) algorithm.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 38
2.3 Three-dimensional Imaging
2.3.1 Acquisition
Three-dimensional seismic experiments tow multiple streamers behind the seismic vessel. Acquisi-
tion vessels are now powerful and sophisticated enough to tow 6–12 streamers of 4–8 km length and
an array of up to 100 airguns. In this way, a three-dimensional survey acquires many vertical slices
of the water column. Spacing between traces is half of the receiver separation along the streamer.
Typical three-dimensional surveys range in size from tens of square kilometres for field development
to several thousand square kilometres for exploration. Today, the bulk of seismic data are three-
dimensional. A survey is carried out by collecting closely spaced parallel lines (Figure 2.16a).
The vessel records line 1, turns with a radius of 5–10 km before shooting parallel line 2 in the
opposite direction (Figure 2.16b). The vessel continues to shoot parallel lines at a lateral shift of
∼1 km from the original. Each pass along the target is called a sail line. This ‘racetrack’ pattern
of acquisition provides a temporal component for water column records. Spatially this type of
acquisition is not truly three-dimensional, rather, it is a series of closely spaced two-dimensional
profiles that are simultaneously acquired. With this in mind, the pseudo-three-dimensional spatial
and temporal component of these seismic surveys provides four-dimensional imaging of the water
column. This method is the most commonly used today, as large amounts of data are acquired in a
cost-effective way. Other acquisition patterns, including spiral-shooting, have been performed but
present difficult challenges when processing.
Multiple airguns in a three-dimensional array fire alternately in a set-up known as flip-flop source.
At each alternate fire of the gun, a number of cross-sections of the water column are generated that
is equal to the number of cables being towed. Gun separation is set to half the cable separation.
This condition ensures that subsurface lines generated by the first gun are interleaved with lines
shot by the second gun (Figure 2.16a). Each source-cable combination yields midpoints along a
slice of the water column allowing multiple cross-sections to be acquired for each pass. A survey
with 10 cables and two sources and will therefore yield 20 cross-sections (Figure 2.16a). Typically
these sections are separated by 25 to 37.5 m. It is difficult to reduce this further without high risk
of cable entanglement.
The horizontal distance enclosed by streamers is given by xC = (nC−1)∆C, where nC is the number
of cables and ∆C is the separation between them (Figure 2.16a). The horizontal distance covered
Seismic Acquisition and Processing 39
Figure 2.16: Schematic of three-dimensional marine seismic acquisition. (a) Acquisition set-up.
Hatched polygon = seismic vessel towing equipment; white polygons = stabilizing floats; thin grey
lines = connecting cables; red/blue circle = airgun array; red/blue dashed lines = subsurface lines
acquired when red/blue airgun fires; thick black lines = streamers. (b) Seismic profiles acquired
using configuration shown in (a). Line 1 is acquired, seismic vessel turns and records parallel line 2.
Each complete loop is laterally shifted by ∼1 km. Thick black lines = recorded profiles; green/red
square = start/end of sail-line; arrow = direction of acquisition. Configuration shown gives 20
subsurface lines per sail-line of vessel. Not to scale.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 40
by all of the recorded cross-sections (i.e. midpoint lines) is given by xM = 0.25∆C × (2nC − 1).
Two airguns and 10 streamers were used in the Uruguay survey, separated by 62.5 and 125 m,
respectively. Therefore, xC = 1.125 km, xM = 593.75 m. In order to control the position of multiple
streamers, large stabilizers called paravanes are deployed, positioning the head of outermost cables
(Figure 2.16a). Dilt floats are smaller devices used to control the position of intermediate cables.
Nevertheless, currents, waves and winds can cause cables to be pushed away from their planned
position, known as feathering. Feathering is a particular issue for three-dimensional acquisition
since the increased length and number of cables make it possible for shifts over several neighbouring
subsurface lines. To account for this, the absolute position of each trace is calculated using global
positioning systems (GPS) stationed along acquisition equipment. GPS continuously record and
store position information alongside trace data, thereby retaining the true geometry of the survey.
The difference between two- and three-dimensional seismic surveying is summarised in Table 2.1.
2.3.2 Acoustic Source
Airgun arrays of O(10) guns are typically used in three-dimensional surveys to mitigate the bubble
pulse effect. Arrays are tuned since each piston holds differing volumes of air. Synchronous firing
of the multiple guns generates bubble oscillations at different frequencies, ensuring that primary
pressure peaks coincide and the bubble pulses are out of phase. In this way, constructive and
destructive interference of the in- and out-of-phase signal significantly improves the quality of the
source.
Source Wavelet Estimation
If auxiliary traces that contain the source signature are not available, it is possible to estimate
the wavelet from seismic data itself. Deterministic methods estimate w by comparing recorded
amplitudes with well-log data. Statistical methods estimate the wavelet from seismic traces and
require some assumptions. Since neither auxiliary nor coeval hydrographic (i.e. equivalent to
well-log information for the water column) information is provided alongside the Uruguay survey,
w is estimated using two statistical methods. These methods assume the seabed reflection is a
convolution of the source signal and the seabed reflection only (Figure 2.17). Seismic records are
windowed around a region where the seabed is approximately flat (Figure 2.17a). The seabed
reflection is flattened by applying constant hyperbolic move-out (Figure 2.17b). All traces are
Seismic Acquisition and Processing 41
Figure 2.17: Two statistical estimation methods used to reconstruct source wavelet.
Blue/red = positive/negative amplitude. (a-d) Statistical estimation using seabed reflection. (a)
Example shot gather from Uruguay survey in which seabed is approximately flat. (b) Flattened
seabed reflection. (c) Stacked trace. (d) Final wavelet estimate. (e-g) Statistical estimation using
inverse Fourier transform. (e) Identical to (a). (f) Average amplitude spectrum of windowed data.
(g) Average phase spectrum of windowed data. (h) Final wavelet estimate from inverse Fourier
transform of (f) and (g). Amplitudes normalised between -1 and 1; dashed line = time zero of
reconstructed wavelet.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 42
stacked in an effort to remove the effects of geology (Figure 2.17c). Considering the typical length
of a source signature is ∼50 ms, signal from deeper geology is removed by cutting off amplitudes
that are more than 50 ms from the seabed reflection. The final wavelet estimate is shown in Figure
2.17d. A second, statistical, method uses spectral analysis to estimate the source wavelet. Seismic
data are windowed around a region of flat seabed (Figure 2.17e). Average amplitude and phase
spectra are calculated as a function of frequency (Figure 2.17f,g). Now it is possible recover the
amplitude and phase of the signal as a function of time by applying an inverse Fourier Transform to
these spectra. A seismic trace is an array of samples representing the amplitude of a seismic signal
as a function of reflection time. A Fourier transform decomposes the signal into its component
frequencies, and the inverse transform returns the signal to the time domain. The wavelet estimate
is recovered by the inverse Fourier Transform (Figure 2.17h).
Both statistical methods imply the source wavelet used in the Uruguay survey is zero-phase (Figure
2.17d–f). The estimated source wavelet is affected by chosen input shots, therefore it is important to
use a region in which the seafloor is approximately flat. As the source changes with time and space,
these estimated wavelets represent averages. Since the two wavelet estimates are non-causal, short
in duration and symmetrical about time zero it is possible to conclude that during the Uruguay
survey a zero-phase w was used as the source signature (Figure 2.17). Average phase spectra further
support this inference (compare Figures 2.5f and 2.17g).
2.3.3 CMP Binning
The increased risk of feathering during three-dimensional surveying often leads to a scattering of
traces across an area as opposed to discrete cross-sectional lines. Binning collects a group of traces
that contain a common geometrical property (i.e. proximity to the same CMP). An ideal bin fits
several criteria. First, bin size is small enough that aliasing is avoided. Secondly, fold within a given
bin is large enough to improve signal-to-noise ratio. Thirdly, the bin interval should be large enough
to contain a broad sampling of all offsets. Finally, the bin should centre the reflection thereby
creating a regular grid. Figure 2.18 demonstrates the concept of binning. Planned subsurface lines
are parallel to the direction of the vessel. However, currents or wind may cause streamers to deflect
from their planned position, resulting in sampled locations that do not match predicted points. It
is now necessary to bin recorded traces so that the seismic volume may be sliced as desired.
Since most surveys are acquired with a geometry approximating a uniform grid, it is advantageous to
transform the survey points (northings/eastings) into a local coordinate system (inlines/crosslines)
Seismic Acquisition and Processing 43
Figure 2.18: Binning three-dimensional seismic reflection data. Arrow = direction of acquisition;
black squares = sampled subsurface points affected by feathering of ∼50 m at far-offsets; red/blue
dashed lines = inlines (Figure 2.16b); grey lines = crosslines orientated perpendicular to inlines.
Inline-crossline grid defines regular bins of 31.25×6.25 m used to group sampled subsurface points.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 44
aligned with the acquisition grid (Figure 2.18). Data are binned by superimposing a regular grid
onto the midpoint plane. All traces that fall within each cell or bin are assigned a midpoint
coordinate equal to the central point of that cell. Nominal bin size is determined by acquisition
parameters. Inline width is equal to half the source separation and crossline width is equal to half
the trace spacing. For the Uruguay survey, these values are 31.25 and 6.25 m, respectively (Figure
2.18).
2.3.4 Uruguay Survey
The three-dimensional survey analysed in this dissertation was acquired between December 2012
and April 2013 onboard the Amani, operated by Polarcus. The acoustic source comprised a pair
of airgun arrays each of which has 36 tuned guns. The airguns had a volume of 70 L (i.e. 4240
in3). These guns were primed with an air pressure of 14 MPa (i.e. 2000 psi). Reflected acoustic
waves were recorded along 10 cables of 6 km length. Each cable had 480 groups of hydrophones
spaced every 12.5 m. The streamers were towed at a depth of 9 m and separated by 125 m. The
turning radius of this acquisition set-up was on average ∼7 km, but varied across the survey. The
record sampling interval was 2 ms. In general, the vessel steamed in straight line segments at a
speed of 2.5 m s−1 and azimuth of 041. Alternate shots were fired every 10 s (25 m), yielding a fold
of cover of 120. The resultant profiles run approximately parallel to the South American coastline
in the southwest Atlantic Ocean. The survey traverses the continental slope and is approximately
220 km east of Montevideo. Water depth varies between 2000 and 3000 m in the surveyed area.
The Nyquist frequency for this survey is 250 Hz. The notch frequencies at the source and receiver
are 96 and 85 Hz, respectively (based on source/receiver depth of 8/9 m). To account for time
delay between shot and the start of recording, a shift of -50 ms was applied to the Uruguay seismic
data.
2.3.5 Signal Processing
Processing techniques that are applied to seismic records are identical for two- and three-dimensional
surveys when the operation treats each trace individually. These operations include frequency fil-
tering, trace muting, gain recover and statistical deconvolution. Three key operations are different;
binning, spatial filtering and any process that spatially repositions data such as migration and dip
move-out. A 20–90 Hz simple zero-phase band-pass filter was applied to the Uruguay survey and
Seismic Acquisition and Processing 45
the seabed was muted using brute stacks. Tractable processing times were of particular concern
when processing this survey, since each raw sail line is ∼0.6 TB. The adaptive subtract algorithm
employed during direct wave removal is computationally expensive, therefore a simple subtraction
was performed instead. This replacement did not significantly affect direct wave removal. Two
additions were made to the processing flow described above that caused significant improvements
to the final images, frequency-wavenumber and time-domain filtering.
Frequency-wavenumber Filtering
The recorded wavefield is equivalent to a synthesis of many plane-wave components and can be
split into its composite dip and frequency components using two-dimensional Fourier Transforms
(Yilmaz, 2001). Here, dip refers to the unique angle from vertical at which energy propagates and
will have an apparent dip on the seismic image in units of ms trace−1. Dip is related to sound
speed of a wave, v, by
Dip =
1000∆x
v
, (2.15)
where the factor 1000 converts from s into ms. Events recorded as a function of time, t, and
x may overlap in the t-x domain yet have different dips (Figure 2.19a–c). A two-dimensional
Fourier Transform expresses signals as a function of temporal frequency, f , and spatial frequency
or wavenumber, k (Figure 2.19d–f). As f is equal to the number of cycles per second in the
temporal dimension (i.e. counting peaks within a unit time), k is proportional to the number of
cycles per unit of distance in the spatial dimension (i.e. counting peaks within a unit distance
along the horizontal axis). Each dip in ms trace−1 contained in t-x space corresponds to a sloping
line through the origin, k = 0, and has a dip governed by Equation (2.15) in f -k space. The zero
dip component maps along the vertical axis. If positive dips are defined as down-dip from left to
right in t-x space, then events with increasing dip will map further into the positive quadrant in
the f -k plane (Figure 2.19d–f). In this way, it is possible to isolate signal from noise based on dip
(i.e. sound speed). However, at certain combinations of frequency and dip the signal may exhibit
a chequerboard pattern in t-x space and it becomes difficult to determine if the dip is positive or
negative (Figure 2.19c; 9 ms trace−1). Reflections are caused by boundaries that occur continuously
across all spatial scales, however by recording traces at discrete spatial locations (∼12.5 m) the
original analogue spatial signal is digitized. In this way, spatial aliasing is similar to temporal
aliasing. An example of spatial aliasing of the direct wave in t-x space is shown in Figure 2.20.
Aliased frequencies are located along linear segments that wrap around to the opposite quadrant
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 46
in the f -k spectrum. The 9 ms trace−1 dipping event shown in Figure 2.19c will map into the
negative quadrant with the wrong dip (Figure 2.19f). Steeper dips result in lower frequencies at
which spatial aliasing occurs. The Nyquist wavenumber, kN , is given by
kN =
1
2∆x
, (2.16)
where ∆x is the trace interval (e.g. receiver spacing for shot gathers). Data above kN wraps around
(aliases) and blends with un-aliased signal. In wrap around, data to the right of +kN continues
rightward from kN (Figure 2.21b). fmax is the threshold frequency below which data is not aliased,
given by
fmax =
va
2∆x sin θ
, (2.17)
where θ is the angle of incidence and can be approximated as 90◦.
Figure 2.19: Schematic showing two-dimensional Fourier Transform of t-x data into f -k domain.
(a) Four mono-frequency signals of 12 Hz with 0, 3, 6 and 9 ms trace−1 dips shown in t-x space.
(b) Same as (a) for signal of 24 Hz. (c) Same as (a) for signal of 60 Hz. (d–f) Corresponding f -k
domain for mono-frequency events shown in (a–c). Black bars = location of events in f -k space.
Each monochromatic signal maps onto a single point in f -k domain.
Figure 2.21a shows an example shot gather from the Uruguay survey that has been Butterworth
Seismic Acquisition and Processing 47
Figure 2.20: Spatial aliasing of direct wave in t-x space. (a) Example shot gather filtered at
25–35 Hz using a simple zero-phase filter; arrow = direction of true dip. (b) Example shot gather
filtered at 85–95 Hz using a simple zero-phase filter; arrow = direction of spatially aliased dip.
band-pass filtered between 20 and 90 Hz. The direct wave is clear as a high amplitude band of
dipping energy, and represents a signal of unique dip that contains different frequencies. The f -k
spectrum of this signal shows that for a given dip, all frequency components map onto the f -k plane
along a radial line that passes through the origin, k = 0 (Figure 2.21b). Events with the same dip
in the t-x domain, regardless of their location in TWTT or offset, map onto a single radial line in
the f -k domain. The range of dips in the t−x domain are transformed to a fan-shaped region in the
f -k domain and the direct wave appears as a strongly dipping band of energy (Figure 2.21c). Using
Equation (2.15), a direct wave travelling at 1450, 1500 and 1550 m s−1 will have an apparent dip of
8.6, 8.3 and 8.1 ms trace−1 respectively (assuming ∆x = 12.5 m). This dip is consistent with the
location of the high amplitude linear energy in f -k space (Figure 2.21b). The high amplitude of the
direct wave, relative to water column reflectivity, is particularly clear in f -k space, demonstrating
the need to remove the direct wave from seismic images of the water column. Swell noise that has
been attenuated using a bandpass filtering of 20–90 Hz is apparent as an absence of amplitude at
f < 20 Hz and f > 90 Hz in f -k space (Figure 2.21b). Using Equation (2.17), for va = 1530 m s
−1
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 48
Figure 2.21: Filtering in f -k space. (a) Example shot gather dominated by direct wave in
t-x space. Swell noise has been attenuated. (b) Shot gather dominated by direct wave in f -
k space. White/blue = high/low amplitudes; radial lines through origin = constant apparent
velocity, va. (c) Schematic of (b). Ellipses indicate regions of signal and noise; blue ellipse = signal;
red/orange/yellow ellipse = noise (i.e. direct wave and aliased signal); bold radial lines = chosen
dip filter passband (−1 to 8 ms/trace); number label = dip in ms trace−1. (d) Shot gather in f -k
space after application of dip filter. Amplitudes normalised between 0 and 1.
and ∆x = 12.5 m, the direct wave is aliased above 61 Hz (Figure 2.21b). At f > 60 Hz, energy
from the spatially aliased direct wave appears as a second band of high amplitude energy in the
negative quadrant (i.e. k < 0 cpm; Figure 2.21b,c). Other spatially aliased energy will appear in
the negative quadrant and may obstruct signal. To attenuate spatially aliased signals and noise
that has negative dips, a dip filter between -1 and 8 ms trace−1 was applied in f -k space to the
Uruguay dataset. This filter effectively removed spatially aliased energy whilst retaining signal
(Figure 2.21d).
Time-frequency Filtering
As discussed above, it is often easier to isolate noise from signal in the frequency domain. Here,
time-frequency domain noise removal has been used to attenuate anomalously high amplitudes.
Noise characterized by anomalous amplitudes, such as surplus marine swell or rig and ship noise,
can be attenuated by transforming traces into the frequency domain and then applying a spatial
median filter. Median trace energy of a presumed good trace or set of traces is calculated and
compared to specified sliding windows. If amplitudes within the window are found to exceed a
certain threshold level above the median they are replaced with the median energy. This process is
Seismic Acquisition and Processing 49
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K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 50
repeated for a range of frequencies and thresholds, and is applied to high-fold CMP gathers. Due
to the variable frequency and amplitude content of seismic surveys, the operation requires careful
testing to determine the parameters that will effectively remove anomalous amplitudes. Figure 2.22
shows an example application of time-frequency domain noise removal. In the Uruguay dataset,
noise spikes across CMP gathers stacked constructively to produce parabolic noise that swamped
certain sections of the final image (Figure 2.22a). The spikes are likely to have been caused by
other acoustic sources in the survey area. The spikes are effectively removed using the technique
described above (Figure 2.22b).
2.4 Water Column Reflectivity
2.4.1 Temperature and Salinity Contributions
Acoustic impedance is controlled by a combination of density, ρ, and sound speed, v. The latter
of which is the dominant effect (Ruddick et al., 2009; Sallare`s et al., 2009). Both of these physical
properties are determined by temperature, T , salinity, S, and pressure. Pressure changes smoothly
with depth, at approximately 1 decibar per metre. v and ρ are controlled primarily by T and S,
respectively. However, in the upper 100 m of the water column T is the primary factor influencing
ρ (Talley et al., 2011). Seismically recorded impedance contrasts can be deconstructed to estimate
the relative contribution of v and ρ, and therefore the T and S at each reflection. Sallare`s et al.
(2009) showed that across a seismic transect acquired in the southwest Iberian margin the mean
contribution of density variation is 5–10%, while 90–95% is due to sound speed variation. On aver-
age, 80% of the observed reflectivity arose from temperature changes. It is possible to conclude that
seismic images of the ocean are primarily maps of vertical temperature gradient. This conclusion
underpins interpretation of water column seismic imagery.
The method of Sallare`s et al. (2009) has been used to derive the contribution of T and S for
the JR298 and Uruguay survey. This method has four stages. First, compute T and S partial
derivatives using the UNESCO formulas for ρ and v (McDougall & Barker, 2011). Secondly,
incorporate the resulting formula into the Zoeppritz (1919) equations for reflection coefficients.
Over a vertical distance of ∆z, there is a change in properties of ∆ρ = ρ2 − ρ1, ∆α = α2 − α1
and ∆β = β2 − β1, where ρ, α, and β are the mean values of density, P-wave and S-wave speeds,
respectively. When these change of properties are very small, such that ratios of ∆ρ/ρ, ∆α/α,
and ∆β/β and approach unity, transmission will largely dominate reflection (i.e. the reflection
Seismic Acquisition and Processing 51
coefficient R will be close to zero). In this case, the first-order effect of small jumps in density
and sound speed are enough to accurately express the transmission/reflection coefficient for plane
waves. Therefore is is possible to use the Aki & Richards (1981) linearised Zoeppritz equations
for this purpose (Equation 2.11). Thirdly, convolve with a source wavelet. Finally, calculate the
relative significance of these properties.
For the water column, where β = 0 and ∆α/α is between 10−3 and 10−4, the expression for
reflection coefficient depends upon the angle of incidence θ, ρ and v contrasts only. The reflection
coefficient R is given as R = Rv +Rρ where,
Rv =
∆v
2v cos2 θ
, (2.18)
and
Rρ =
∆ρ
2ρ
. (2.19)
The relative contribution of ∆ρ and ∆v can be calculated as Rv/R and Rρ/R.
Ignoring the effect of pressure variation (i.e. assuming there is no depth component), ∆ρ and ∆v
can be expressed as function of temperature and salinity variations, ∆T and ∆S,
∆ρTS =
∂ρ
∂T
∆T +
∂ρ
∂S
∆S, (2.20)
and
∆vTS =
∂v
∂T
∆T +
∂v
∂S
∆S, (2.21)
where ∂ρ/∂T , ∂ρ/∂S, ∂v/∂T and ∂v/∂S are the partial derivatives of density and sound speed with
respect to T and S. Combining Equations (2.18), (2.19), (2.20) and (2.21) gives RTS = RT +RS ,
where
RT =
∆T
2
[
∂ρ/∂T
ρ
+
∂v/∂T
v cos2 i
]
, (2.22)
and
RS =
∆S
2
[
∂ρ/∂S
ρ
+
∂v/∂S
v cos2 i
]
, (2.23)
correspond to the contribution to the reflection coefficient made by ∆T and ∆S, respectively. The
relative contribution of ∆T and ∆S is then estimated as RT /RTS and RS/RTS (Sallare`s et al.,
2009).
Coeval or near-coeval hydrographic profiles of T , S and depth are sampled regularly every 5 m.
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 52
Figure 2.23: Diagrams of physical properties and their T and S partial derivatives of v and ρ.
Physical properties from near-coeval profiling float acquired on 17th February 2013 during Uruguay
survey. (a,c,e) T , S and pressure against v and ρ, respectively; black line = v; blue line = ρ. (b,d,f)
T , S and pressure against partial derivatives for v and ρ, respectively; solid black line = ∂v/∂T ;
dashed black line = ∂v/∂S; solid blue line = ∂ρ/∂T ; dashed blue line = ∂ρ/∂S. After Sallare`s
et al. (2009), Figure 2.
Seismic Acquisition and Processing 53
Using the Gibbs Sea Water Toolbox, corresponding profiles of pressure, v and ρ are calculated
(McDougall & Barker, 2011). Equations 2.20 and 2.21 are solved using ∆T and ∆S of 0.5 ◦C and
0.5 psu, taking a local gradient as the partial derivative. A value of 0.5 is used as significant sound
speed and density variations occur at this magnitude of change, using smaller values introduces
noise (Sallare`s et al., 2009). Local partial derivatives are calculated by taking the mid-point-value
of T , S and pressure for each set of three consecutive points. Then the value of v and ρ at each
end-point is calculated using the UNESCO formulas keeping S(T ) and pressure constant. ∆T (∆S)
is added or subtracted to the mid-point value of T (S). The gradient of sound speed and density
at the mid-point depth is calculated using the known change in T of 1◦C(S = 1 psu). The results
are convolved with a 30 Hz Ricker wavelet that represents a typical seismic source. Finally, the
contribution made to the reflection coefficient by T and S is calculated using Equations (2.22) and
(2.23).
Figure 2.23 shows diagrams of v, ρ and their T and S partial derivatives. Sound speed increases
with increasing temperature and salinity but decreases up to depths of 1000 m before increasing
(Figure 2.23a,c,e, black lines). Density decreases with increasing T and S and increases with depth
(Figure 2.23a,c,e, blue lines). Partial derivatives clearly show that the most substantial changes
occur within ∂v/∂T (Figure 2.23b,d,f, solid black lines). Partial derivatives with respect to S
hardly change (Figure 2.23b,d,f, dashed lines). ∂ρ/∂T increases slightly with increasing T and S,
and decreases slightly with depth (Figure 2.23b,d,f, solid blue lines). It is clear from the calculated
partial derivatives that the major contribution to water column reflectivity is from ∆v through
T . This conclusion is consistent with previous research that also shows the influence of ∆v and T
is major compared to ∆ρ and S in the water column (e.g. Nandi et al., 2004; Krahmann et al.,
2008; Sallare`s et al., 2009). The median percentage of the relative contribution of T to water
column reflectivity is 87% and 91% in the region surrounding for the JR298 and Uruguay surveys,
respectively. These values are similar to, if slightly higher than, 80% calculated in the Gulf of Cadiz
by Sallare`s et al. (2009). It is expected that the contribution of T and S will regionally vary.
2.4.2 Vertical and Horizontal Resolution
Vertical resolution, rvert, is controlled by the final frequency content of the image, which is a function
of source frequency content and attenuation. rvert can be defined as the minimum distinguishable
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 54
vertical separation between reflectors, given by Widess (1973) as
rvert =
λdom
4
, (2.24)
where λdom is the dominant wavelength of the source. Horizontal resolution, rhor, is a function of
depth and λdom. rhor can be defined as the minimum lateral spacing between two points so that
they are distinguishable from each other. rhorz is given by the Fresnel zone as
rhor =
√
λdomz
2
, (2.25)
where z is depth. As z increases, vertical and horizontal resolution decrease due to changes in the
frequency content of propagating source energy.
2.5 Conclusions
This chapter presents an outline of the core principles and techniques that underpin analysis of seis-
mic oceanographic imagery. The first part of this chapter describes the experiment configuration
and processing of two-dimensional seismic data. These data are collected along single lines that pro-
vide a two-dimensional cross-section of the water column. Two-dimensional acquisition is described
with the aid of a survey acquired in the Bellingshausen Sea, Southern Ocean. A typical three stage
processing flow is outlined that has been applied to this dataset. First, noise is mitigated with a
view to increasing signal-to-noise ratios and overall quality of the seismic records. Secondly, veloc-
ity analysis is performed at dense horizontal intervals to determine a two-dimensional sound speed
model across the seismic profile. Thirdly, seismic records are sorted into common midpoint gath-
ers, corrected for normal move-out, and stacked to produce the final image. Post-stack processing
should be applied considering the way in which the seismic imagery will be further analysed.
Three-dimensional seismic acquisition consists of multiple lines that are simultaneously acquired.
There are significant differences between the equipment configuration of two- and three-dimensional
seismic surveying which are summarised in Table 2.1. Processing techniques that operate on a
trace-by-trace basis are identical. Additional noise removal techniques that have been applied to
three-dimensional data are outlined. The seismic processing flow that has been applied to two and
three-dimensional seismic surveys that are discussed in this dissertation is summarised in Figure
2.24 and Appendix A.
Seismic Acquisition and Processing 55
K.L. Gunn, Ph.D. Dissertation
Seismic Acquisition and Processing 56
Figure 2.24 (previous page): Stacked seismic images that show each stage of processing flow
applied to water column reflection records. (a) Raw stack. (b) Swell noise removed using zero-
phase bandpass filter of 20–90 Hz. (c) Seabed and deeper reflections set to zero. (d) Direct
wave removed using linear move-out techniques. (e) Spatially aliased energy attenuated using
frequency-wavenumber dip filter of -1 to 8 ms trace−1. (f) Anomalous amplitudes attenuated using
time-frequency filtering. (g) Velocity profiles have been picked every 1.25 km and applied to CMP
gathers producing final stack. (a–f) stacked assuming constant velocity of 1530 m s−1.
Table 2.1: Comparison between two- and three-dimensional seismic survey acquisition parameters.
Parameter JR298 Uruguay
Survey type 2D 3D
Total airgun volume 5 L (300 in3) 2 × 70 L (4240 in3)
Airgun pressure 1.4 MPa (2000 psi) 1.4 MPa (2000 psi)
Shot point interval 10 s 10 s
Source tow depth/Separation 3-4 m 8 m/62.5 m
Near-offset 112.5 m 140 m
Streamer length 2.4 km 10 × 6 km
Number of receivers 192 480
Receiver group interval 12.5 m 12.5 m
Streamer tow depth/Separation 4.5 m 9 m/125 m
Fold of coverage 50-60 120
CMP spacing 6.25 m 6.25 m
Sampling rate 1 ms 2 ms
Original record length 9.5 s 6 s
Seismic reflections from the water column are caused by variations in temperature and salinity which
cause changes in acoustic impedance. The contribution of temperature and salinity to reflectivity
in the water column is calculated following the method of Sallare`s et al. (2009). It is found that
temperature contributes over 90% of the observed reflectivity across the Uruguay survey. This
result is consistent with average temperature contributions that are found to dominate salinity.
Finally, the resolution of seismic imagery is described based on the classic equations used for the
solid Earth.
Chapter 3
Warm-Water Transport across West Antarctic
Shelf
3.1 Introduction
Analysis of satellite observations from the Pacific margin of West Antarctica suggests that in-
creased basal melt rates of the ice shelf are a leading cause of ice mass loss (Rignot et al., 2008;
Pritchard et al., 2012). Widespread and intensifying glacial acceleration has been linked to on-shelf
transport of Circumpolar Deep Water (CDW) that is ∼3◦C warmer than the sea-surface freezing
point (Martinson et al., 2008). CDW is a major component of the Antarctic Circumpolar Cur-
rent (ACC). This current transports ∼140 × 106 m3 s−1 of water in a continuous eastward loop
around Antarctica. At the southern boundary of the ACC, this flow is concentrated along the
Southern Antarctic Circumpolar Current Front, SACCF (Figure 3.1). In the Bellingshausen Sea,
the average position of the SACCF is beside the continental shelf edge. Due to this proximity,
cross-shelf exchange of CDW occurs through a series of bathymetric troughs. Interaction between
ice shelves that terminate offshore and intruding CDW could increase basal melting, thus boosting
glacial acceleration and ice mass loss (Rignot et al., 2008; Klinck & Dinniman, 2010; Wa˚hlin et al.,
2010). In this way, ice mass loss could be promoted on annual and decadal timescales, and has the
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 58
Figure 3.1: Bellingshausen Sea regional context. (a) Bathymetric map of portion of Belling-
shausen Sea (inset: arrow = location of experiment; dotted line = mean location of Southern
Antarctic Circumpolar Current Front). Faint black lines = 500 and 1000 m contours delineating
shelf edge and bathymetric troughs; black dotted line labelled <SACCF> = mean location of
Southern Antarctic Circumpolar Current Front (Orsi et al., 1995); red dotted line labelled SACCF
= instantaneous location of Southern Antarctic Circumpolar Current Front, identified from sea-
surface velocity and temperature observations shown in panels (b) and (c), during period of seismic
experiment; thin black lines = seismic reflection profiles; thick black lines = portions of seismic pro-
files (Figures 3.3 and 3.11); TID = Thurston Island Drift; BeT = Belgica Trough; AID = Alexander
Island Drift; MT = Marguerite Trough; BiT = Biscoe Trough. (b) Map of sea-surface velocity field
determined from Ocean Surface Current Analyses Real-time (OSCAR) satellite measurements (five
day composite centred on 5th February 2015; Bonjean & Lagerloef, 2002). Black arrows = velocity
vectors. (c) Map of sea-surface temperature determined from Multi-scale Ultra-high Resolution
Sea-Surface Temperature (MUR-SST) satellite measurements (monthly mean for February 2015).
White circles = loci of coeval hydrographic measurements; dotted line = mean location of SACCF;
thin/thick black lines = seismic reflection profile where label refers to profile number.
Warm-Water Transport across West Antarctic Shelf 59
potential to moderate adjacent sea-ice cover, affect formation of dense shelf waters, and control the
amount of nutrients available for primary production (Pre´zelin et al., 2000, 2004; Hellmer et al.,
2012). A more refined understanding of warm-water transport will help to underpin the nature of
physical and biological processes that are active along Antarctic continental shelves.
Despite its fundamental importance, the mechanism of warm-water intrusion is poorly understood
due to the relative sparsity of hydrographic measurements across the Southern Ocean. Further-
more, the Bellingshausen Sea has been studied less intensively than other Antarctic marginal seas
(e.g. Zhang et al., 2011; Graham et al., 2016). Existing mooring observations and World Ocean
Circulation Experiment (WOCE) transects have horizontal resolutions of 20–50 km that are unable
to capture mesoscale (i.e. 10–100 km) and sub-mesoscale (i.e. 1–10 km) variability of advecting
water masses. Nevertheless, previous studies have shown that there are four possible intrusive
mechanisms associated with CDW: general upwelling (Pre´zelin et al., 2000; Martinson et al., 2008);
episodic diversion of the ACC onto the shelf (Dinniman & Klinck, 2004); flow onto the shelf caused
by interaction of ACC with bathymetry (Klinck et al., 2004); and eddy transport (Moffat et al.,
2009; Klinck & Dinniman, 2010; St-Laurent et al., 2013; Stewart & Thompson, 2015; Graham et al.,
2016).
Regional numerical models of oceanic circulation with resolutions as high as 1 km suggest that an
energetic eddy field is a leading cause of on-shelf intrusion (Stewart & Thompson, 2015; Stewart
et al., 2018). Unfortunately, only a limited amount of hydrographic observations have been acquired
that enable the existence and variability of this putative field to be quantified (Zhang et al., 2011;
Graham et al., 2016). Here, a calibrated seismic reflection survey is presented and analysed with a
view to investigating cross-shelf thermohaline structure. The survey was acquired during research
cruise JR298, which is described in Chapter 1. Seismic imaging exploits conventional multi-channel
equipment and can be used to constrain oceanic fine structure down to abyssal depths with spatial
resolutions of O(10) m (Holbrook et al., 2003; Biescas et al., 2008; Ruddick et al., 2009; Sheen
et al., 2009). Calibration of these vertical slices through the water column with coeval hydrographic
measurements demonstrates that acoustic reflectivity is mainly produced by temperature changes
as small as 0.03◦C (Nandi et al., 2004; Ruddick et al., 2009; Sallare`s et al., 2009).
A principal goal of this chapter is to demonstrate that calibrated seismic surveying can be used
to constrain the mesoscale to sub-mesoscale eddy field and to quantify its physical properties. In
this way, our understanding of shelf-slope exchange processes and their contribution to ice mass
loss can be improved. First, the nature of the problem is outlined by describing regional water
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 60
Table 3.1: Coeval hydrographic measurements from cruise JR298 used to calibrate seismic profiles.
Name Type Date, dd/mm/yy Time, hh:mm:ss Latitude, ◦S Longitude, ◦W
X1 XCTD 19/02/2015 12:33:56 66.47 71.57
X2 XCTD 22/02/2015 14:21:19 66.56 71.35
X3 XBT 22/02/2015 15:06:37 66.57 71.24
X4 XCTD 22/02/2015 15:54:43 66.53 71.13
X5 XBT 22/02/2015 16:56:04 66.48 70.98
X6 XCTD 22/02/2015 18:29:24 66.40 70.77
mass structure within the region of interest and by summarising hydrographic observations of
warm-water intrusions. Secondly, specific acquisition, processing and calibration techniques that
have been developed for this seismic reflection survey are described. A complete discussion of
acquisition, processing and calibration is given in Chapter 2. Finally, it is shown how the resultant
seismic images can be converted into temperature distributions and used to isolate and quantify
mechanisms of warm-water transport.
3.2 Oceanographic Setting
Figure 3.2 shows the regional setting along the western edge of the west Antarctica Peninsula
where ice shelves extrude onto the shallow water shelf. During cruise JR298, a total of 39 hydro-
graphic casts were deployed: five Conductivity-Temperature-Depth (CTD) casts; 11 Expendable
Conductivity-Temperature-Depth (XCTD) casts; and 23 Expendable Bathythermograph (XBT)
casts. The temperature-salinity relationship of these observations is shown in Figure 3.2b. This
relationship typifies that of austral summer, closely matching the results determined by 12 years
of legacy hydrographic observations acquired between 1993 and 2004 during the Palmer Antarctica
Long-Term Ecological Research (PAL-LTER) program (Figure 3.2b; Smith et al., 1995; Martinson
et al., 2008). Of these coeval hydrographic measurements a selection were used to calibrate seismic
records (Table 3.1).
Water masses within the Bellingshausen Sea along the Pacific Ocean side of the Antarctic Peninsula
are broadly divisible into Antarctic Surface Water (AASW) and CDW (Figure 3.2a). AASW is
a cold, fresh surface layer with a thickness of <100 m that is formed by modification of CDW,
which rises to shallow depths south of 40 ◦S. AASW can be further sub-divided into a warmer
surface-mixed layer (SML) and a cooler Winter Water (WW) layer. This cooler layer sits at the
temperature minimum of the entire water column (Figure 3.2b). The boundary between SML
and WW is marked by a pronounced and seasonal thermocline/halocline/pycnocline across which
Warm-Water Transport across West Antarctic Shelf 61
Figure 3.2: (a) Cartoon of physical oceanographic context highlighting impingement of warm-
water intrusions onto shallow continental shelf. AASW = Antarctic Surface Water; SML = Surface
Mixed Layer; WW = Winter Water; UCDW = Upper Circumpolar Deep Water; LCDW = Lower
Circumpolar Deep Water; m-UCDW = modified UCDW; polygon with hatching = grounded ice
sheet with floating ice shelf. (b) Temperature-salinity plot. Blue circles shaded according to depth
= hydrographic measurements acquired during Cruise JR298; gray circles = legacy hydrographic
measurements collected on RVIB Nathaniel B. Palmer cruise as part of Antarctica Long-Term
Ecological Research (PAL-LTER) database (Smith et al., 1995); boxes = locus of Winter Water and
Upper Circumpolar Deep Water; dashed line = freezing temperature of seawater. (c) Sound speed
measurements as function of depth acquired during cruise JR298.
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 62
temperature, T , decreases by >2◦C over ∼10 m. The base of WW represents the permanent
thermocline between AASW and CDW where there is a gradational change in water properties; a
consequence of a mixing process, probably dominated by turbulent diffusion. Below this depth, T
increases by >2◦C over ∼200 m. Away from the continental shelf, more uniform CDW lies beneath
AASW (Figure 3.2a).
Upper Circumpolar Deep Water (UCDW) is characterized by a temperature maximum of ≥1.6◦C
(Figure 3.2a). Lower Circumpolar Deep Water (LCDW) occurs at depths of >600 m and is brack-
eted by a gradual increase in salinity and by a decrease in temperature. On the continental shelf,
the CDW water mass becomes cooler as it mixes with surface waters that thicken toward the coast,
forming modified UCDW (m-UCDW; Figure 3.2a). In this way, the entire West Antarctic conti-
nental shelf is flooded by m-UCDW (Costa et al., 2008). During acquisition of the survey reported
here, there was little physical oceanographic change between hydrographic sites (Figure 3.2b,c).
The standard deviations for temperature and salinity profiles acquired during cruise JR298 are
0.2◦C and 0.05 psu, respectively.
On-shelf transport of warm water is thought to be influenced by the presence of a series of bathy-
metric troughs (Klinck et al., 2004; Moffat et al., 2009; St-Laurent et al., 2013; Couto et al., 2017).
For example, Marguerite Trough is a site where intrusions are known to occur (Figure 3.1a). Here,
warm-core eddies formed of CDW with horizontal and vertical length scales of ∼10 km and a few
hundred metres, respectively, have been observed. These eddies are thought to transport warm
water onto the shelf at a frequency of 3–5 per month (Figure 3.2a; Moffat et al., 2009; Martinson
& McKee, 2012; Couto et al., 2017). They can be generated by baroclinic instabilities in the ACC
and advect onto the shelf with a speed of O(10−2) m s−1 (Moffat et al., 2009; Martinson & McKee,
2012; St-Laurent et al., 2013). Along the eastern edge of the Marguerite Trough, a filament-like
intrusion transports UCDW, and possibly LCDW, southward with a speed of 0.05 m s−1 (Moffat
et al., 2009; St-Laurent et al., 2013). This filament might be caused by interaction of the ACC
with undulating long wavelength bathymetry along the shelf edge. Numerical modeling with a
resolution of 1.5 km suggests that Belgica Trough is also a region of elevated eddy kinetic energy,
implying a greater on-shelf transport of heat than was previously estimated (Figure 3.1a; Graham
et al., 2016). Furthermore, St-Laurent et al. (2013) suggest that the existence of coastal troughs
within the Bellingshausen Sea can enhance heat transport as a result of the accumulation of warm
anticyclonic eddies. Observations of warm m-UCDW across the continental shelf obtained from
tagged seals broadly support these numerical results (Zhang et al., 2016).
Warm-Water Transport across West Antarctic Shelf 63
3.3 Seismic Imaging
3.3.1 Acquisition and Processing
The seismic reflection survey was acquired during February 2015 onboard RRS James Clark Ross
as part of research cruise JR298, described in Chapter 1. The resultant profiles traverse parts of the
continental shelf in the vicinity of the Bellingshausen Sea (Figure 3.1). Water depth varies between
400 and 4000 m in the surveyed area. The acoustic source comprised a pair of Generator-Injector
(GI) airguns, each of which had a volume of 2.46 l (i.e. 150 in3). These guns were primed with
an air pressure of 13.5 MPa (i.e. 1960 psi) and fired every 10 s in harmonic mode. Reflected
acoustic waves were recorded along a 2.4 km streamer that had 192 groups of hydrophones spaced
every 12.5 m. The streamer was towed at a depth of 5 m. In portions of the surveyed area, the
length of the streamer was reduced by one half to safeguard against iceberg hazard. The record
sampling interval was 1 ms. In general, the vessel steamed in straight line segments at a speed of
2.5 m s−1 and shots were fired every 25 m, yielding a fold of cover of 60 (i.e. each discrete point
along a traverse is repeatedly sampled 60 times). During the acquisition programme, sea-surface
conditions were variable, and at times adverse, so that a proportion of the seismic records have a
poor signal-to-noise ratio. Standard techniques that are adapted from those used to build seismic
images of the solid Earth have been applied (Chapter 2).
There are three important processing steps. First, a 20–100 Hz Butterworth bandpass filter is
used to reduce the effect of swell noise. Reflections from the solid Earth are carefully muted
out. The direct wave is excised using an adaptive linear filter. Seismic amplitudes are corrected
for spherical divergence of the wavefield as it propagates through the water column. Secondly,
shot records are sorted into common midpoint (CMP) records and corrected for normal move-out.
This normal move-out correction relies on carefully choosing the root-mean-square (rms) sound
speed of seawater, vrms, as a function of two-way travel time. Although sound speed through the
water column generally varies between only 1440 and 1540 m s−1, these rms functions must be
chosen and applied with considerable care. At this stage, CMP gathers are stacked to produce the
final seismic image. Excessive frequency stretching at distant offsets is minimized by applying a
stretch mute of 1.5. Stacked images are stochastically deconvolved to mitigate the ringing effects
of the acoustic source. To locate reflected signals correctly within the spatial domain, post-stack
seismic images have been migrated using a standard frequency-wavenumber algorithm (Stolt, 1978).
Finally, seismic records are displayed as a function of depth. Two-way travel time is converted into
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 64
depth using the average sound speed. The final stacked images are characterized by numerous bright
reflections (Figure 3.3). These reflections are principally generated by thermohaline variations
within the upper 300 m. Progressively fainter reflections are visible down to a depth of ∼500 m,
below which no obvious reflectivity is visible. Further details of the seismic reflection experiment
acquisition and processing can be found in Chapter 2.
3.4 Temperature Conversion
Seismic reflectivity is generated by changes in acoustic impedance, I, which is the product of sound
speed, v, and density, ρ. Within the water column, it has been shown that I is dominated by
the spatial and temporal variation of v rather than ρ (Chapter 2). In turn, the variation of v is
determined by temperature, T , salinity, S, and pressure. In principle, therefore, the reflective field
contains information about physical water properties that can be recovered.
Signal processing is designed to ensure that the acoustic amplitudes recorded on each stacked
image are representative of the variation of acoustic impedance within the water column. These
amplitudes can then be scaled with respect to the seabed, yielding acoustic reflection coefficients,
R, using the method described by Warner (1990). An important challenge concerns the way in
which acoustic amplitudes and reflection coefficients are converted into oceanographically significant
observations (i.e. temperature, salinity). Previously, amplitudes of reflections have been used to
estimate temperature and salinity by two different approaches: an iterative procedure and full-
waveform inversion (e.g. Wood et al., 2008; Papenberg et al., 2010; Tang et al., 2016). These
different approaches perform well with accuracies that vary between 0.03 and 0.10◦C. Here, the more
straightforward and pragmatic iterative approach is exploited in order to determine temperature
from acoustic reflectivity.
Papenberg et al. (2010) developed an iterative two-stage procedure that enables seismic surveys,
which are densely calibrated with hydrographic measurements, to be converted into spatial maps
of temperature and salinity. First, this procedure exploits the temperature-salinity relationship
determined from CTD casts, together with the empirical equation of state for seawater, to calculate
how sound speed varies with depth and distance. By interpolating between CTD casts along
a given seismic image, this calculation yields the long wavelength, O(102) m, pattern of sound
speed. The amplitude of each acoustic reflection is used to determine the pattern of varying
reflection coefficients with depth and distance across the seismic image. Given the sound speed
Warm-Water Transport across West Antarctic Shelf 65
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K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 66
at the sea-surface, this pattern is used to recursively calculate how sound speed is perturbed on
short wavelengths, O(10) m, from the top to the bottom of the image. The final sound speed
pattern is obtained by summation of the smooth background and perturbed models. Secondly,
this combination of models is used to compute temperature and salinity. An iterative two-stage
procedure is particularly effective when sound speed is dominated by temperature and only weakly
affected by salinity such that there exists a unique pair of temperature and salinity values for a
given sound speed (Papenberg et al., 2010; Padhi et al., 2015).
A combination of long and short wavelength sound speed models is necessary because seismic
reflection images are dominated by short wavelength vertical components of T and S which vary
on length scales of 15–150 m. This limitation is a direct consequence of the band-limited nature
of the impulsive seismic source (frequencies of 10–100 Hz). Acoustic inverse methods are therefore
restricted since closely spaced coincident hydrographic observations of sound speed variations are
required to provide a long wavelength background profile on length scales longer than 150 m.
Unfortunately, coincident hydrographic measurements can be sparse, or even unavailable, which
means that there may be distances of hundreds of kilometres between calibration points.
In the Bellingshausen Sea, a significant drawback is the paucity of dense underway hydrographic
measurements upon which this iterative procedure relies. Consequently, the method of Papen-
berg et al. (2010) has been adapted by calculating the smooth background model of sound speed
variation directly from seismic records instead of relying upon a dense distribution of independent
hydrographic measurements. In this way, temperature conversion is divorced from the restriction of
requiring coincident and densely sampled hydrographic measurements. This modified approach is
also more computationally efficient compared to alternative schemes. The methodology described
here can be applied to any uncalibrated seismic survey, which means that substantial archives of
legacy surveys covering most continental margins can be exploited.
3.4.1 Development of Adapted Sound Speed Model
The long wavelength variation of sound speed is calculated from large numbers of vrms profiles that
are obtained during sound speed analysis of pre-stack seismic data (Chapter 2; Figure 3.4). vrms
is defined by
vrms =
√
v21t1 + v
2
2t2 + · · ·
t1 + t2 + · · · , (3.1)
Warm-Water Transport across West Antarctic Shelf 67
Figure 3.4: Sound speed analysis of two different CMP gathers from Profile 52. (a) Uncorrected
CMP gather at range 1.25 km plotted as function of horizontal trace number and two-way travel
time (TWTT). (b) Semblance plot that shows root mean square sound speed, vrms, as function
of TWTT. Warm colours = optimal values of vrms that yield correct time delays on CMP gather;
white circles = chosen vrms picks. (c) Over-corrected CMP gather where selected vrms values are
too slow. (d) Optimally corrected CMP gather using vrms picks shown in panel (b). (e) Under-
corrected CMP gather where selected vrms values are too fast. (f)–(j) Equivalent panels for CMP
number at range 112.5 km . Lines with open circles = over- and under-corrected reflection; lines
with solid circles = optimally corrected reflection.
where ti and vi are the two-way travel time down to, and interval sound speed of, the i
th layer.
Thus vrms can be regarded as a running average of sound speed within the water column which
is representative of the long wavelength component. Sound speed analysis is carried out every
1.25 km along the image.
It is straightforward to convert vrms into interval sound speed, vint, using the Dix equation (Dix,
1955). This equation makes three assumptions about the nature of the acoustic medium. First,
the medium is assumed to consist of horizontal layers of constant sound speed. Secondly, acoustic
rays are assumed to travel in straight lines within each layer according to Snell’s law. Thirdly, the
small aperture approximation for a seismic experiment applies (Yilmaz, 2001).
In the oceanic realm, reflection surfaces dips generally do not exceed 5◦. On the seismic profiles
presented here, dip generally does not exceed 1◦ and so the water column is composed of nearly
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 68
horizontal layers. Laterally, acoustic sound speed does not vary by more than 2% (i.e. ∼30 m s−1)
along twice the length of the streamer (i.e. 4.8 km). Therefore, observed horizontal sound speed
variations are no greater than 0.4%, so that reflections exhibit hyperbolic move-out as a function of
horizontal offset (Lynn & Claerbout, 1982). The ratio of maximum offset to target depth ensures
that both the straight ray path and the small aperture approximation conditions are met. Thus,
the Dix equation will accurately recover interval sound speeds from the picked vrms field. Before
and after application of the Dix equation, sound speed fields are smoothed using horizontal and
vertical moving averages. An example of this procedure is shown in Figure 3.5.
In this way, the long wavelength component of the sound speed model is recovered every 1.25 km
along a given profile. The density of this recovery is a significant improvement on the spacing of
coincident hydrographic measurements acquired during cruise JR298, which are spaced irregularly
with average intervals of 10 km. Furthermore, this density is much greater than could be rea-
sonably achieved during a typical hydrographic experiment. Assuming a continuous vessel speed
of 2.5 m s−1, expendable casts would have to be deployed every ∼8 minutes to achieve 1.25 km
spacing.
Detailed processing of seismic data yields a series of reflection coefficients, R, through time and
space that are related to short wavelength changes of sound speed, v, and, to a smaller degree,
density, ρ. Assuming near-normal incidence, the short wavelength component is extracted using
R =
v2ρ2 − v1ρ1
v2ρ2 + v1ρ1
, (3.2)
where subscripts 1 and 2 represent layers above and below a reflecting interface, respectively (Yil-
maz, 2001). Density variations make a minor contribution to R. Thus, it is reasonable to assume
that ρ varies as a function of depth in accordance with regional hydrographic measurements.
Long and short wavelength sound speed fields are then merged and the final sound speed model
is converted into temperature using the iterative method described by Papenberg et al. (2010).
The calculated variation of temperature along each seismic reflection image is shown in Figure
3.6. Coeval, but widely spaced, hydrographic measurements are unable to reveal the level of small
mesoscale to sub-mesoscale (i.e. <50 km) detail visible on these converted images. Due to some-
times adverse weather conditions, seismic records acquired during cruise JR298 can suffer from low
signal-to-noise ratios. As a result, shorter wavelength, O(10) m, variations of sound speed, and
therefore temperature, are not always accurately recovered (Figure 3.7). It is important to empha-
Warm-Water Transport across West Antarctic Shelf 69
Figure 3.5: Sound speed development for adapted inversion procedure with portion of Profile 52
shown in Figure 3.3b. (a) Root mean square sound speed, vrms, as function of range. White circles
= loci of sound speed profiles that were picked every 1.25 km; black triangle = location of CMP
gather shown in Figure 3.4a–e. (b) vrms as function of range that has been horizontally smoothed
using sliding window of 6.25 km. (c) Interval sound speed, vint, as function of range calculated
from vrms using equation from Dix (1955). (d) vint as function of range that has been vertically
smoothed using sliding window of 0.1 s.
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 70
size that this limitation is not a serious problem since the primary interst is in constraining the
overall size, shape and temperature anomalies of eddies that occur on kilometre-scale wavelengths
rather than the details of their internal structure.
3.5 Additional Datasets
3.5.1 High Frequency Acoustic Data
High frequency (i.e. 18–200 kHz) acoustic echo-sounder surveys were acquired during cruise JR298.
These surveys provide sub-metre resolution imaging over ranges of 10s-100s of kilometres but
depth penetration is limited due to absorption and scattering effects within the water column.
Echo-sounding is a tool for estimating the distribution and abundance of biomass (e.g. fish, zoo-
plankton). Detectable echoes are also produced by suspended sediment fractions, bubbles, and, in
some cases, by temperature and salinity gradients. The use of echo-sounders for identifying and
mapping oceanic microstructure is not common but it has been shown to be a promising technique
(Goodman, 1990; Warren et al., 2003; Lavery et al., 2010). The main drawback is the shallow
penetration depth that results from using high frequency acoustic pulses. There is also ambiguity
in interpreting resultant profiles due to a wide variety of possible biological and physical sources
that can simultaneously act to scatter acoustic energy (Ross et al., 2007). Significantly, Warren
et al. (2003) and Lavery et al. (2010) have shown that at frequencies of <100 kHz, backscattering
is dominated by reflections from microstructure rather than zooplankton.
During cruise JR298, an EK60 bio-acoustic echo-sounder with frequencies of 38, 70, 120 and 200 kHz
was used to acquire profiles along portions of the seismic survey. This echo-sounder was used in
free-run mode, pinging approximately every 6 s. The EK60 device was not synchronized with other
acoustic methods since a primary aim of the JR298 cruise was to obtain high quality sub-bottom
profile observations. Consequently, echo-sounder data were exposed to a considerable amount of
ambient and systematic noise. Where echo-sounder and seismic profiles coincide, preliminary results
show that there is a strong, albeit intermittent, correlation between both datasets. Selected profiles
were processed using a straightforward processing flow in which account was taken of: the position
of the transducers beneath the hull; measurements above 13 m were muted due to interference of
the hull which causes high amplitude ringing; pings from other instruments were muted; and a 3×3
convolution was used for spatial and temporal smoothing. A coincident echo-sounding profile is
shown for seismic Profile 62 (Figure 3.10d). For a thorough description of the theory and methods
Warm-Water Transport across West Antarctic Shelf 71
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K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 72
Figure 3.7: Comparison of converted temperature profiles obtained from adapted iterative in-
version procedure with coeval measurements. (a) Profile 61. Labelled triangles = loci of coeval
CTD casts X1 and X2. Four panels along base compare observed and calculated sound speed and
temperature profiles at X1 and X2. Black lines = observed profiles; red lines = calculated profiles
determined by iterative inverse procedure. (b) Same for Profile 62.
involved with high frequency scattering methods see Warren et al. (2003); Lavery et al. (2003,
2010).
3.5.2 Acoustic Doppler Current Profiler
Acoustic Doppler Current Profiling (ADCP) is used to obtain continuous measurements of particle
velocity of oceanic currents as a function of depth. It exploits four transducers that transmit and
receive acoustic pulses within a frequency range of 30–200 kHz. Acoustic energy is scattered by
small particles such as zooplankton, suspended sediments, or other solid particles that are assumed
to drift according to local currents. The beams transmit sound at a known frequency into the water
column, which reflects from moving particles and returns with a different frequency according to
the velocity of water it traverses. This Doppler shift effect exploits the frequency shift measured by
each transducer and in this way the ADCP can compute the vector component of particle velocity
along the beam direction. Four beams are used to measure three velocity components so that
the vector of particle velocity relative to that of the vessel is determined. To obtain the correct
velocity, the current profiler subtracts the vessel velocity from that of the measured currents. This
correction is carried out either by using the bottom-tracking option or by using global positioning
system navigation data.
Warm-Water Transport across West Antarctic Shelf 73
An RDI 75 kHz ADCP was used intermittently during cruise JR298 to acquire water current velocity
measurements. This system was configured using an 8 m pulse length with 100 × 8 m depth
bins using two minute ensemble averages. This configuration generated velocity measurements
for a depth range of 8–800 m. Bottom tracking was disabled for the entire cruise since water
depths greater than 500 m were generally encountered. ADCP observations are processed using
the Common Oceanographic Data Access System (CODAS) developed by Firing and Hummon at
the University of Hawaii. Heading corrections are made using GPS data acquired by the onboard
Seapath system.
3.6 Seismic Images
A suite of five seismic profiles and their accompanying temperature conversions that have a com-
bined length of ∼500 km are presented and interpreted (Figure 3.1c). These profiles have been
compared with coeval hydrographic measurements and their interpretation is complemented by
underway high frequency (i.e. 38 kHz) echo-sounder and by Acoustic Doppler Current Profiler
(ADCP) measurements where possible.
The seismic and physical oceanographic observations can be considered at two levels of scale.
First, large-scale (>100 km) patterns of reflectivity are described and interpreted. This pattern
is consistent across the whole seismic survey and is probably typical of the acoustic structure of
the water column during austral summer. Secondly, small mesoscale (i.e. 10–100 km) and sub-
mesoscale (i.e. 1–10 km) patterns of reflectivity are described. These more detailed patterns are
caused by warm-water intrusions and by other thermohaline structures.
3.6.1 Large-scale Patterns of Reflectivity
Profiles 52, 61 and 62 reveal complex patterns of reflectivity (Figures 3.3). These patterns can be
separated into three general observations. First, a bright and continuous reflection dominates the
upper portion of each profile. This reflection undulates between 30 and 80 m depth and represents
the strongly seasonal boundary between SML and WW. The amplitude of this reflection is controlled
by a dramatic temperature gradient of >2◦C over ∼10 m depth (Figure 3.2c). Secondly, weaker
and more discontinuous reflections occur at the gradual transition from AASW to CDW between
depths of 100 and 300 m. Finally, reflections almost completely disappear beneath about 300–500 m
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 74
depth. This acoustic transparency is a consequence of homogeneity of the thermohaline structure
of CDW. These large-scale patterns are typical of each profile in this region and are consistent with
the known water-mass structure (Figure 3.2a,b and Figure 3.7).
Calculated temperature distributions for Profiles 52, 61 and 62 reveal a two layer structure whereby
cooler AASW overlies warmer CDW (Figure 3.6). The WW layer is strikingly visible as a cold band
of water at depths of 50 to 100 m. The temperatures of this layer are obtained by iterative inverse
modelling and range between −1 and −2◦C. This calculated range agrees with the observed range
of values constrained by the temperature-salinity field (Figure 3.2b; −1.2 to −1.8◦C). As expected,
the WW layer is coldest on the shelf (Figure 3.6c,d). The gradual increase of temperature with
depth reflects the transition from AASW to CDW. It is evident that both sharp and gradational
boundaries above and below the WW layer are reproduced by the iterative inversion procedure,
providing confidence in the adapted scheme that is used here to extract temperature estimates from
seismic reflectivity (Figure 3.7).
3.6.2 Small Mesoscale to Sub-Mesoscale Structures
On shorter length scales, Profiles 52, 61 and 62 show that there are numerous lens-shaped structures
characterized by curved reflections that wrap around acoustically transparent centers (Figure 3.3).
The two clearest examples occur on the central portion of Profile 52 where the upper and lower
surfaces of both lenses are outlined by convex-shaped reflections (Figure 3.3b). The sides of these
lenses are delineated by terminations of numerous reflections. The detailed shapes of these reflec-
tions are characterized by periodic oscillations that are interpreted as internal waves. Lens-shaped
structures are commonly observed on seismic images and are generally thought to be indicative
of eddies (e.g. Biescas et al., 2008; Sheen et al., 2009; Me´nesguen et al., 2012). It is important
to emphasize that these images are vertically exaggerated and that eddy dimensions yield aspect
ratios consistent with regional estimates of N/f where N is the buoyancy frequency and f is the
Coriolis parameter (Charney, 1971).
Up to 22 eddies are observed along Profile 52 (Figure 3.3a,b and Figure 3.8a). These eddies become
visible >100 km north of the shelf edge at Belgica Trough. Moving southward and approaching
the trough itself, eddy density increases and they gradually merge with each other, particularly
south of a range of 120 km along profile L52. These eddies vary considerably in size, with lengths
of 0.75 to 11.00 km and thicknesses of 100–150 m, spanning the characteristic sub-mesoscale range.
Warm-Water Transport across West Antarctic Shelf 75
Figure 3.8: (a) Portion of Profile 52; black arrows = inferred position of putative Antarctic
Slope Front. White circles = locations where lens-shaped reflectivity patterns coincide with warm
temperature anomalies shown in (c). (b) Same portion of Profile 52 overlain with residual tem-
perature anomalies. (c) Same portion of Profile 52 showing residual temperature anomalies alone.
Thin black lines = contours of temperature plotted every 0.4◦C where top and bottom contours
represent 0.2◦C.
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 76
It is important to emphasize that these seismic images are two-dimensional vertical slices through
three-dimensional structures, which means that lengths and thicknesses are probably lower bounds.
These structures always lie directly beneath the WW layer in water depths of 50–200 m. Typically,
the continuous reflection that marks the overlying boundary between WW and SML reflection is
deflected upward over each eddy (Figure 3.3).
The calculated temperature distribution for Profile 52 shows that the cores of these eddies are char-
acterised by temperature anomalies of +0.4 to +1.6◦C, indicative of UCDW (Figure 3.8b,c). These
anomalies have been calculated by subtracting the average temperature structure as a function of
depth from the seismically determined temperature structure (PAL-LTER hydrographic database;
Smith et al., 1995). To account for regional variation of UCDW temperature structure, the PAL-
LTER database was divided into off-shelf and shelf areas, each of which was averaged. Residual
anomalies are larger than both the standard deviation of the PAL-LTER mean (i.e. ±0.2◦C) and
the root-mean-square uncertainty estimated for the seismically determined structure (i.e. ±0.3◦C).
For example, between 50 and 200 m depth, residual temperature anomalies are clearly warmer
than average such that interpreted eddies encompass the highest temperatures (e.g. Figure 3.8c).
A clear example occurs at a range of 100–110 km along Profile 52 (Figure 3.8b). In some instances,
seismically determined temperature anomalies are overestimated (> +2.5◦C). Nonetheless, residual
temperature anomalies are broadly consistent with independent observations obtained from tagged
seals that reveal shallow temperature anomalies of up to +1◦C, which extend shelfward in the
vicinity of Belgica Trough (Zhang et al., 2016).
A prominent eddy is visible at a range of 60–75 km on Profile 61 (Figure 3.9a). It is located 6.4 km
inshore of the shelf edge at the western side of Marguerite Trough. This eddy is 10.40 ± 0.06 km
long and 250± 10 m high. A coeval XCTD cast, X2, intersects the eddy at a range of 71 km. The
temperature profile has two abrupt excursions of ≥0.3◦C which form characteristic steps that are
typical of warm core eddies and reminiscent of double-diffusive interfaces (Figure 3.9b; Ruddick,
1992; Meinen & Watts, 2000; Song et al., 2011). Temperature within the core is ≥1.6◦C, indicative
of UCDW. The calculated temperature distribution provides corroborative evidence since warm
(>1.6◦C) water coincides with eddy reflectivity (Figure 3.9c,d). A second XCTD cast, X1, is
located at a range of 55 km further north along this profile (Figure 3.3c). In this case, no warm-
water intrusion is present and, as expected, the temperature profile lacks abrupt excursions (Figure
3.9b).
A poorly imaged eddy is visible at a range of 25 to 35 km along Profile 62 (Figure 3.10). Here, a
Warm-Water Transport across West Antarctic Shelf 77
Figure 3.9: (a) Portion of Profile 61 showing eddy-like feature. Labeled black triangle = location
of coeval XCTD cast; open circles = depths at which significant temperature changes occur. (b)
Black line = temperature as function of depth for XCTD cast at X2; arrows = depths at which
significant temperature changes occur that are indicative of a warm core eddy; dotted line =
temperature as function of depth for XCTD cast at X1 for comparison; red line = seismically
determined temperature as function of depth at position where cast X2 was acquired; red dotted
line = inverted temperature as function of depth at position where cast X1 was acquired. (c)
Black line = residual temperature anomaly as function of depth for XCTD cast at X2; dotted line
= residual temperature anomaly as function of depth for XCTD cast at X1 for comparison; red
line = seismically determined residual temperature anomaly as function of depth at position where
cast X2 was acquired; red dotted line = seismically determined temperature anomaly as function
of depth at position where cast X1 was acquired. (d) Same portion of Profile 61 overlain with
seismically determined residual temperature structure. (e) Same as panel (b). (f) Same as panel
(c).
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 78
bright convex-upward reflection appears to delineate the top of the eddy which is 10.70± 0.06 km
long (Figure 3.10a). Clear reflections are absent along the probable base and sides of this struc-
ture. However, a coincident 38 kHz echo-sounder profile provides corroborative evidence that it
is probably an eddy (Figure 3.10b). A coeval XBT cast, X6, intersects this eddy at a range of
29 km. The step-wise temperature increase of ∼+0.5◦C coincides with the bright reflection. A
similar increase of temperature is visible on the calculated temperature distribution (Figure 3.10c).
At depth, the temperature profile for X6 has a small step-wise temperature decrease. Similar re-
flections are observed at a range of 11 to 18 km on the western end of this profile where a coeval
XBT cast, X5, at a range of 16 km records a pronounced increase in temperature at depth that
correlates with bright reflectivity (Figure 3.10b). Although the most likely explanation for these
relatively poorly imaged structures is that they are warm-core eddies, it is also conceivable that
Profile 62 has imaged the upper surface of a warm, filament-like structure that has pooled within
the deeper corrugated parts of the Marguerite Trough (Figure 3.1a). Such a structure may extend
up to 25 km across this trough and would be consistent with observations of a general upwelling
of ACC along the eastern side of the trough (Klinck et al., 2004; Moffat et al., 2009; St-Laurent
et al., 2013).
A group of three sloping reflections that dip ∼1 ◦ southwards occur at a range of 115 km along
Profile 52 (Figure 3.8a). The geometry of these tripartite reflective strands is characteristic of an
oceanic front (Holbrook et al., 2003). Although Profile 52 crosses the SACCF’s mean position, it
is unlikely that these reflections are associated with this front since the sea-surface velocity field
determined by OSCAR satellite measurements shows that the southernmost extent of the ACC,
delineated by the SACCF, is located about 50 km north of Profile 52 (Figure 3.1a). Furthermore,
hydrographic measurements from WOCE transect SO4P demonstrate that the SACCF dips in the
opposite direction and has a horizontal width of > 20 km in contrast to what is observed
(http : //www.woceatlas.ucsd.edu). One plausible explanation is that this group of dipping re-
flections is associated with the Antarctic Slope Front (ASF), which marks the boundary between
cold, fresh waters of the continental shelf and warm, saline waters of the abyssal ocean. The ASF
has a characteristic ‘V-shaped’ structure that consists of a southward-dipping northern limb and
northward-dipping southern limb (Talbot, 1988; Jenkins & Jacobs, 2008). This geometry is strik-
ingly similar to that which is imaged on Profile 52 at a range of 110–130 km. Here, reflections dip
in opposite directions with a downward-pointing apex at a range of 122 km and a depth of 350 m
(Figure 3.8a). The ASF is normally associated with the shelf break, but this observation places
the ASF ∼40 km north of this break. It is possible that this frontal structure moves with respect
Warm-Water Transport across West Antarctic Shelf 79
Figure 3.10: (a) Portion of Profile 62 showing a less well imaged eddy (or possibly filament-like
feature) at range of 23–34 km and depth of 180–290 m. Labeled black triangles = locations of
coeval XCTD/XBT casts; open circles = depths at which significant temperature changes occur;
solid circles = depths to crest of eddy/filament recorded on coincident echo-sounder profile shown in
panel (d). (b) Black line = temperature as function of depth for XCTD cast at X5; arrow = depth
at which significant temperature change occurs; dotted line = temperature as function of depth for
XBT cast at X3 for comparison; red line = seismically determined temperature as function of depth
at position where cast X5 was acquired; red dotted line = seismically determined temperature as
function of depth at position where cast X3 was acquired. (c) Black line = residual temperature
anomaly as function of depth for XCTD cast at X5; dotted line = residual temperature anomaly as
function of depth for XCTD cast at X3 for comparison; red line = seismically determined residual
temperature anomaly as function of depth at position where cast X5 was acquired; red dotted line
= seismically determined residual temperature anomaly as function of depth at position where cast
X3 was acquired. (d) 38 kHz echo-sounder profile that coincides with Profile 62. (e) Black line
= temperature as function of depth for XCTD cast at X6; arrow = depth at which significant
temperature change occurs; red line = seismically determined temperature as function of depth
at position where cast X6 was acquired; red dotted line = seismically determined temperature as
function of depth at position where cast X3 was acquired. (f) Black line = residual temperature
anomaly as function of depth for XCTD cast at X6; dotted line = residual temperature anomaly as
function of depth for XCTD cast at X3 for comparison; red line = seismically determined residual
temperature anomaly as function of depth at position where cast X6 was acquired; red dotted line
= seismically determined temperature anomaly as function of depth at position where cast X3 was
acquired. (g) Same portion of Profile 62 overlain with seismically determined residual temperature
anomaly structure. (h) Same as panel (e). (i) Same as panel (f).
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 80
to the shelf edge (Thompson et al., 2014; Zhang et al., 2016).
The possible presence of the ASF at this location implies that the lateral circumpolar extent of
this front continues further east than previously suggested. This hypothesis is consistent with
hydrographic observations (Talbot, 1988; Jenkins & Jacobs, 2008; Zhang et al., 2016). These
seismic profiles suggest that warm-core eddies occur on either side of this tripartite front. Close
inspection of these sloping reflections implies that they do not cross the seasonal thermocline (i.e.
they do not extend above ∼200 m; Figure 3.8a). This seismic observation is consistent with the
subsurface nature of the ASF (Talbot, 1988; Jenkins & Jacobs, 2008). The ASF might affect eddy
transport whereby ‘V-shaped’ pycnoclines can act as barriers to onshore transport (Thompson
et al., 2014). Thus the local presence of the ASF may play a role in moderating the spatial and
temporal variability of warm-water intrusions. Since the ASF sits beneath the seasonal thermocline,
and warm-core eddies appear on each side of the frontal structure, the tripartite front may not
be acting as a significant dynamical barrier, impeding warm-water intrusion. Nevertheless, it is
conceivable that this putative front moderates the spatial and temporal variability of intrusion
(Armitage et al., 2018).
Finally, a series of concave-upward, bowl-shaped reflections are visible on Profiles 55 and 57 above
Alexander Island Drift. These two crossing profiles are orthogonal to each other and offer a partially
three-dimensional perspective of this unusual structure (Figures 3.1c and 3.11). The bowl extends
over about 60 km in a southeast-northwest direction and over about 40 km in a southwest-northeast
direction. It has a height of 200 m and a volume of >125 km3. ADCP observations demonstrate
that both north and east components of velocity are 0.2 m s−1 faster than that of surrounding water,
suggesting that the bowl is decoupled from the surrounding water (Figure 3.11d,e). Reconstruction
of the velocity vector indicates that the bowl structure is probably translating northwestward (i.e.
a direction that bisects Profiles 55 and 57). Whether or not this structure is also rotating about a
vertical axis cannot be determined from these observations.
3.6.3 Eddy Propagation
On-shelf transport of warm water has been documented within Marguerite Trough using hydro-
graphic observations and numerical experiments. For example, Moffat et al. (2009) use a set of
discrete temperature and current metre measurements to infer the presence of eddy-like excursions
that advect southward with speeds of O(10−2) m s−1. Martinson & McKee (2012) analyse mea-
surements from five thermistor moorings and infer that eddies drift southward past these moorings
Warm-Water Transport across West Antarctic Shelf 81
Figure 3.11: (a) Profile 55. Labeled box = zoomed portion shown in panel (c); vertical dashed
line = locus of intersection with Profile 57. (b) Profile 57. Labeled box = zoomed portion shown in
panel (d); vertical dashed line = locus of intersection with Profile 55. (c) and (d) Conjoined zooms
of orthogonal Profiles 55 and 57. (e) Conjoined zooms overlain with north component of water
current velocity from vessel-mounted ADCP record. (f) Same as (e) overlain with east component
of water current velocity from vessel-mounted ADCP record. (g) Same as (e) overlain with residual
temperature anomalies.
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 82
in accordance with the background velocity field at speeds of O(10−2) m s−1. St-Laurent et al.
(2013) examine mechanisms responsible for warm-water circulation by running three-dimensional
oceanic models and infer a southward (i.e. on-shelf) flow of 0.05 m s−1.
Although similar hydrographic observations have not been acquired within Belgica Trough, Graham
et al. (2016) present two regional numerical models with spatial resolutions of 4 and 1.5 km in order
to simulate physical oceanographic processes within both Marguerite and Belgica Troughs. Their
higher resolution model implies southward heat transport onto the shelf is augmented as a result
of increased eddy activity within these troughs. Other high resolution regional studies also suggest
that the shelf break hosts a high energy, mesoscale eddy field (e.g. Thompson et al., 2014; Stewart
et al., 2018).
Here, seismic profiles from both troughs are presented. Significant numbers of eddies are observed
(Figure 3.3). On Profile 52, which traverses Belgica Trough, I am confident that the observed
eddies do not occur at the frontal zone of the SACCF itself, even though the average position of
this front appears to bisect this seismic profile (Figure 3.1a). The seismic survey was acquired
during February 2015 and the average sea-surface velocity field determined from OSCAR satellite
measurements for a five day period centred on 5th February 2015 shows that the region of fast
flowing (i.e. ≥0.3 m s−1) surface currents associated with the ACC is positioned about 0.5 ◦ north
of Profile 52 (Figure 3.1b). This observation is corroborated by the observed mean sea-surface
temperature for February 2015 (Figure 3.1c). The location of eddies far to the south of the SACCF
implies that they are not being swept within strong eastward currents which dominate the ACC.
Thus a combination of hydrographic observations, numerical modeling, as well as the locus of the
seismically observed eddies with respect to the SACCF can be used to infer southward transport of
the eddy field. In comparison, the along-slope component of the velocity field south of the SACCF
is probably significantly smaller than the on-shelf component, although it is reasonable to expect
it to be non-zero.
Validity of the hypothesis of southward transport of eddies can be tested by estimating the trans-
lation of individual seismic reflections along Profile 52 using pre-stack common mid-point (CMP)
gathers (Figure 3.12). As a result of the redundancy built into seismic acquisition, each CMP gather
consists of a group of 60 ray paths that span a finite period of time. The in-plane, horizontal speed
of a given reflection is determined by measuring its slope in shotpoint-CMP (i.e. time-distance)
space (Figure 3.12f,j,n; Sheen et al., 2009; Tang et al., 2016). In this way, slope measurements at
different locations along Profile 52 can be used to determine the velocity field (Figure 3.12a). The
Warm-Water Transport across West Antarctic Shelf 83
Figure 3.12: (a) Portion of Profile 52. Right-/left-pointing black arrows = measured southward
(i.e. on-shelf)/northward (i.e. off-shelf) speeds of individual reflections; white arrows = examples
shown in (f), (j) and (n). (b) Horizontally averaged speed measurements as function of depth
along Profile 52. Thin arrows = individual horizontally averaged measurements; thick arrows =
measurements within UCDW layer that yield average speed of 0.07±0.04 m s−1. (c–e) Set of normal
move-out corrected shot gathers at three different times separated by ∼40 s that show detectable
translation of reflections. Filled circle = position of given reflection on given shot gather; open
circle(s) = earlier position(s) on later shot gather(s). (f) Corresponding time-distance diagram
where amplitude of reflection is plotted as function of time (i.e. shot number) and distance (i.e.
CMP number). Value of speed and its uncertainty shown in bottom right-hand corner are indicated
at location marked by letter (f) on panel (a); pair of black arrows = measured slope representing
speed of reflection; black half-arrow = speed of vessel (i.e. ∼2.5 m s−1). (g–j) Equivalent set of
panels for location indicated by letter (j) on panel (a). (k–n) Equivalent set of panels for location
indicated by letter (n) on panel (a).
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 84
validity of this approach is confirmed by examining sets of shot gathers that have been corrected
for normal move-out which show individual mappable reflections moving horizontally and vertically
with speeds of fractions of a metre per second (e.g. Figure 3.12c-e). Horizontal speed as a function
of depth for profile L52 is shown on Figure 3.12b where the average value within the Upper Cir-
cumpolar Deep Water (UCDW) layer is 0.07± 0.04 m s−1 southward. Higher values are observed
in the upper 50 m and the rapid decrease in speed with depth is attributable to the presence of an
Ekman spiral structure.
Although this method only measures the speed of internal waves, it is probably a reasonable
representation of the mean flow when values are averaged along the length of the profile. The
result show an average value of 0.07±0.04 m s−1 which is within the uncertainty of observations of
onshore advection (Moffat et al., 2009; Martinson & McKee, 2012; St-Laurent et al., 2013). Thus
horizontal speeds measured along Profile 52 are consistent with, if not slightly greater than, observed
shelfward transportation rates of O(10−2) m s−1 from Marguerite Trough. It is reasonable to infer
that the heat transported by these eddies makes a significant contribution to ice mass loss along
the shelf. It is possible to conclude that a combination of hydrographic observations, numerical
modelling, as well as the position of the seismically observed eddies with respect to the SACCF
can be used to infer southward transport of the eddy field.
3.7 Discussion
3.7.1 On-shelf transport of warm-water
Seismic reflection images are presented that reveal the detailed geometry of an energetic sub-
mesoscale and small mesoscale eddy field from the Bellingshausen Sea of the Southern Ocean.
Transects calibrated by coeval hydrographic measurements suggest that on-shelf transport of warm
water is occurring within bathymetric troughs along the shelf edge of the West Antarctic Penin-
sula. The longest transect crosses the continental slope seaward of Belgica Trough and images
up to 22 eddies with typical lengths and thicknesses of 0.75–11.00 km and 100–150 m, respec-
tively. The number, size and temperature anomalies of these observed structures suggest that
such sub-mesoscale eddies are indeed a significant contributor to warm-water transport within this
trough. However, it is important to emphasize that these two-dimensional seismic images represent
essentially instantaneous two-dimensional ‘snapshots’ of the water column.
Warm-Water Transport across West Antarctic Shelf 85
These seismic observations are broadly consistent both with physical oceanographic measurements
and with the results of numerical modeling. For example, Martinson & McKee (2012) used thermis-
tor moorings to demonstrate that eddy-like intrusive structures occur within Marguerite Trough
during 2007, 2008 and 2010. These structures have mean diameters of 8.2 ± 1.0, 9.9 ± 1.4 and
10.2± 0.9 km, respectively. Moffat et al. (2009) used discrete temperature and current metre mea-
surements to infer the existence of two similar features at the same location. These features had
horizontal length scales of 4.2± 2.5 and 4.3± 3.5 km. Couto et al. (2017) used glider deployments
within Marguerite Trough and within a trough located further east. They observed 34–40 subsur-
face eddies which had widths of O(10) km. These eddies passed the mooring location over a period
of a year, implying an eddy intrusion frequency of up to 3 per month. Both studies suggest that
these eddies are several hundred metres thick.
Here, previously reported eddy dimensions are corroborated and refined using seismic observations.
For example, the single eddy on Profile 61 is 10.40 ± 0.06 km long and 250 ± 10 m high (Figure
3.9a). In general, seismic imaging enables the aspect ratios of these structures to be measured with
greater certainty, which better constrains the geometry of intrusive events. Calculated temperature
distributions for these seismic profiles suggest that the observed eddies have warm-water cores
(e.g. Figure 3.8c). This inference is corroborated by a limited number of coeval hydrographic
observations which suggest that this adapted iterative procedure for determining temperature can
reliably recover at least long wavelength temperature structure from seismic reflection imagery.
This adapted approach is less reliable at recovering shorter wavelength temperature structure of
O(10) m— a limitation that is primarily a function of low signal-to-noise ratios in sometimes adverse
sea-surface conditions.
Since these warm-core eddies advect toward the shelf and remain at the same depth, it is possible
to assume that these features are neutrally buoyant (i.e. average eddy density is equal to that of
the surrounding fluid). As seismic reflections are primarily caused by temperature variations in
the water column, these lenses record the temperature contrast between the eddy and surrounding
water. Under the additional assumption that these eddies are neutrally buoyant it may be possible
to extract constraints on the salinity difference between the eddy and surrounding water. The
positive temperature anomalies of these eddies acts to reduce their density. Under the assumption
of neutral buoyancy and based on the T–S relationship across the west Antarctic Peninsula (Fig-
ure 3.2b), the warm-core of these eddies implies that they have a corresponding positive salinity
anomaly (i.e. increases density thereby maintaining neutral buoyancy). Identifying the salinity
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 86
change may lead to identification of the source water mass and therefore inform discussions of
the formation mechanisms of these lenses. This additional constraint may not be true in general,
however for special cases these arguments should apply and would be an interesting refinement of
this inversion process.
Scaling arguments can be used to inform these seismic observations. The Rossby radius of defor-
mation, LR, is the horizontal length scale at which rotation effects become significant and is given
by
LR =
Nh
npi|f | , (3.3)
where N is buoyancy frequency, h is the characteristic height and n=1, 2... represents the nth
baroclinic wave. The Coriolis parameter, f , is given by
f = 2Ωsinψ, (3.4)
where Ω is the rotation rate of Earth and ψ is latitude. Here, f ≈ −1 × 10−4 s−1 for ψ = 65 ◦S
and N = 0.0075 s−1. If h = 100 m, LR ≈ 2 km which is consistent with the horizontal length scale
of the seismically imaged eddies.
LR is combined with the Rossby Number, Ro, to determine a characteristic eddy velocity, U , as
Ro = U/(LRf). Ro is a dimensionless number that describes the ratio of inertial forces. It also
provides a scaling for the relative vorticity of the flow compared with rotation, which is determined
by the Coriolis parameter. When |Ro| << 1, flow is in geostrophic balance. In the oceanic realm,
it is reasonable to assume that |Ro| is of order unity, particularly for sub-mesoscale eddies (Gill,
1980). Thus by setting |Ro| = 1 and LR = 2 km, the assumption is that eddies are in the typical
sub-mesocale regime which yields U ≈ 2 × 10−1 m s−1. This assumption if corroborated by the
size of the eddies that are observed, i.e. O(1–10) km (Figure 3.3). Note that this velocity scaling
is associated with eddy itself and it may differ from the translational (i.e. on-shelf) eddy velocity.
However, it is largely consistent with, if somewhat higher than, observed shelfward transportation
rates of O(10−2) m s−1 at Marguerite Trough (Moffat et al., 2009; Martinson & McKee, 2012; St-
Laurent et al., 2013). More convincingly, this estimate of the characteristic translational velocity
is consistent with the measured speeds of reflections along Profile 52 that indicate an average
southward (i.e. shelfward) propagation of 0.07 ± 0.04 m s−1 within the UCDW layer. Therefore
providing confidence that this value is a reasonable estimate of the characteristic translational
velocity of these eddies as well as an estimate of the eddy velocity used to gauge Ro.
Warm-Water Transport across West Antarctic Shelf 87
Eddies constitute a well-known mechanism of warm-water intrusion along the western shelf of the
West Antarctic Peninsula and within the Bellingshausen Sea. However, a number of studies have
suggested that their contribution may have been underestimated and it has been proposed that
they do, in fact, represent the dominant intrusive mechanism (Thompson et al., 2014; Stewart &
Thompson, 2015). Previously, eddy frequency, fe, has been estimated at 3–5 per month (Moffat
et al., 2009; Martinson & McKee, 2012; Couto et al., 2017). This value is primarily based upon
observations from Marguerite Trough and, as yet, no equivalent hydrographic measurements are
available for Belgica Trough. Qualitative assessment of the seismic profiles presented here suggest
that a significant number of eddies have been imaged within a period of several hours. This
observation qualitatively supports the view that eddies are the dominant intrusive mechanism.
These spatial observations are now used to constrain the likely frequency and duration of eddies.
Parameters used in the following scaling analysis are given in Table 3.2.
Table 3.2: Constants and variables used in scaling analysis
Symbol Description Unit
α Scaling constant -
K Vertical diffusivity m2 s−1
B Burger number -
C Eddy concentration -
η Perturbation from maximum water depth m
f Coriolis parameter s−1
fe Eddy intrusion frequency # per month
h Vertical length scale m
H Maximum water depth m
Ho Depth beyond topographic obstacle m
λ Decay rate s−1
L Horizontal length scale m
Lo Length of topographic obstacle m
LR Rossby radius m
n nth baroclinic wave -
N Buoyancy frequency s−1
Ω Rotation rate of Earth s−1
φ Latitude ◦S
Q Potential vorticity m−1 s−1
Ro Rossby number -
τ Decay time s
U Characteristic velocity m s−1
v Advection velocity m s−1
ζ Relative vorticity s−1
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 88
3.7.2 Frequency and Duration of Eddies
On Profile 52, a train of 22 anticyclonic eddies is imaged (Figure 3.13a,b). It is hypothesised
that the decay time of these eddies is larger than the observation time shown in Figure 3.13a. If
this hypothesis is true, eddies are expected to advect onto the shelf and therefore contribute to
warm-water transport which may increase basal ice-shelf melt rates. This hypothesis is tested by
comparing the observed concentration of eddies with modelled values.
It is straightforward to calculate eddy concentration, C, from seismic observations. Here, C is
estimated from the ratio of black to white pixels where black pixels represent eddies that have been
interpreted from the seismic section. C is calculated using moving windows that are 20 km wide
and incremented in 5 km steps. Different widths and increments do not significantly affect these
results. There is clearly an increase of C with distance across the rapidly shoaling shelf (Figure
3.13c).
The behaviour of C can be modelled using a partial differential equation which assumes that C
is a function of one spatial dimension, x, and time, t. This one-dimensional advection-diffusion
equation is given by
∂C
∂t
= −v∂C
∂x
− λC, (3.5)
where v is the velocity in the positive x direction at which C horizontally advects and λ determines
the decay rate. This equation assumes that the local rate of change of concentration balances
advection by the prevailing flow and decay caused by a range of processes. At steady state, Equation
(3.5) becomes
v
dC
dx
= −λC (3.6)
The solution to Equation (3.6) is given by C = C◦ exp(−x/τv) where τ = 1/λ is the characteristic
decay time. Using the cross-sectional area of Marguerite Trough, hydrographic observations suggest
that C◦ ≈ 0.03, v ≈ 0.1 m s−1 and τ ≈ 1 month (Moffat et al., 2009; Martinson & McKee, 2012;
St-Laurent et al., 2013). From Equation (3.6), these values suggest that C should decrease by
a factor of two along Profile 52. Equation (3.6) is a significant simplification however as a first-
order analysis it is possible to use this model to test the above hypothesis. Finally, an estimate
of concentration on the shelf may be informed by considering published estimates of eddy flux, f ,
and τ ,
f =
C ×A
τ
(3.7)
Warm-Water Transport across West Antarctic Shelf 89
where A is the area of the shelf given by A = 6× 107 m2. Rearranging Equation (3.7) for C, and
assuming τ ≈ 1 month and f ≈ 4 per month, C approaches 0 (Moffat et al., 2009; Martinson &
McKee, 2012; St-Laurent et al., 2013). This value suggests that eddies will decay completely before
reaching the shelf.
Modelled C does not agree with the values calculated from seismic observations (Figure 3.13c). It is
possible to conclude that previously observed frequency and longevity of eddies are underestimates,
that other fluid dynamical processes are playing a significant role (e.g. decay time is incorrect), or
that the flow is not in steady state.
Analysis of the eddies shown in Figure 3.13a suggests that their lengths, L, and thicknesses, h, are
changing with distance. A single eddy is observed at a range of 10 km. Elsewhere, eddies can be
divided into two regimes based upon their aspect ratios. Regime 1 occurs at a range of 40–100
km and comprises relatively tall and thin eddies. Regime 2 occurs at a range of 100–170 km and
comprises relatively short and wide eddies. The aspect ratio of each eddy, L/h, is plotted on Figure
3.13d. When equilibrium is achieved, the aspect ratio of an eddy should stabilize at a value given
by ∼N/f . Varying estimates of h and L coupled with gradual shoaling of the seabed suggests that
the relative vorticity of these eddies is changing as a consequence of conservation of the potential
vorticity, Q. Thus spin-up or spin-down of a given eddy is associated with either an increase or a
decrease of relative vorticity, ζ.
During spin-up, the shape of an eddy evolves from a pancake into an oblate spheroid of smaller
aspect ratio. ζ is estimated for each eddy using
ζ =
U
L
, (3.8)
where U is the characteristic velocity and L is the observed length of an eddy. Note that if the
relative vorticity, ∇×u, varies spatially then ζ could differ from U/L. In the southern hemisphere,
positive values of ζ correspond to anticyclonic eddies.
ζ necessarily contributes to the potential vorticity, Q, of individual eddies. Q describes the absolute
circulation of a fluid parcel. In the absence of dissipation, it is a materially conservative property
given by
Q =
f + ζ
H + η
, (3.9)
where f + ζ is absolute vorticity and H + η is water depth at a given distance (Rossby, 1936,
1938). As a first approximation, the shallow water definition for Q is used rather than the Ertel
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 90
Figure 3.13: (a) Interpretation of Profile 52 (see Figure 3.3a and b). Black blobs = identifiable
eddy structures; vertical dashed line = boundary between two portions of profile. (b) Red ellipses
= best-fitting ellipses to observed eddies; L = horizontal length of eddy; h = height of eddy; sloping
line = seabed; H = maximum water depth at left-hand end of profile; η = height perturbation
above maximum water depth; regimes 1–2 are referred to in text. (c) Solid circles = concentration
of eddies, C, as function of range calculated using pixel counting method; black line = concentration
as function of range calculated using Equation (3.6) with parameter values described in text. (d)
Black circles = aspect ratios (i.e. L/h) of eddies as function of range calculated using best-fitting
ellipses; black dashed line = N/f . (e) Black circles = potential vorticity, Q, for each eddy as
function of range calculated assuming U = 0.2 m s−1; black dashed line = constant value of Q used
in (f). (f) Black circles = characteristic velocity, U , for each eddy as function of range calculated
assuming Q = 1× 10−8 m−1 s−1; black dashed line = constant value of U used in (e).
Warm-Water Transport across West Antarctic Shelf 91
definition, which exploits the depth of a particular density layer (Ertel, 1942). Shallow water Q is
used because, to leading order, both the water depth and the depth to any individual layer exhibit
the same rate of reduction in the on-shelf direction.
This seismic interpretation suggests that L and h of the eddies changes as they propagate toward the
shelf. This observed change in aspect ratio implies that ζ varies across the profile; within Regime
1, where water depth starts to shoal, an increase in ζ occurs, which causes spin-up and make eddies
taller and thinner (Figure 3.13a). If ζ increases and water depth decreases, overshooting can occur.
Between Regimes 1 and 2, eddies adjust again by a decrease in ζ, which causes spin-down and makes
eddies shorter and fatter (Figure 3.13a). For an individual eddy, there are no measurements that
describe the spatial variation of its velocity and so the implications of two alternative assumptions
are considered: conservation of U and conservation of Q (i.e. varying U).
Constant U
U ∼ 2× 10−1 m s−1 is selected, which is a representative value that is consistent with independent
estimates (Moffat et al., 2009; Martinson & McKee, 2012; St-Laurent et al., 2013). ζ adjusts
according to the changing aspect ratio of eddies along the profile and is calculated based on the
observed L or each eddy and constant U (Equation 3.8). As eddies become flatter, aspect ratio
increases and ζ decreases, which suggest that eddies are spinning down toward the shelf. Given the
oscillatory nature of both aspect ratio and ζ, it is hypothesised that, far from the shelf edge, eddies
are generated out of geostrophic balance. Subsequently, these eddies attempt to equilibrate toward
N/f as they advect shelfward (Figure 3.13d). In this way, an oscillatory pattern can develop that is
superimposed upon an overall trend of declining values of ζ, consistent with spin down. A constant
value of U implies a specific behavior for the shelfward variation of Q (Figure 3.13e). As a result of
the shoaling bathymetry, Q would be expected to increase from a value close to 1× 10−8m−1 s−1
within Regime 1 (Figure 3.14a).
By assuming dQ/dt ∼ U × dQ/dx, it is possible to construct an estimate of eddy lifetime. The
reciprocal of this rate suggests that eddies could last for tens of thousands of years. Although this
estimate is unrealistically large, it does imply that significant eddy decay cannot be inferred within
this particular reference frame.
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 92
Constant Q
A value of Q = 1× 10−8 m−1 s−1 is chosen for eddies within Regime 1 (Figure 3.13e). This value
corresponds to U ' 2 × 10−1 m s−1 (Figure 3.13f). For each eddy, the value of ζ is calculated
based on the observed values of H, η and constant values of Q and f . ζ is then used to calculate
U according to the changing aspect ratio (i.e. L) of eddies along the profile (Equation 3.8). In this
case, a possible mechanism for eddy formation is that eddies develop from a large-scale baroclinic
instability within the ACC and that they are close to geostrophic balance with small values of
Ro. As bathymetry shoals, a constant value of Q implies that ζ (and hence U) increases markedly
so that Ro tends to ∼ 1, which is consistent with these eddies being identified as sub-mesoscale
(Figure 3.14b). This view is also consistent with the trend of increasing values of Ro towards the
shelf edge which has been reported in numerical simulations (Stewart & Thompson, 2016). However,
the inferred values of U reach non-trivially large (and possibly unrealistic) values of O(1) m s−1
within Regime 2 (Figure 3.13f).
Dissipative processes are expected to cause some variation of Q. An estimate for frictional spin-
down is given by
τ =
h√
2K|f | , (3.10)
where h ∼ 100 m is the vertical scale of motion and K is the vertical diffusivity of an eddy (Pedlosky,
1987). Limited observational studies and numerical studies suggest that K is O(10−5) m2 s−1 and
O(10−4) m2 s−1, respectively (Smith & Klinck, 2002; Howard et al., 2004). This range of values
yields a τ of between 16 and 52 days, which implies that the observed eddies do not rapidly
diffuse away. Thus, under the assumption of either constant U or constant Q, the eddies are
adjusting toward a long-lived state and contributing to on-shelf transport of heat. This observation
is consistent with the existence of persistent intra-thermocline eddies that can have life spans of
several years (Ruddick & Hebert, 1988; Armi et al., 1989). It is possible to conclude that, while the
simplest spin-down mechanisms that cause eddy decay can be eliminated, the precise mechanism
of decay is beyond the scope of this study.
Eddy Frequency
These seismic images can be used to estimate eddy frequency, fe. It is assumed that the train
of eddies flows southward toward the shelf edge with a speed of v ≈ 0.07 m s−1 (Figure 3.12b).
In a given month, each eddy is expected to travel about 180 km. This estimate is comparable to
Warm-Water Transport across West Antarctic Shelf 93
Figure 3.14: Cartoon showing assumption of constant U and constant Q. Antarctic Circumpolar
Current (ACC) flows into the pae; ellipses = interpreted spin-up and spin-down of eddies along
profile; straight/curved arrows = direction and magnitude of U/Q. (a) Constant U ; Q increases
shelfwards. (b) Constant Q; U increases shelfwards.
that gauged from observations of long-lived intra-thermocline eddies (Armi et al., 1989). For eddy
lengths of 2–5 km, each of which are separated by one eddy length, these observations anticipate
that 19–46 eddies flow across the shelf per month (Figure 3.3). This estimate of fe is one order of
magnitude greater than that determined from sparse hydrographic observations. It is conceivable
that ‘piling up’ of eddies (i.e. slowing of on-shelf translation as bathymetry shoals) acts to reduce
the value of fe (Figure 3.13a).
It is possible to conclude that, within this region centred on Belgica Trough, eddies are both
numerous and long-lived. Simplified calculations suggest that the frequency of supply of intrusions
into this trough is much higher than for Marguerite Trough. It is proposed that each of these
troughs has experienced different frequencies of warm-water intrusion. It appears that Belgica
Trough is exposed to a significantly higher amount of warm-water transport by eddies and that the
effect of this transport on basal melting of ice shelves has been underestimated. Differences between
the two troughs may also reflect changes in the shelf-break jet, bathymetric variations, and local
surface forcing (Stewart & Thompson, 2015; Graham et al., 2016). Thus seismic imaging implies
that the poorly sampled Belgica Trough region is a significant location for on-shelf transport of
warm water.
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 94
Couto et al. (2017) use autonomous underwater vehicles to characterise the spatial distribution of
UCDW and construct a simple two-dimensional heat budget for the continental shelf of the West
Antarctic Peninsula. They argue that the heat supply from the ocean is dissipated by either melting
ice or heat loss to the atmosphere. In this way, the shelf ocean reaches a thermal equilibrium. Their
gliders encountered 33 eddies in 186 days (i.e. ∼5 eddies per month). The flux of eddies that has
been estimated here (i.e. 19–46 per month) is three times greater than this observation, implying
that the eddy heat flux to the shelf if similarly three times greater. Increased eddy heat flux will
either lead to enhanced ice melt or heat loss to the atmosphere. Couto et al. (2017) calculated a
total annual heat flux onto the shelf that is equivalent to 150-342 eddies per year, equivalent to
13–29 eddies per month. These eddies have an average temperature of 1.7◦C across a diameter of
12 km, similar to the temperature and seismic observations presented here. Based on their glider
observations, Couto et al. (2017) conclude that eddies may account for up to 50% of the onshore
heat flux, with the remainder likely to come from upwelling and advection of the ACC onto the
shelf. The match between the eddy frequency that is estimated here and the rate required for the
total annual heat flux that is estimated by Couto et al. (2017) implies that 100% of the onshore
heat flux may be provided by eddies. Understanding the rate at which heat contained in the ocean
is melting the ice is crucial to predicting how much ice will be lost in the warming climate.
3.7.3 Off-Shelf Structures
The three-dimensional perspective provided by orthogonal Profiles 55 and 57 combined with cal-
culated temperature distributions and coincident ADCP observations suggests the presence of a
discrete north-westward moving bowl of warm water (Figure 3.11). Together, these observations
imply that this structure is a warm-core eddy-like feature. The locus of the bowl over the Alexan-
der Island Drift suggests it may be a consequence of flow from the ACC interacting with local
bathymetry (Figure 3.1a).
Interaction between topographic or bathymetric obstacles and a rotating flow has been the subject of
investigation for over one hundred years (e.g. Taylor, 1923; Meredith et al., 2015). Different studies
show that a stagnant cylinder of fluid can develop above an obstacle within the path of rotating flow.
Subsequently, circulation can take the form of a set of vertical columns of fluid that lie outside the
stagnant region and move without changing their length (Taylor, 1923). Known as Taylor columns,
these phenomena are the result of flow interacting with an isolated obstacle. Due to the compressive
forces that act upon the water column at the upstream flank of an obstacle, a precursor to Taylor
Warm-Water Transport across West Antarctic Shelf 95
column development is formation of an anticyclonic eddy-like upwelling and a cyclonic eddy-like
downwelling (vice versa in the northern hemisphere). These eddy-like structures will rotate about
the obstacle and, under certain conditions, the cyclonic vortex is discharged downstream whilst
the anticyclonic vortex adheres to the top of the mound (i.e. Taylor column). McCartney (1976)
investigated the relevance of Taylor columns within the Southern Ocean, specifically in the context
of an eastward flow of ACC impinging upon a seamount or contourite drift. He found that this
interaction led to the generation of a warm-core anticyclonic eddy above the obstacle.
To assess the applicability of Taylor column dynamics to the observed off-shelf structure, a scaling
analysis was carried out, following Huppert (1975) and Meredith et al. (2015). The Burger Number,
B, relates the importance of local stratification compared with rotation so that
B =
NHo
|f |Lo , (3.11)
where N and f are the buoyancy frequency and the Coriolis parameter, respectively. Ho and Lo are
the depth beyond the obstacle and length of the obstacle. If N = 0.0075 s−1, f ≈ −1 × 10−4 s−1,
Ho = 4 km, Lo = 95 km, B ≈ 3.
An appropriate Rossby Number for the Alexander Island Drift is Ro = U/(Lof) = 2× 10−2. U ≈
0.2 m s−1 is obtained from instantaneous velocities determined from the vessel-mounted ADCP
(Figure 3.11e,f). Scaled obstacle height is ho = h/Ho where h is the height of the obstacle. For the
Alexander Island Drift, ho ≈ 0.25. For B ≈ 3, the critical height for formation of a stratified Taylor
column is ho/Ro ∼ 0.5–1.0 (Huppert, 1975). In this example, ho/Ro ≈ 14 which is one order of
magnitude greater than the critical height. This value indicates that the combination of rotation,
stratification and bathymetry at this locality is conducive to Taylor column formation.
The observed circulation does show characteristics of a Taylor column: seismic images exhibit
lens-shaped reflections typical of eddies that are several times the Rossby radius (Figure 3.11a,b);
ADCP velocities within the structure indicate a northwestward direction that is possibly the oblique
expression of anticyclonic motion; and the calculated temperature distribution suggests a warm
core, in agreement with downwelling of isotherms evident on coeval hydrographic measurements.
These observations are consistent with the characteristics of Taylor columns observed elsewhere in
the Southern Ocean (McCartney, 1976; Meredith et al., 2003, 2015).
Alternatively, this off-shelf structure is generated by a local excursion of the SACCF. Sea-surface
velocity measurements show that rotation occurred in the vicinity of this region about two weeks
K.L. Gunn, Ph.D. Dissertation
Warm-Water Transport across West Antarctic Shelf 96
before seismic acquisition (Figure 3.1b). However, the dimensions of this near-surface feature is
much greater than the size of the bowl and it would also have drifted too far eastward by the time
of seismic acquisition.
3.8 Conclusions
Calibrated seismic images of the water column from the Bellingshausen Sea of the Southern Ocean
are presented and analysed. The pattern of large-scale reflectivity is consistent across the entire
seismic survey and appears to be typical of that expected during the austral summer. First, a bright
and continuous reflection is observed at depths of 30–80 m that represents the boundary between
the Surface Mixed Layer and the Winter Water layer. Secondly, weaker and more discontinuous
reflections occur at depths of ∼100–300 m, representing the gradational transition from Antarctic
Surface Water to Circumpolar Deep Water. Thirdly, all of the seismic images are acoustically
transparent below depths of ∼500 m due to the homogeneity of Circumpolar Deep Water.
Seismic reflections from the water column contain useful information about the temperature and
salinity structure that can be extracted using an iterative procedure. Application of this procedure
is limited in the absence of in situ sound speed measurements that are required to provide a
long wavelength background model. Here, an adaptation is described and applied whereby long
wavelength sound speed information is extracted directly from the seismic observations. This
modified approach yields reliable background models of sound speed that obviate the need for
large amounts of coeval hydrographic observations. The resultant temperature distributions for
seismic images demonstrate that significant numbers of warm-water intrusions occur in the vicinity
of the Marguerite and Belgica Troughs on the shelf edge of the west Antarctic Peninsula and
Bellingshausen Sea.
The observed intrusive mechanisms are interpreted as small mesoscale to sub-mesoscale to eddies
with some evidence of filament structures. These seismic observations have been calibrated by a
set of coeval hydrographic observations that are consistent with previous oceanographic studies.
The density of eddies and the significantly higher estimate of intrusive frequency, combined with
hydrographic and seismic estimates of on-shelf advection, all suggest that warm-water transport
across the shelf has been significantly underestimated. A direct consequence of this underestimate
is the potential impact upon basal melting of ice shelves. A set of sloping reflections characteristic
of an oceanic front is interpreted as the Antarctic Slope Front. This interpretation positions the
Warm-Water Transport across West Antarctic Shelf 97
circumpolar influence within the Bellingshausen Sea further east than previously suggested. Finally,
a substantial warm-core anticyclonic circulation feature is observed above the Alexander Island
Drift, which appears to be characteristic of a stratified Taylor column. Scaling analysis suggests
that a combination of local bathymetry and circulation are conducive to the formation of this flow
feature.
K.L. Gunn, Ph.D. Dissertation

Chapter 4
Time-lapse Imaging of the Brazil-Falkland
Confluence
4.1 Introduction
Zonal (i.e. east-west) components of low latitude easterlies and mid-latitude westerlies induce
anticyclonic upper ocean circulation patterns known as subtropical gyres (Vallis, 2006). The South
Atlantic Gyre is composed of westward flowing trans-Atlantic South Equatorial Current in the
south, and eastward flowing South Atlantic Current in the north. The western (eastern) limb flows
southwards (northwards) along the continental shelf edge completing the circulation loop. At the
continental shelf of Cabo de Sao Roque, Brazil, the South Equatorial Current bifurcates: water
that flows north and south becomes the North Brazil and Brazil Currents, respectively (Stramma
et al., 1990; Podesta´ et al., 1991). The Brazil Current is the intensified western limb of the South
Atlantic Gyre. Western boundary currents are warm, deep, and narrow jets that are intensified
due to the zonal asymmetry of subtropical gyres. This westward shift of the gyre centre is caused
by the increase of Coriolis force with latitude, which results in a steeper pressure gradient on the
western side of ocean basins (Stommel, 1948). At 36–42 ◦S the Brazil Current meets the northern
component of the Antarctic Circumpolar Current retroflection branch, the Falkland (Malvinas)
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 100
Current (Figure 4.1a). The meeting of these two currents generates one of the most energetic
regions of the world’s ocean, the Brazil-Falkland Confluence (Olson et al., 1988; Gordon, 1989;
Peterson & Stramma, 1991).
The large-scale dynamics of the confluence and associated water masses are well known (Fig-
ure 4.1a). Conductivity-depth measurements collected every 15–50 km have revealed that waters
north of the confluence are generally warmer and saltier than water in the southern portion of this
ocean (Figure 4.1b,c; Piola & Matano, 2017). The markedly different characteristics of water in the
Brazil and Falkland Currents means that their meeting generates a frontal zone (Gordon, 1989).
A frontal zone is a region in which there are rapid, horizontal changes in physical properties of the
ocean (Cromwell & Reid, 1956). Spatial thermal gradients are typically O(0.1) ◦C km−1. A two-
dimensional plane exists in the frontal zone known as the frontal interface. Maximum changes in
spatial gradients occur along this plane (e.g. ≤10 ◦C km−1). The complex current and frontal sys-
tem generated at the Brazil-Falkland Confluence sweeps out across the southwest Atlantic Ocean
(Figure 4.1a). Frontal systems are generally associated with enhanced exchanges at the ocean-
atmosphere boundary and are believed to be regions of water mass transfer between the surface
mixed layer and stratified interior of the ocean (e.g. Spall, 1995; D’Asaro et al., 2011). Fronts
are often associated with strong vertical circulation (e.g. Palla`s-Sanz et al., 2010b; Nagai et al.,
2012). Since vertical transport brings nutrient rich water to the euphotic zone, fronts are often sites
of high biological productivity (Taylor & Ferrari, 2011; Tilstone et al., 2014). Consequently, the
southwest Atlantic Ocean is marked at all depths by circulation patterns and exchange processes
that are critically important to regional oceanographic, biological and carbon cycling systems. The
region has been described as the ‘cross-road of the world ocean circulation’ because it hosts water
formed in remote regions brought together by large-scale circulation (Piola & Matano, 2017).
At smaller scales, hydrographic surveys in the Argentine Basin have revealed a complex array
of eddies, rings and filaments (Gordon, 1989). At even smaller scales, vertical fine-structure of
temperature and salinity has been observed to increase toward the Brazil-Falkland Front (Provost
et al., 1996). Despite the ubiquitous nature of fronts, few measurements have both the coverage
and resolution to observe the extensive range of spatial and temporal scales that they occupy. For
example, the Confluence 3 cruise of 1990 acquired hydrographic information spaced every ∼22 km
across the Brazil-Falkland Confluence (Provost et al., 1996). At the other end of the observation
scale, a high resolution (∼100 m) survey of hydrographic measurements across the Kuroshio Front
has been performed (D’Asaro et al., 2011). These measurements spanned a grid of ∼10 km2 that
Time-lapse Imaging of the Brazil-Falkland Confluence 101
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K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 102
extended to 50 m depth. Furthermore, sub-mesoscale frontal effects are currently unaccounted for
in climate models since their inclusion incurs excessive computational costs (Callies et al., 2015).
For these reasons, little is known about cross-frontal movement of water that provides a connection
between subantarctic and subtropical waters, generation of eddies that diffuse heat and nutrients,
and coupling of the ocean and atmosphere which is intensified at fronts. Finally, it is well known
that the location of the Brazil-Falkland Confluence shifts on annual and semi-annual frequencies,
however, the effect of its passage on local and regional thermohaline structure is poorly understood
(Garzoli & Garraffo, 1989).
Seismic images of the water column are able to resolve vertical temperature gradients at resolutions
of O(10) m across two-dimensional profiles that traverse hundreds of kilometres and extend a few
kilometres beneath the seabed. For this reason, seismic oceanography studies are able to bridge
the observational gap introduced when investigating frontal dynamis using standard hydrographic
tools. In this chapter, a three-dimensional seismic survey acquired between December 2012 and
April 2013 is presented and analysed. The survey is 20 TB in size and contains 70 three-dimensional
swaths across the southwest Atlantic Ocean. 20 swaths have been carefully selected with a view to
investigating the spatial and temporal nature of the Brazil-Falkland Confluence. The principal goal
is to demonstrate that seismic surveying can be used to constrain the mesoscale to sub-mesoscale
nature of a front at high resolution. In this way, our understanding of frontal dynamics and its
effect on the surrounding water masses can be improved. First, the nature of the problem is out-
lined by describing regional water mass structure at the confluence. Secondly, specific acquisition,
processing and calibration techniques that have been developed for this seismic reflection survey
are outlined. A complete discussion of these techniques is given in Chapter 2. Thirdly, thermoha-
line structure revealed by the selected seismic swaths is described. Seismic images are converted
into temperature and salinity distributions from which potential density, buoyancy frequency and
geostrophic currents are calculated. These distributions are used to quantify the properties of this
frontal system. Fourthly, pre-stack seismic records are used to measure the speed of internal waves
which can be used to constrain large-scale current flow. Finally, these observations are compared
with theoretical and numerical models to isolate the dynamics of this confluence.
Time-lapse Imaging of the Brazil-Falkland Confluence 103
4.2 Oceanographic Setting
Figure 4.1a shows the pattern of sea-surface temperature across the southwest Atlantic Ocean. In
this region, sea-surface temperature is a useful proxy to highlight the location of the confluence
(Saraceno et al., 2004). Between ∼9 ◦S and ∼38 ◦S, the Brazil Current transports warm subtropical
water, >26◦C at the surface, southward along the eastern edge of South America. The current
core is generally confined to the ∼1000 m isobath (Peterson & Stramma, 1991). The Falkland
Current transports cold, <7 ◦C at the surface, and relatively fresh sub-Antarctic water northwards.
This intense, narrow current is strongly steered by bottom topography along the South American
continental slope; a shoreward branch continues moving northwards along the continental shelf
edge; the offshore branch retroflects cyclonically back upon itself at ∼38 ◦S. The return flow follows
the 2000 m isobath until turning eastward at 49◦W forming the Subantarctic Front (Figure 4.1a;
Saraceno et al., 2004). At the confluence, the Brazil Current departs from the continental shelf and
splits into two branches; one branch turns northwards forming a recirculation cell, with a meander
amplitude of 100–300 km (Gordon, 1989); the second branch is deflected southeast away from R´ıo
de la Plata, and is known as the Brazil Current Overshoot (Figure 4.1a). The overshoot returns
to the northeast at about 45 ◦S and becomes the South Atlantic Current (Figure 4.1a; Peterson &
Stramma, 1991; Saraceno et al., 2004).
Figure 4.1b and c highlight the different vertical temperature structures of the Brazil and Falkland
Currents. These cross-sections of temperature are interpolated from hydrographic casts collected
along World Ocean Circulation Experiment (WOCE) transects A10 collected during austral winter
1992 and transect A11 acquired during austral winter 2002, respectively (Figure 4.1). Horizontally
averaged profiles of temperature, salinity, sound speed, in situ density and buoyancy frequency
are calculated across each WOCE transect and are shown in Figure 4.2. Average profiles for A10
and A11 are coloured by light and dark grey circles and are used to typify unmodified water
mass structure of the Brazil and Falkland Currents, respectively. During seismic surveying, 7
hydrographic casts were deployed in the confluence zone that were acquired within four months of
the seismic images presented here (Table 4.1). Temperature, salinity, sound speed, in situ density
and buoyancy frequency are calculated for each cast and are coloured by depth (Figure 4.2). These
near-coeval measurements show vertical structure that is characteristic of the Brazil, Falkland
and Confluence zone water mass properties depending upon the date and location of acquisition
(Bianchi et al., 1993).
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 104
Table 4.1: Near-coeval hydrographic measurements acquired during seismic surveying. Locations
shown in Figure 4.3c.
Name Date, dd/mm/yy Time, hh:mm Latitude, ◦S Longitude, ◦W
T1 15/11/12 12:30 53.36 36.86
T2 28/11/12 09:00 53.08 36.43
T3 4/12/12 14:00 53.40 36.72
T4 12/12/12 13:00 53.02 36.43
T5 20/12/12 19:00 53.32 36.60
T6 29/12/12 13:30 52.97 36.36
T7 9/1/13 17:50 53.04 36.66
In this region, the Brazil Current extends to approximately 2000 m depth (Piola & Matano, 2017).
Tropical Water (TW) lies in the upper ∼70–100 m of the water column, and is characterised
by high potential temperature and salinity, S > 36 psu (Figure 4.1b and 4.2a,b). A thin, fresh
layer caps TW, caused by mixing with adjacent shelf and river waters. The thermocline and
halocline lie beneath TW, where temperature decreases from 20 to 10◦C across several hundred
metres, and defines South Atlantic Central Water in this region (SACW; Figure 4.1b and 4.2a,b).
SACW has a stable T -S pattern with only minor variations induced by winter sea-air interactions
near the southern limit of the Brazil Current (36–42 ◦S; Figure 4.2c; Piola & Matano, 2017). At
intermediate depths, 700–1000 m, the Brazil Current transports old Antarctic Intermediate Water
(AAIW). Here, AAIW originates from deep water convection along the sub-Antarctic zone and
anticyclonic recirculation into the Argentine Basin. This recirculated AAIW is characterised by a
salinity minimum of S < 34.3 psu (Figure 4.2b). Below the Brazil Current, North Atlantic Deep
Water (NADW) flows poleward and is the primary source of well-ventilated waters beneath the
thermocline. At ∼30 ◦S, NADW has relatively high temperature and salinity (Figure 4.2a,b; ∼3◦C
and ∼ 38 psu). These strong vertical variations in physical properties are reflected in the sound
speed profiles of the water masses (Figure 4.2d). Coloured salinity profiles are offset by up to
0.5 psu at depths over 1000 m. These salinity values have been calculated from measurements of
conductivity acquired during seismic surveying (Table 4.1). The offset is probably caused by poor
calibration of the instrument prior to sailing. Nevertheless, temperature measurements across all
hydrographic casts are consistent.
The upper few hundred metres of the Falkland Current is formed of Sub-Antarctic Water (SAAW),
which is substantially colder and fresher than SACW, with T < 15◦C and S < 34.2 psu (Figure
4.1c and 4.2a). At intermediate depths, the current carries newly formed AAIW equatorward into
the Argentine Basin. Below 800–1000 m, Circumpolar Deep Water (CDW) flows northward with
the Falkland Current. Here, the maximum depth of the Falkland Current is defined as the bottom
Time-lapse Imaging of the Brazil-Falkland Confluence 105
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 106
Figure 4.2 (previous page): Physical oceanographic properties of southwest Atlantic Ocean.
Potential temperature, T , salinity, S, sound speed, v, in situ density, ρ, and buoyancy frequency,
N , as function of depth, z. (a) T -z. (b) S-z. (c) S-T . (d) v-z. (e) ρ-z. (f) N2-z. N calculated from
T and S measurements pre-smoothed using 200 m-long Gaussian filter. Coloured circles = measure-
ments from 7 near-coeval hydrographic casts acquired during seismic surveying coloured by depth
according to scale on right; light/dark grey circles = average measurements across WOCE transect
A10/A11; dotted line = approximate water mass depth. Labelled water masses as in Figure 4.1
of Upper-CDW, approximately 1500–2000 m. Due to mixing along the equatorward path, CDW
now has a lower salinity than NADW (Figure 4.2b). Consequently, when NADW joins the return
flow of the Falkland Current at the confluence, it splits Upper-CDW (UCDW) and Lower-CDW
(LCDW). LCDW is the densest water entering the basin and flows along the continental slope at
3000–3550 m depth (Piola & Matano, 2017). Since this study does not extend to depths greater
than ∼3000 m it is unlikely that LCDW plays a role in the observation here (Figure 4.2).
The confluence itself is marked by sharp sea-surface temperature gradients of O(1) ◦C km−1 (Figure
4.1a). The band of intermediate temperature water in the confluence zone is reported to reach up
to 300 km width (Olson et al., 1988; Gordon, 1989). It extends from the confluence origin eastward,
encompassing the region between the SAC and SAF, and can be traced as a coherent strip far into
the Atlantic Ocean interior (Figure 4.1a). Although having different T and S values, the confluent
water masses occupy the same density range and so mixing results in alternate layers of subtropical
and sub-Antarctic waters, causing distinct interleaving and fine-structure. This mixing is apparent
in the vertical structure of physical properties shown in Figure 4.2, which reveals that measure-
ments from the confluence zone fall in-between horizontally averaged profiles from WOCE transects
A10 and A11 (Figure 4.2; coloured points). Light and dark grey profiles typify the Falkland and
Brazil Currents, respectively, however, coloured points from measurements within the confluence
zone show interleaving of different water masses (Figure 4.2a). The meeting of these two currents
spawns an intense eddy field composed of both warm and cold eddies either side of the intersec-
tion. These features can have anomalous temperature of over 10◦C, and occur over timescales of
∼2 months. Warm-core rings are frequently entrained into the south Atlantic gyre, and therefore
represent an important component of meridional heat and salt transfer. Similar entrainment is
observed from cold-core eddies flowing northwards into the Brazil Recirculation Cell. The latitude
of the confluence, 36–42 ◦S, is variable on annual and semi-annual scales. In general, the con-
fluence is farther north and east during austral winter (July–September), presumably in relation
to general seasonal shifts of wind systems and seasonal meridional shifts of the subtropical gyre
(Olson et al., 1988; Peterson & Stramma, 1991). Mean conditions of circulation vary significantly,
Time-lapse Imaging of the Brazil-Falkland Confluence 107
and more recent evidence shows that the annual shifts in the confluence position is likely related
to meteorological anomalies (Assireu et al., 2003). Within a period of approximately one month,
the confluence oscillates around its mean position and the velocity of displacement can vary from
10–50 km day−1, with mean velocities of 10 km day−1 (Garzoli & Garraffo, 1989).
4.3 Seismic Acquisition and Processing
The seismic reflection survey was acquired between November 2012 and April 2013 onboard the
Amani and operated by Polarcus. This survey used a standard three-dimensional ‘racetrack’ acqui-
sition pattern, whereby seismic data are acquired over many parallel lines with the same azimuth
(Figure 4.3a). Once data have been acquired for a single line, the vessel will begin turning onto a
parallel sail-line a set perpendicular distance away. In this way, subsequent lines are acquired in
the opposite direction and create a racetrack-like loop . Each complete loop is displaced laterally
from the preceding loop until the entire area has been covered. Here, the resultant profiles are
parallel to the coastline (041). The survey traversed the continental slope 220 km west of the R´ıo
de La Plata estuary, where maximum water depth is ∼3000 m (Figure 4.3b).
The acoustic source comprised a pair of airgun arrays, each of which had 36 guns with a combined
volume of 70 L (i.e. 4240 in3). These guns were primed with an air pressure of 14 MPa (i.e.
2000 psi) and fired every 10 s or ∼25 m. Reflected acoustic waves were recorded along 10 streamers
of 6 km length separated by 125 m, towed at a depth of 9 m. Each streamer had 480 groups of
hydrophones spaced every 12.5 m. The record sampling interval was 2 ms. The vessel steamed
with an average survey azimuth of 041 in a racetrack pattern at 2.5 m s−1, yielding a nominal fold
of cover of 120. Each pass of the vessel acquired a swath of data of ∼600 m width and ∼147 km
length (Figure 4.3). Continuous loops were made, except in the case of failed acquisition. In this
case, the line was re-shot. Seismic processing techniques, that are adapted from those used to build
seismic images of the solid Earth, have been applied (Chapter 2).
4.4 Seismic Images
Due to the racetrack pattern of seismic surveying, profiles are acquired at interleaving times and
locations (Figure 4.3a). During each sail-line of the seismic survey, a three-dimensional swath of
oceanic acoustic information is collected using 10 streamers and two airgun arrays (Figure 4.3b).
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 108
Figure 4.3: Three-dimensional seismic survey configuration and setting. (a) Cartoon showing
racetrack acquisition of three-dimensional seismic data. Black dashed lines = path of seismic
vessel; thick coloured lines = three-dimensional swath of ocean collected during each pass coloured
by time of acquisition; arrows = direction of acquisition; thick black box = zoomed portion of swath
shown in (b). (b) Zoomed portion of single swath acquired as vessel steams NE which shows that
10 vertical cross-sections are simultaneously acquired. Black arrows indicate vertical cross-sections
shown in Figure 4.4. (c) Bathymetric map of seismic survey region. Grey shading = seafloor
dip; labelled black lines = Set A–E seismic reflection profiles labelled as in Table 4.2; thin black
arrows = direction of acquisition; labelled circles = location of near-coeval hydrographic data
acquired during seismic surveying labelled as in Table 4.1; red circles = near-coeval hydrographic
profiles used to calculate east-west geostrophic current.
This acquisition configuration acquires a three-dimensional swath of data that is approximately
140–150 km in length, 600 m in width and 4.5 km deep. Each swath is evenly gridded so that
seismic traces are correctly located. The along-swath direction is orientated approximately NE–
SW with an azimuth of 041. The cross-swath direction is perpendicular with an azimuth of 131.
The nominal spacing between traces along these two orientations is 6.25 and 31.25 m, respectively.
20 seismic profiles are presented, discussed and analysed. Each profile is a vertical slice extracted
from the central portion of a three-dimensional swath except where otherwise stated. The swaths
were acquired between 1st February and 28th April 2013 and demonstrate the spatial and temporal
variability of the confluence region (Table 4.2). These 20 seismic images have been split into five
sets of four profiles labelled A–E based on their location and time of acquisition (Table 4.2 and
Figure 4.3b). Set A–D contain profiles that are grouped spatially and were collected at interleaving
times. Set E is a selection of four seismic profiles acquired before and after Set A and B.
Time-lapse Imaging of the Brazil-Falkland Confluence 109
Table 4.2: Seismic reflection profile acquisition information.
Set Label Length, km Date, dd/mm/yy Max. water depth, m Acquisition direction
A
1 142 11/02/2013 2500 SW–NE
2 142 13/02/2013 2500 SW–NE
3 141 14/02/2013 2500 SW–NE
4 140 17/02/2013 2500 SW–NE
B
5 148 11/02/2013 2800 NE–SW
6 149 12/02/2013 2800 NE–SW
7 150 14/02/2013 2800 NE–SW
8 150 16/02/2013 2800 NE–SW
C
9 145 22/04/2013 3000 NE–SW
10 148 24/04/2013 3000 NE–SW
11 150 26/04/2013 3000 NE–SW
12 152 28/04/2013 3000 NE–SW
D
13 145 21/04/2013 3100 SW–NE
14 148 23/04/2013 3100 SW–NE
15 150 25/04/2013 3100 SW–NE
16 152 27/04/2013 3100 SW–NE
E
17 126 01/02/2013 2300 SW–NE
18 147 31/01/2013 2300 NE–SW
19 139 15/03/2013 2800 NE–SW
20 146 18/03/2013 2800 SW–NE
4.4.1 Patterns of Reflectivity
Figure 4.4a–c shows three profiles extracted from the western, central and eastern portion of Pro-
file 2. These profiles were acquired simultaneously and are separated by ∼190 m in the cross-swath
direction. These seismic images reveal complex reflectivity patterns across all depths. A spec-
tacular set of northward dipping (<2 ◦), high amplitude and continuous reflections are observed.
These dipping reflections outcrop at the sea-surface and extend to ∼1800 m depth. Reflectivity to
the south of the bright dipping reflections is shorter and more discontinuous than on the northern
side, suggesting that these seismic profiles image two distinct regions of thermohaline structure.
Dipping reflectivity is interpreted as a frontal interface separating a wedge of northern water from
southern water. Rapid changes in physical properties, that occur close to a front, will manifest in
seismic profiles as bright reflections. Furthermore, the frontal interface (along which the strongest
gradients occur) is clearly identifiable as the bright dipping reflections. Dipping reflectivity is typ-
ical of oceanographic fronts seen in seismic section (e.g. Holbrook et al., 2003). At this confluence
zone warm Brazil Current flows south to meet the cold northward flowing Falkland Current. In
the upper 1000 m of the water column the Brazil Current is O(1) kg m−3 lighter than the Falkland
Current (Figure 4.2c,e). The lighter Brazil Current forms a wedge over its heavier counterpart,
which creates a sloping boundary between the water masses. This boundary manifests as bright
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 110
Time-lapse Imaging of the Brazil-Falkland Confluence 111
Figure 4.4 (previous page): Intersecting perpendicular seismic images from Profile 2 showing
three-dimensional thermohaline structure (see Figure 4.3c for location). Red/blue stripes corre-
spond to positive/negative acoustic impedance contrasts caused by temperature and/or salinity
variations within water column. (a–c) Along-swath profiles from western, central, and eastern por-
tion of three-dimensional swath (Figure 4.3b; black arrows). Along-swath profile azimuth 041. Sep-
aration between each cross-section 0.19 km in cross-swath direction (i.e. 131). Dashed lines = loci
of cross-swath profiles shown in (d-f); labelled boxes = zoomed portions of profile shown in Figure
4.5. (d–f) Cross-swath profiles. Six cross-sections sample deep eddy imaged at 40–80 km range
in along-swath profiles shown in (a–c). Cross-swath profile azimuth 131. Separation between each
cross-section 6.25 km in along-swath direction (i.e. 041). Open circles = location of reflectivity
patterns present in both along- and cross-swath orientations.
dipping reflections observed in each seismic profile. The interface reaches 1800 m depth indicating
that these two currents are separated across almost the entire length of the water column. This
observation combined with the location of this seismic survey implies that the boundary imaged
here is a major density front within the Brazil-Falkland Confluence (Figure 4.1a).
Simultaneously collected profiles reveal that across a distance of 380 m the front is highly consis-
tent suggesting that thermohaline structure varies little in the cross-swath direction (Figure 4.4a–c).
This inference is tested using six simultaneously acquired cross-swath profiles (Figure 4.4d–i). These
profiles are extracted from the three-dimensional swath at an azimuth of 131. Each profile is sep-
arated by 6.25 km along-swath (Figure 4.4a–c). Horizontal reflections are clear in all cross-swath
profiles and correspond to dipping reflectivity observed in the along-swath images. These horizontal
reflections extend across the entire width of the cross section, implying that thermohaline struc-
ture varies little in the NW–SE direction. However, between each cross-swath image, the depth of
reflectivity changes by hundreds of metres indicating that thermohaline structure is significantly
more variable in the along-swath direction (Figure 4.4d–i). Since there is no apparent change in the
amplitude or slope of NW–SE orientated reflections, it is reasonable to assume that the NW–SE
thermohaline structure is consistent across greater distances than imaged here. The inference that
the front is fairly isotropic in the NW–SE direction is consistent with three-dimensional hydro-
graphic observations of a shallow front in the California Current system which reveal small changes
in cross-front properties between profiles spaced approximately 20–50 km apart (Palla`s-Sanz et al.,
2010a).
Two distinct zones of reflectivity are observed on either side of the front. On the dense side of the
front (i.e. 0–40 km range) reflectivity is short and disrupted at all depths (Figure 4.5i). On this
side of the front, numerous, bright reflections are observed in the upper 400 m of the water column.
A ∼1 km thick acoustically blank patch of water is observed directly beneath this layer. Deeper
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 112
Figure 4.5: Zoomed portions of central cross-section from Profile 2. Zooms from Figure 4.4b.
(i) Disrupted reflections from southwest portion of profile. (ii) Horizontally continuous reflections
from northeast portion of profile. (iii) Bright reflections from frontal interface observed between
100 and 500 m depth. (iv) Bright reflections from frontal interface observed between 1400 and
1800 m depth. (v) Large, deep eddy observed on dense side of frontal interface.
Time-lapse Imaging of the Brazil-Falkland Confluence 113
than 1400 m, water is characterised by bright and discontinuous reflectivity. Several lens-shaped
patches of water are observed (e.g. Figure 4.4a; 40–50 km range, 1600-1800 m depth). The depth
of these layers is consistent with the vertical structure of the Falkland Current (Figure 4.1c). The
upper layer is interpreted as SAAW, followed by AAIW and finally CDW at depths >1400 m.
On the light side of the front (i.e. 40–139 km range) reflectivity is generally flat and continuous
(Figure 4.5ii). There appears to be a distinct separation between surface (0–800 m), intermediate
(800–1600 m), and deep water (≥1600 m). This separation is controlled by the frontal interface
which splits into 2–5 branches at 300–750 m depth. These bright strands are laterally coherent
and extend toward the north creating acoustically blank slabs between 800 and 1600 m depth, that
reach a thickness of 750 m at the NE edge of the profile. The depth of these layers is similar to
the vertical extent of SACW and AAIW of ∼700 m and ∼1800 m, respectively (Figure 4.1b). The
upper layer of the water column (0–800 m) is interpreted as TW and SACW. Between 800 and
1600 m lies AAIW. The horizontal reflectivity that is observed at 2000 m depth between 90 and
139 km range likely represents the upper boundary of NADW. Internal waves on the dense and light
side of the front have wavelengths of O(1) km and of O(10) km, respectively (Figure 4.5i,ii). The
horizontally continuous reflections observed on the light side of the front suggests that the water
here is highly stratified and therefore quiescent relative to the disrupted reflectivity on the dense
side of the front. The frontal interface clearly delineates these two zones of reflectivity (Figure 4.5).
At ∼200 m depth the frontal interface splits before outcropping at the sea-surface (Figure 4.5iii).
A similar split is observed at ∼1500 m depth. At this depth, the front bifurcates and continues to
dip toward the north (Figure 4.5iv).
Perhaps most striking is a small mesoscale double-convex (i.e. lens-shaped) set of reflectivity (Figure
4.5v). Horizontal length and thickness is approximately 40 km and 500 m, respectively. This classic
lens-shape is characterised by curved reflections which wrap around acoustically transparent centres
and suggests that this structure is an eddy (e.g. Biescas et al., 2008). The eddy appears to be
tilted parallel with the frontal interface (∼0.5◦) and lies on the dense side of the front. The acoustic
centre appears to be a composite of one large lens (55–65 km range) and up to 8 smaller lenses that
lie at the corners (e.g. 46–51 km range, 750–920 m depth). Reflections directly above and below
the eddy are long and continuous suggesting that stratification is high here. This may be caused
by isopycnals compressing due to the curved upper and lower boundaries of the lens. Disrupted
internal waves and fainter reflections are observed at the corners of the lens, implying that mixing
is high here. Cross-front profiles that image the eddy reveal horizontal reflections that bound the
upper and lower boundary of the lens (Figure 4.4d–i). The cross-front profiles from Profile 2 do not
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 114
Figure 4.6: 7 synthetic seismograms generated from hydrographic casts and projected onto Profile
2. Derivitive quantities calculated as a function of depth from TSDip 7 data acquired during seismic
surveying (Table 4.1). (a) dT/dz. (b) dS/dz. (c) dv/dz. (d) dρ/dz. (e) Synthetic seismogram. (f)
Numbered synthetic seismograms projected onto Profile 2 (see Figure 4.3 for location).
show curved reflections that would indicate the eddy edge has been imaged. Rather the thickness
of the acoustically blank lens remains constant. This eddy is particularly deep with its core at
∼800 m.
Qualitatively, there is a strong coherence of seismic imagery and hydrographic data. To first order,
numerous bright reflections are observed in the upper ∼1000 m of the water column. Hydrographic
measurements reveal that sharp contrasts of up to 5◦C and 1 psu on vertical length scales of 100 m
are common in the upper ∼1000 m (Figure 4.2). Such contrasts are expected to give rise to clearly
visible seismic reflections. Temperature and salinity profiles are collected for each near-coeval pro-
file and are used to calibrate the reflectivity revealed by these images. The vertical gradient of
temperature and salinity reveals changes of O(0.1) in the upper ∼1000 m of the water column
(Figure 4.6a,b). Vertical temperature gradient reveals variations as high as 0.2 ◦C m−1 near the
surface. Profiles of temperature and salinity have been converted into sound speed and density
Time-lapse Imaging of the Brazil-Falkland Confluence 115
using the Gibbs Sea Water Toolbox (McDougall & Barker, 2011). The vertical gradients of sound
speed and density reveal a similar pattern to temperature and salinity, as expected (Figure 4.6c,d).
Notably, vertical gradients of salinity and density are close to zero whilst temperature and sound
speed gradients often exceed a magnitude of 0.1. The product of sound speed and density provides
a profile of impedance. At this stage it is possible to calculate reflection coefficients as a function
of time, R(t), using Equation (2.6). Since recorded seismic amplitudes are primarily a convolution
of R(t) with the source response, these reflection coefficient have been convolved with a 40 Hz
Ricker wavelet producing a synthetic seismic trace (i.e. seismogram; Figure 4.6e). The choice of
Ricker frequency does not significantly effect calculated seismograms. Synthetic seismograms were
computed for 7 hydrographic casts that were acquired during seismic surveying (Table 4.1 and
Figure 4.3c). Seismograms have been projected onto Profile 2 (Figure 4.6f). Seismograms 1 and
3 show high amplitude reflections in the upper part of the seismogram that are consistent with a
∼400 m thick band of reflectivity that lies below the sea-surface. On the light side of the front, the
maximum depth of bright reflectivity deepens toward the north. This pattern correlates well with
high amplitudes that extend to greater depths moving northwards (Figure 4.6f; seismograms 2, 4
and 6). Seismograms 5 and 7 reveal high amplitude reflections to depths of 1300 m. Since these
seismograms have been calculated from hydrographic data that is not coeval it is not possible to
quantitatively compare the calculated and observed signals. There are some discrepancies between
the synethtic and observed seismic traces. For example, seismogram 7 reveals high amplitudes to
depths of 1200 m, however, the projected position of this record crosses the acoustically blank cen-
tre of an eddy. Furthermore, at ∼2000 m seismic imagery reveals reflectivity that is consistent with
the depth of the AAIW/NADW water mass boundaries, yet these deep temperature contrasts are
not apparent in synthetic seismograms. These inconsistencies are not unexpected due to the large
separation in space and time of the hydrographic measurements and seismic records. Nevertheless,
the clear zonation of water masses on either side of the front is revealed by the synthetic seismo-
grams and suggests that the distinct water masses on either side of the front have been faithfully
reproduced. Thus, the seismic images cohere with the patten of reflectivity suggested by vertical
gradients of hydrographic measurements. These observations are consistent with current meter
and hydrographic observations across the Brazil and Falkland Current that reveal the seasonal
thermocline of the latter is shallower that the former (Vivier & Provost, 1999).
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 116
4.4.2 Spatial and Temporal Variation of Reflectivity
Set A and B are separated by a perpendicular distance of ∼14 km (Figures 4.7 and 4.8). Within each
set, seismic images are shown sequentially in time and are separated by ∼1 day and ∼1 km. Due
to the racetrack pattern of acquisition, profiles between sets are interleaving. Thus seismic swaths
were acquired in the following order: 1,5,2,6,3,7,4,8 (Table 4.2 and Figure 4.3). Each adjacently
acquired swath is separated by ∼12 hours (e.g. swath 1 and 5).
Clear, coherent and complex reflections occur across all depths of each profile acquired between
the 10th and 17th February 2013. The frontal interface is observed in each profile (Figures 4.7 and
4.8). The location of outcropping reflections correlates well with coeval sea-surface temperature
measurements that show large gradients (0.3 ◦C km−1) at similar positions, confirming the presence
of a strong thermal front (Figures 4.7 and 4.8 b,d,f,h). The strength of this front is similar to a
thermal front of 0.2 ◦C km−1 identified as the Brazil-Falkland Confluence in 1984 using sea-surface
temperature measurements (Gordon, 1989). A clear southward migration of the frontal interface
of O(10) km day−1 is observed during this period of seismic acquisition and is calibrated with
sea-surface temperature measurements. Large-scale movement reveals that migration speeds are
greatest near the surface, up to 20 km day−1, and reduced at depth, ∼9 km day−1. These values
are similar to mean velocities of 10–50 km day−1 reported by Garzoli & Garraffo (1989). It is
important to note that these cross-sections may be oblique expressions of the front, therefore it is
possible this speed is underestimated. After the 17th February 2013, the frontal interface moves
beyond the region of observation. The advecting front maintains its mesoscale structure during the
observation period of 7 days, suggesting the structure is long-lived. Advection of the frontal zone
implies that the seismic survey region is increasingly composed of warm, northern Brazil Current
as time progresses. This pattern is also implied in the distinct zonation of water masses on either
side of the front, since continuous horizontal reflections (which mark the Brazil Current) extend
further toward the southwestern edge of the later profiles within in each set.
Sea-surface temperature profiles across the southwest Atlantic Ocean are analysed for the time
period encapsulated by Set A and B (Figure 4.9). These maps reveal a surface thermal front
migrating southwestward. As time increases, warm surface waters move southwards to cover the
seismic survey region. These satellite data yield three important observations. First, warm northern
water travels southwards to cover the seismic survey in the same time period (∼1 week) and at the
same speeds (∼10 km day−1) as has been inferred from seismic data. Secondly, the thermal front
between warm and cold water is approximately perpendicular to the seismic survey azimuth of
Time-lapse Imaging of the Brazil-Falkland Confluence 117
Figure 4.7: Seismic reflection profiles from Set A shown with coeval sea-surface temperature
measurements (see Figure 4.3c for location). (a) Profile 1. (b) Coeval sea-surface temperature
across seismic survey region. Data acquired on 11th February 2013 (distributed by NOAA, available
at https : //coastwatch.pfeg.noaa.gov/erddap/index.html). Blue/red colours = colder/warmer
temperature according to scale at right; thin black lines = temperature contours every 0.5 ◦C; thick
black line = location of seismic profile shown in (a). (c) Profile 2. (d) Same as (b) for 13th February
2013. (e) Profile 3. (f) Same as (b) for 14th February 2013. (g) Profile 4. (h) Same as (b) for 17th
February 2013. Black arrows = position of outcropping frontal interface along seismic profile and
corresponding location on map.
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 118
Figure 4.8: Seismic reflection profiles from Set B shown with coeval sea-surface temperature
measurements (see Figure 4.3c for location). (a) Profile 5; labelled box = zoomed portion of profile
shown in Figure 4.10i. (b) Coeval sea-surface temperature across seismic survey region. Data
acquired on 11th February 2013. Thin black lines = temperature contours every 0.5 ◦C; thick black
line = location of seismic profile shown in (a). (c) Profile 6; labelled box = zoomed portion of
profile shown in Figure 4.10ii. (d) Same as (b) for 12th February 2013. (e) Profile 7; labelled
box = zoomed portion of profile shown in Figure 4.10iii. (f) Same as (b) for 14th February 2013.
(g) Profile 8. (h) Same as (b) for 16th February 2013. Black arrows = position of outcropping
frontal interface along seismic cross section and corresponding location on map
Time-lapse Imaging of the Brazil-Falkland Confluence 119
Figure 4.9: Regional sea-surface temperature variation during seismic surveying (10th–17th Febru-
ary 2013). (a) Regional context of sea-surface temperature across southwest Atlantic Ocean on 10th
February 2013. Thick black box = location of seismic experiment; thick black line = orientation of
seismic profiles. (b-h) Sequential sea-surface temperature maps from 11th to 17th February 2013.
041. Fortuitously, this means that the along-swath orientation also corresponds to the along-front
direction. Finally, the thermal front extends across the entire diagonal length of the survey, up
to 200 km, consistent with seismic observations of a deep-reaching front that varies little in the
cross-front (i.e. NW–SE) direction. It is possible to conclude that the three-dimensional spatial
nature of the front is characterised by small cross-front variability and large along-front variability.
The deep (i.e. 400–1200 m) eddy is imaged in all 8 seismic profiles (e.g. Figure 4.7a; 60–90 km
range, 500–1000 m depth). It is always observed on the dense side of the frontal interface and
migrates southwestwards with the front. The horizontal and vertical length scales of the eddy
change significantly between each seismic image. Horizontal lengths vary from less than 10 km
(e.g. Figure 4.8a) to >30 km (e.g. Figure 4.8e). Maximum thicknesses are 500 m (e.g. Figure
4.7c). Since the diameter is ∼10–30 km and eddies tend toward symmetrical ellipsoid shapes, it is
reasonable to assume that Set A and B have imaged the same eddy since the sets are separated
by ∼14 km (Charney, 1971). This inference is supported by three-dimensional reflectivity patterns
which suggests that there is little variation in the depth of the upper and lower boundary of the lens
in the cross-front direction (Figure 4.4). The core of the eddy is characterised by a near complete
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 120
lack of reflections. The lower boundary and edges of each lens is marked by alternating bands of
blank and bright reflectivity. Each band is up to 100 m thick and wraps around the eddy (Figure
4.8e; 50 km range, 900 m depth). This reflectivity is interpreted as spiral arms that surround the
eddy. These tendrils of water are likely to be intrusion-water that has been removed from the
periphery of the lens (Song et al., 2011). The observations of this deep eddy are similar to other
seismic oceanography studies that map Meddies (i.e. anticyclonic eddies with a homogeneous core
of Mediterranean Undercurrent water; Armi et al., 1989). Meddies are often seismically imaged
in the southwest Iberian Peninsula and have horizontal length scales of O(50) km and vertical
length scales of O(500) m (Biescas et al., 2008; Pinheiro et al., 2010; Song et al., 2011). Critically,
these eddies are often observed between 500 and 1500 m depth. For example, Song et al. (2011)
imaged a Meddy that is 75 km in length, 1200 m thick and centred near 1000 m depth. Meddies
are characterised by an acoustically blank centre and layered upper and lower boundaries. The
well-defined fine-structure observed at the upper and lower boundaries of these lenses has been
attributed to double-diffusive vertical mixing and intrusions (Armi et al., 1989; Ruddick & Hebert,
1988).
Numerous other small mesoscale and sub-mesoscale reflectivity patterns are observed. These in-
clude deep lens-shaped structures characterized by curved reflections that wrap around acoustically
transparent centres (e.g. Figure 4.7c; 50–60 km range, 1500–2000 m depth and Figure 4.8a; 10–30
km range, 1200–1800 m depth), large acoustically blank patches, and short disrupted reflectivity
close to the seafloor (e.g. Figure 4.7c; 90–130 km range, ≥2000 m depth). Seismic profiles in Set B
image the evolution of a series of unusual small mesoscale and sub-mesoscale reflectivity patterns
(Figure 4.8). Figure 4.10 highlights these changes. Deformation of a thin, circular band of reflectiv-
ity that encloses an acoustically blank centre is observed. This patch of water lies between 12 and
22 km range and 1200–1700 m depth in Profile 5 (Figure 4.10i). The patch is approximately 9 km
in length and 500 m in thickness. The shallowest portion of the patch is disrupted. Approximately
one day later the same structure appears to have been flattened and lengthened (Figure 4.10ii).
Long continuous reflections extend northward from the flattened patch toward the frontal interface
and deep eddy. At this point in time, the frontal interface is approximately 60 km northeastward
of the acoustically blank patch (Figure 4.8c). A day later, the same patch now appears to be
stretched between 12 and 30 km at 1200–1500 m depth (Figure 4.10iii). Isolated strands of reflec-
tivity also exhibit similar stretching behaviour. These strands are first seen in Profile 5 between 30
and 70 km range and 1000–2000 m depth, and appear to have lengthened and moved to shallower
depths in Profile 6 (Figure 4.10i,ii). These reflections are interpreted as the same thermohaline
Time-lapse Imaging of the Brazil-Falkland Confluence 121
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 122
Figure 4.10 (previous page): Zoomed portions of Profiles 5, 6 and 7 with line-drawing inter-
pretation of thermohaline structure evolution. Swath (zoom) location shown in Figure 4.3c (Fig-
ure 4.8a–c). (i) Zoomed portion of Profile 5. (ii) Zoomed portion of Profile 6. (iii) Zoomed portion
of Profile 7. (iv) Line-drawing interpretation of thermohaline structure evolution. Black/red/blue
lines = interpretation of Profiles 5/6/7.
structures, which are being deformed over time. Since each successive image is only separated by
1 km and 1 day, this inference implies that deformation is rapid (Figure 4.10iv). The apparent
decay of these thermohaline structures appears to correlates with a tripling in size of the deep eddy
(Figure 4.8). During this time, the eddy grows spiral arms separated by up to 4 km from the main
body. Correlation between reflectivity deformation and eddy growth implies the lens may increase
in size by pulling in these deeper water masses. This interpretation would imply a vertical flux
of water over a few hundred metres and across several tens of kilometres. Furthermore, it would
suggest the deep eddy rotates about a horizontal axis with vertical movement of 400 m. This rather
speculative interpretation is important to note as it could be energetically significant. The presence
of this structure suggests large-scale vertical stirring. Stirring over length scales of ∼400 m would
be energetically expensive unless the density contrasts between the fluids is small. Since bright
reflectivity is an indicator of large temperature changes, a large salinity difference between the
fluids is needed to compensate the density change induced by temperature. Bianchi et al. (1993)
observe numerous intrusions in the Brazil-Falkland Confluence that have positive temperature and
salinity anomalies of up to 7◦C and 0.95 psu, respectively. Based on the T–S relationship in this
region, these anomalies will compensate each other and may lead to large-scale vertical mixing
(Figure 4.2c). To inform this discussion further, development of the adapted inversion procedure
using additional constraints of neutral buoyancy combined with dense velocity analysis should be
considered in future work (Chapter 3).
Oceanic vertical overturns are generally restricted to a few tens of metres due to the oceans stratifi-
cation (Vallis, 2006). However, under conditions of high shear, Kelvin-Helmholtz (K-H) instabilities
can be generated. Given an initial wavelike perturbation, mass conservation requires horizontal ac-
celerated flow above and below the wave crests and troughs. Vertical velocity perturbations are
generated that amplify the original wave, resulting in positive feedback and rapid growth of the in-
stability. Large trains of K-H instabilities have been observed within the Kuroshio Current. Chang
et al. (2016) observed billows using echo-sounder data that extended 200 m horizontally and 100 m
vertically. Although rarely observed, long-term moored observations suggest that K-H billows are
nearly persistent over a period of 6 months (Chang et al., 2016). However, the scales of vertical
Time-lapse Imaging of the Brazil-Falkland Confluence 123
and horizontal motion observed here are several orders of magnitude larger that typical vertical
overturns of centimetres to tens of metres (Dillon, 1982). For this reason, it is possible that the
evolution highlighted by Figure 4.10 is an effect of out of plane deformation rather than vertical
stirring. Nevertheless, it is clear that the front distorts this portion of the water column since
no similar distortion is observed before and after the frontal system migrates through the seismic
survey (see Figure C.3). It is possible to conclude that the effect of the front extends over several
tens of kilometres and down to abyssal depths.
Seismic imagery collected prior to and after Set A and B are used to constrain the temporal nature
of the front. In April 2013, 8 seismic profiles were acquired approximately 30 km from Set A and
B (Set C and D). Set C and D are separated by a perpendicular distance of ∼6 km (Figure 4.3).
Seismic images are shown sequentially in time and are separated by ∼1 day and ∼1 km. Due to
the racetrack pattern of acquisition, profiles between sets are interleaving and the profiles were
acquired in the following order: 9,13,10,14,11,15,12,16 (Figure 4.3a and Table 4.2). All 8 profiles
from Set C and D are shown in Appendix C (Figures C.1 and C.2). Here, five profiles are selected
to demonstrate the reflectivity observed in these sets (Figures 4.11 and 4.12). These seismic images
reveal bright reflectivity in the upper 1200 m of the water column. A set of northward dipping,
high amplitude and continuous reflections are observed, extending to maximum depths of 1800 m
(e.g. Figure 4.12b). This reflectivity is interpreted as a deep reaching front that separates water
in the north from the south. The dipping wedge implies that water at the northeastern edge of
the profiles is less dense than the water in the southern portion. A small mesoscale lens-shaped
set of reflectivity is characterized by curved reflections that wrap around acoustically transparent
centres. The lens is observed on the dense side of the front with lengths and thickness of up to 25 km
and 500 m, respectively (Figure 4.11b; 15–40 km range, 500–1000 m depth). Due to the classic
double-convex shape this structure is interpreted as an eddy. Since Set C and D are separated by a
perpendicular distance of 6 km, it is reasonable to assume that the eddy imaged in each set is the
same. The cross-sectional area of the eddy changes rapidly with time (e.g. Figure C.2a,c,e). As in
Set A and B the eddy lies on the dense side of the front at 400–1200 m depth. The two observation
periods reveal similar horizontal and vertical length scales of the deep eddy. The lower boundary
of the lens observed here is wrapped by layers of acoustic blankness and bright reflectivity that are
a few hundred metres thick. Set C and D bear a strong resemblance to seismic imagery shown in
Set A and B, however, two differences are apparent. First, dipping reflectivity is less steep (∼0.5◦)
than similar patterns observed in Set A and B. Since dipping reflectivity outcrops close to the SW
corner of these profiles it is not possible to determine if water masses on either side of the front
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 124
F
ig
u
re
4
.1
1
:
S
eism
ic
refl
ectio
n
p
rofi
les
9
an
d
10
from
S
et
C
(see
F
igu
re
4.3c
for
lo
cation
).
(a)
P
rofi
le
9.
(b
)
P
rofi
le
10.
Time-lapse Imaging of the Brazil-Falkland Confluence 125
Figure 4.12: Seismic reflection profiles 13, 14 and 15 from Set D (see Figure 4.3c for location).
(a) Profile 13. (b) Profile 14. (c) Profile 15.
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 126
have distinct characteristics. Secondly, the majority of bright reflectivity is constrained to the upper
1200 m rather than extending to abyssal depths. The Brazil-Falkland Confluence is marked by a
complex frontal system (Saraceno et al., 2004). It is not possible to determine if Set A/B and Set
C/D have imaged the same front within the confluence zone. Nevertheless, what is striking about
these seismic images is the dual observations of a front and deep eddy that bear strong resemblances
to each other. The similarities between reflectivity patterns (i.e. thermohaline structure) suggests
that similar dynamical processes are occurring during February and April 2013. Although this area
is one of the most energetic regions in the world’s oceans, the repeated observations imply that a
few key processes may be common and are perhaps ubiquitous to fronts in this area.
Four further seismic profiles have been processed and analysed based on their location, time of
acquisition, and the observed southwestward migration of the entire frontal zone in Set A and B.
These four profiles are shown in Appendix C (Figure C.3). Two profiles have been carefully selected
from Set E that typify the water mass structure before and after the front travels across the seismic
survey region (Table 4.2 and Figure 4.3c). These profiles are shown in (Figure 4.13). Profile 18 was
acquired approximately 10 days before the start of the acquisition period of Set A and B (Figure
4.13a,c). For this reason it is expected that these profiles will reveal the thermohaline structure
of the Falkland Current (Figure 4.13a). In a similar way, Profile 19 was acquired approximately
1 month after Set A and B, and is expected to characterise thermohaline structure of the Brazil
Current (Figure 4.13b). These seismic images clearly reveal different water mass structures. Profile
18 shows discontinuous reflectivity and multiple mesoscale lenses and fingers (e.g. Figure 4.13a: 40–
60 km range, 1000–1400 m). The upper 750 m of Profile 19 displays long continuous reflectivity that
does not exceed dips of 0.1◦. Assuming that the front is not affecting the thermohaline structure
of these profiles, it is possible to conclude that the Brazil and Falkland Current have significantly
different water mass characteristics. Furthermore, the reflectivity patterns imply that the Falkland
Current contains more energetic mesoscale and sub-mesoscale processes, whilst the Brazil Current
is fairly quiescent. In this way, Profiles 18 and 19 bear a strong resemblance the water masses
on the light and dense side of the front imaged in Set A/B, respectively. This observation (i.e.
that profiles interpreted as imaging the Brazil and Falkland current are consistent with each other,
irrespective of time) implies that although the frontal interface clearly separates these two water
masses, it may not significantly alter the water mass characteristics on either side.
Time-lapse Imaging of the Brazil-Falkland Confluence 127
F
ig
u
re
4
.1
3
:
S
ei
sm
ic
re
fl
ec
ti
on
p
ro
fi
le
s
18
an
d
19
fr
om
S
et
E
(s
ee
F
ig
u
re
4.
3c
fo
r
lo
ca
ti
on
).
(a
)
P
ro
fi
le
18
.
(b
)
P
ro
fi
le
19
.
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 128
4.4.3 T , S, ρθ, N
2, and ugy
Typical of subpolar waters, the Falkland Current is strongly barotropic (i.e. density stratification is
closely related to the pressure field rather than temperature or salinity variations; Piola & Matano,
2017). The Brazil Current is primarily baroclinic, with varying relative importance of salinity and
temperature as a function of depth (Piola & Matano, 2017). At the surface, density is influenced
by temperature and salinity. At >50 m depth, the temperature effect on density dominates the op-
posing salinity effect, therefore density closely follows the temperature distribution (Provost et al.,
1996). It is possible to quantify the contribution of temperature and salinity to observed reflec-
tivity. Following the method of Sallare`s et al. (2009) and using hydrographic data listed in Table
4.1, the contribution of temperature to observed reflectivity is estimated (Chapter 2). In the upper
1000 m, the median contribution of temperature to observed reflectivity is calculated as 91%. This
result suggests that the sound speed of seawater in the Brazil-Falkland Confluence is predominantly
controlled by temperature, which means that acoustic reflectivity accurately represents tempera-
ture changes within the water column. Therefore, it is reasonable to iteratively invert seismic
imagery into profiles of temperature (and salinity) using the adapted inversion scheme described
in Chapter 3.
Temperature distributions for Set A and B have been calculated using an adapted iterative pro-
cedure. Calculated distributions for Profile 2 and 4 are are shown in Figure 4.14 (all 8 profiles
shown in Figures C.4 and C.4). Isotherms of 20, 15, 10, 5 and 4 ◦C mark the transitions between
TW, SACW, SAAW, AAIW and UCDW (Bianchi et al., 1993; Piola & Matano, 2017). Calculated
temperature distributions clearly reveal a wedge of warm sub-tropical water, SACW 10–20 ◦C,
overlying cool sub-Antarctic water, SAAW <10◦C (Figure 4.14a,c). The warm-water wedge deep-
ens to ∼600 m in the north, mirroring the bright dipping reflectivity of the frontal interface. The
thickness and temperature of the wedge matches expected values of SACW well (Figure 4.2a).
The brightest reflectivity across each seismic image occurs at the outcrop of dipping reflections
with the sea-surface, suggesting spatial gradients of physical properties are strongest here. Tight-
ening and shallowing of isotherms match the location of this bright reflectivity and outcropping
reflections well. TW (>20 ◦C) is observed as a cap of surface water of approximately 100–300 m
thickness across profiles. Large temperature gradients across the thermocline are accurately repro-
duced by the adapted inversion scheme and match hydrographic measurements (Figure 4.14b,d).
Furthermore, the depth of the thermocline matches WOCE transects A10 and A11 that cross the
Brazil and Falkland Current further north and south of the confluence zone, respectively (Figure
Time-lapse Imaging of the Brazil-Falkland Confluence 129
F
ig
u
re
4
.1
4
:
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to
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la
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ed
w
at
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m
as
se
s
gi
ve
n
in
F
ig
u
re
4
.1
b
,c
.
(c
)
P
ro
fi
le
4.
(d
)
S
a
m
e
a
s
(b
).
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 130
4.1b,c). A 250 m increase in thermocline depth across the frontal interface is typical in frontal
zones (Spall, 1995; Ou & Gordon, 2002). Slabs of acoustically blank water, bounded by bright
reflectivity, thicken toward the north and correlate well with converted temperature distributions.
Specifically, the lower boundary of these slabs aligns with the 4 ◦C isotherm (e.g. Figure 4.14a).
These slabs are interpreted as re-circulated AAIW based on their temperature, depth and location
within the Brazil Current (Figure 4.1b; Piola & Matano, 2017). Mid-slab depth is consistent with
the core of AAIW, 3–5 ◦C, that lies at ∼1000 m (Figure 4.2). The bottom boundary of the slab
is tilted, with a slope of up to 1◦. It is possible that these tilted slabs are caused by the confluent
flow of less dense AAIW with colder and more saline CDW (Figure 4.2c). The southward flow
of AAIW may be deflected upward by the northward flow of denser water masses. Beneath this
depth, temperatures of 4 and 3 ◦C indicate UCDW and NADW, respectively. It is unlikely that
LCDW has been observed in these images, since it is the densest water entering the Argentine
Basin and closely follows the 3000–3500 m isobath, which is beyond the vertical extent of these
profiles. Deepest reflectivity in both sets of seismic imagery occurs at ∼2000 m, even though water
depth increases by approximately 600 m in Set B. The depth of these reflections is consistent with
the ∼2000 m isobath that NADW follows along its southward path (Figure 4.2; Piola & Matano,
2017). Furthermore, converted temperature profiles reveal fairly homogeneous temperature struc-
ture around 3 ◦C that is consistent with the characteristics of NADW. Therefore, this reflectivity
is interpreted as the upper boundary of NADW (Section 4.2; Figure 4.1b,c).
Lens-shaped mesoscale reflectivity that lies on the dense side of the front appears anomalously cold,
-4 ◦C, and fresh compared with the surrounding water (Figure 4.14a and Figure 4.15a). Another
prominent eddy is visible at a range of 100–125 km on Profile 3 on 14th February and at 50–70 km
on Profile 4 on 17th February (Figure 4.7e,g). These two observations are interpreted as the same
eddy that has advected southwestward. The eddy lies at 500 m depth, is 400 m thick and 20 km
long. A similar structure is not observed in the equivalent profiles of Set B (Figure 4.8g,h). It
is possible that this eddy does not extend 14 km in the east-west direction or that Set A seismic
cross-sections have sliced the edge of the eddy. Unlike the deep eddy discussed above, the lens
observed here has a consistent shape across the three day observation period. The temperature and
salinity distributions for Profile 4 reveal that this lens is anomalously warm, T ∼ 15 ◦C, and salty,
S ∼ 35.5 psu, suggesting that this eddy is formed of SACW (Figure 4.14c). Since these eddies are
warm-core they have anti-clockwise rotation here in the southern hemisphere. These observations
are reminiscent of a number of relatively warm salty intrusions of a few hundred metres thickness,
found within the 12 to 17 ◦C layer of the thermocline along 38 ◦S (Gordon, 1981). Gordon (1981)
Time-lapse Imaging of the Brazil-Falkland Confluence 131
attributed these lenses to SACW eddies that contribute to the poleward transport of warm-water.
Poleward extension of warm water is expected to enhance ocean-atmosphere heat flux by increasing
the contrast of ocean and air temperatures. These eddies may also represent a significant source
of heat for the Antarctic zone (Gordon, 1981; Gordon & Greengrove, 1986). Provost et al. (1995)
identified a lens of anomalously warm and salty water (+4◦C and 0.5 psu) of 50 km length and
350 m height. This lens was observed between 50 and 400 m depth and was attributed to a large
coherent lens of TW that has detached itself from the front. An intensification of the temperature
anomaly plus brightening of seismic amplitudes between the observations on the 14th and 17th
of February is observed. It is possible that these changes are evidence of recent spawning and
intensification of the warm-core eddy.
There is a clear difference in vertical temperature structure on either side of the frontal interface
that matches the variation in acoustic reflectivity. Horizontally averaged temperature profiles as
functions of depth are shown for each profile (Figure 4.14b,d). The average profiles are compared
with hydrographic data collected from WOCE transects A10 and A11 that cross the Brazil and
Falkland Current, respectively, as well as near-coeval measurements acquired during seismic sur-
veying. Average temperature profiles distributions are most similar to the thermohaline structure
of the Brazil Current (WOCE transect A10). This similarity is due to the larger contribution of
Brazil Current to the measured thermohaline distribution as the confluence migrates southwards.
It is evident that both distinct temperature structures of the Brazil and Falkland Current are re-
produced by the iterative inversion procedure, providing confidence in the adapted scheme that is
used to extract temperature estimates from seismic reflectivity.
Temperature profiles show a well-defined thermohaline structure tracking the movement of this
frontal system. Temperature distributions are maintained across the observation period of ∼7 days
and advect southwestwards at least 100 km. These observations suggest the front is long-lived
(compare Figure 4.14a and c) and are consistent with acoustic observations. Southward migration
of a thermal front is also observed in coeval sea-surface temperature data (Figure 4.9). Bianchi
et al. (1993) use CTD data collected between 1984 and 1989 to quantify cross-front temperature
and salinity distributions. They find upper ocean cross-front structure of the large-scale fields
is constant, consistent with the observations discussed here. As the front migrates southwards,
horizontally averaged profiles show the thermocline deepening as the Brazil Current pushes the
confluence southwards (compare Figure 4.14b and d). Furthermore, a deep thermocline of ∼1000
m thickness is observed in seismic profiles acquired 1 month after the passage of the front suggesting
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 132
that the confluence does not retreat northwards in this time period (Figure 4.13b).
Distributions of temperature, T , and salinity, S, can be used to calculate potential density ρθ,
buoyancy frequency, N2, and geostrophic currents, ugy (Figure 4.15). Figure 4.15 shows these
distributions for Profile 2 since it is representative of the long-lived thermohaline structure of the
front. T and S profiles reveal a wedge or warm, salty subtropical water overlying cold, fresh sub-
Antarctic water (Figures 4.14a and 4.15a). Long wavelength thermohaline structure is faithfully
reproduced and matches observed data well (Figure 4.15b,d,f,h). However, the salinity minima of
recovered profiles is 0.2 psu less than the minima observed in hydrographic data. This discrepancy
is a consequence of the method that is employed to extract physical properties. The adapted
inversion scheme allows distributions of temperature and salinity to be calculated from seismic
imagery without the need for coeval hydrographic data. However, a local T -S-z relationship is
required to calculate S which is ideally derived from local hydrographic measurements. T -S-z
relationships are based on the best approximation of the instantaneous relationship; in this case an
average of near-coeval hydrographic data (Figure 4.2). In a dynamic oceanographic region such as
the Brazil-Falkland Confluence it is a challenge to produce the instantaneous T -S-z relationship.
Therefore, small changes in T with z may result in erroneous S. Despite this limitation inverted
physical properties reproduce the large-scale structure and the relative salinity relationship is sound
(converted profiles show a salinity minima at the correct depth), providing confidence that the
distribution of salty and fresh water is accurate.
ρθ, N
2 and ugy are calculated from the converted temperature and salinity distributions (Figure
4.15c–g). Between 40 and 140 km isopycnals dip northwards by ∼ 0.2◦ suggesting that the conflu-
ence of these two currents is indeed a density front (Figure 4.15c). In potential density the front
appears less sharp which may be due to partial compensation of temperature and salinity (Rud-
nick & Ferrari, 1999). Significant baroclinicity still exists as isopycnals slope downward toward
the north. The horizontally averaged profile of potential density compares well with hydrographic
measurements at depths greater than 400 m (Figure 4.15d). In the upper 400 m converted ρθ
are lighter than hydrographic data from WOCE lines A10 and A11. This disparity is caused by
the lower salinity minima reproduced by the converted profiles. Nevertheless, the overall trend
of increasing density is recovered in the upper 400 m. Isopycnals of 1025, 1027, and 1028 kg m3
are approximate indicators of the transition between TW, SACW and UCDW and match the wa-
ter masses corresponding isotherms (Piola & Matano, 2017). At depths >300 m, stratification
is weaker on the light side of the front as seen by the widened isopycnals. The distribution of
Time-lapse Imaging of the Brazil-Falkland Confluence 133
Figure 4.15: Seismic reflection Profile 2 converted into salinity, S, potential density, ρθ, buoyancy
frequency, N2, and geostrophic current, ugy. Isolines smoothed over 20 km horizontally and 100 m
vertically. Corresponding temperature profile shown in Figure 4.14a. (a) S. Black line = contours
every 0.5 psu. (b) Comparison of converted S measurements shown in (a) with hydrographic data.
Coloured points = horizontally averaged converted S measurements coloured according to scale at
right; light grey points = average S profile from WOCE transect A10; dark grey points = average
S profile from WOCE transect A11; black points = near-coeval measurements. (e) ρθ. Black lines
= contours every 0.5 kg m−3. (f) Same as (b) for ρθ. (g) N2 calculated from converted T and
S distribution smoothed over 12.5 km horizontally and 620 m vertically. (h) Same as (b) for N2.
(i) ugy. Black lines = contours every 0.2 m s
−1; red/blue shading = flow into/out of page (i.e.
northwest/southeast flow). (j) Same as (b) for ugy. Black points = ugy estimated between two
near-coeval hydrographic profiles that form a near-parallel line with seismic profiles (Figure 4.3c
and Table 4.1).
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 134
buoyancy frequency also shows that high stratification is limited to the upper 200 m on the light
side of the front (Figure 4.15e). Highest stratification follows the frontal interface. Comparison
with hydrographic data shows that the vertical buoyancy frequency is well recovered. However,
between 100 and 500 m depth there is a band of high stratification that reaches 0.6×10−4 s−2. This
high stratification zone is comparable to hydrographic data collected in the confluence zone but its
magnitude is larger than average profiles of stratification across the Brazil and Falkland Currents
(Figure 4.15f).
These gradients of temperature and potential density imply the presence of horizontal pressure gra-
dients (Figure 4.15). At large-scales in the ocean, pressure gradients are balanced by the Coriolis
force and associated geostrophic currents. Geostrophic currents estimated in this way are orien-
tated perpendicularly to seismic profiles (i.e. NW–SE). Based on the temperature distribution it is
possible to infer that the column of water at 40 km is overall denser and therefore shorter than at
140 km, generating a pressure gradient force from right to left (i.e. southwestward). The Coriolis
force balances the pressure gradient force and acts to the left of geostrophic flow. Sloping isopyc-
nals suggest flow at the northern end of the profile is southeastward (i.e. out of the page). This
qualitative assessment is corroborated by quantitative estimates of geostrophic current. Profiles are
extracted from converted temperature and salinity distributions every 20 km that act as pseudo-
CTDs. The dynamic height anomaly and geostrophic current are calculated (Figure 4.15i). Based
on ρθ, a level of no motion at 1500 m is assumed (Figure 4.15c). Geostrophic currents, ugy, indicate
strong velocities orientated out of the page. Southeastward currents of up to 0.8 m s−1 are focused
in the upper 500 m and are constrained by sloping isopycnals that correspond to the frontal inter-
face (Figure 4.15c). Elsewhere, southeast-northwest motion is close to zero. Geostrophic velocities
calculated from converted profiles of temperature and salinity are shown in Figure 4.15g. These
estimates are compared with independent measurements of ugy calculated between two near-coeval
hydrographic measurements, T1 and T6 (Figure 4.15h). T1 and T6 were acquired approximately
three months apart (Figure 4.1; Table 4.1). The cross-section between the two casts lies approx-
imately parallel to acquired seismic transects and therefore provides a comparable estimate of
southeast-northwest orientated geostrophic currents. ugy calculated between T1 and T6 also show
high southeastward speeds of up to 0.6 m s−1 near the surface, and decrease to zero at 1000 m depth.
At large-scale frontal zones such as the Brazil-Falkland Confluence density gradients are surface
intensified. The gradient has an associated geostrophic shear along the frontal axis. For a front,
the geostrophic shear is strongest at the surface and forms a jet orientated along the frontal axis,
i.e. southeast-northwest direction (McWilliams, 2016). It is hypothesised that the large eastward
Time-lapse Imaging of the Brazil-Falkland Confluence 135
velocities calculated here are caused by the frontal jet that is associated with surface intensified
density gradients (Figure 4.15).
4.4.4 Current Field
As a result of the redundancy built into seismic acquisition, each spatial location is sampled many
times and each CMP gather consists of a group of 120 ray paths that span a finite period of
time. The in-plane, horizontal speed of a given reflection is determined by measuring its slope in
shotpoint-CMP space (i.e. time-distance; Chapter 3). In this way, slope measurements at different
locations along seismic transects can be used to determine the speed of internal waves (Figure
4.16). The validity of this approach is confirmed by examining sets of shot gathers that have been
corrected for normal move-out which show individual mappable reflections moving horizontally and
vertically with speeds of fractions of a metre per second (Figure 4.16c–m). Speed measurements
indicate confluent flow at the frontal interface as expected.
Measurements of internal wave speed are taken across the entire range and depth of each seismic
transect in Set A (Figure 4.17). Speed measurements indicate northeastward movement of subpo-
lar water and southwestward movement of subtropical water, and are consistent with the general
northward and southward flow of the Falkland and Brazil Currents, respectively. Horizontally av-
eraged current speed as a function of depth is consistent across each transect, revealing three main
flow features (Figure 4.17b,d,f,h). First, large southwestward velocities of >0.1 m s−1 are observed
in the upper 200 m of the water column across the entire horizontal range (e.g. Figure 4.17a). Sec-
ondly, the frontal interface and mid-depth water, 300–1000 m, is characterized by northeastward
velocities of 0.02±0.01 m s−1. Finally, at greater depths current speed is ∼0.03±0.01 m s−1 south-
westward. This southwestward motion is consistent with southwards advection of NADW at these
depths. The southward/northward flow of mid/deep water implies there is vertical shear between
water masses at approximately 1500 m depth. Internal wave speed measurements are compared
with geostrophic velocities that are orientated in approximately the same direction. Geostrophic
velocities have been calculated from two CTDs that were acquired on the 1st March 2013 to the
north of the seismic survey (Figure 4.1a). The casts are 49 km apart and form a line that is approx-
imately perpendicular to the seismic survey azimuth. Therefore these CTDs are positioned such
that it is possible to calculate geostrophic velocities in the direction of seismic surveying (i.e. 041).
The maximum depth of the CTDs is 920 m and a level of no motion has been chosen at 650 m
based on the flat isopycnals at this location. Calculated geostrophic currents are southwestwards
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 136
F
ig
u
re
4
.1
6
:
In
tern
al
w
av
e
sp
eed
m
easu
rem
en
ts
across
P
rofi
le
2.
(a)
P
rofi
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2.
R
igh
t-/left-p
oin
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b
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arrow
s
=
m
easu
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orth
east-
w
ard
/
so
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th
w
estw
ard
sp
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s
o
f
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id
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a
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w
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(A
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(B
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an
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(C
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sh
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=
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T
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th
a
t
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ow
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osition
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given
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zero
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ssin
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tal
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vertical
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istan
ce
b
ars
in
m
etres.
Time-lapse Imaging of the Brazil-Falkland Confluence 137
Figure 4.17: Measuring internal wave speed from pre-stack seismic data. (a) Profile 1. Right-
/left-pointing black arrows = measured northward/southward speeds of individual reflections. (b)
Horizontally averaged speed measurements as function of depth along profile in (a). Thin lines = in-
dividual horizontally averaged measurements every 50 m. (c) Profile 2. (d) Same as (b). (e) Profile
3. (f) Same as (b). (g) Profile 4. (h) Same as (b). Black line = In-plane geostrophic currents
calculated from XBT data acquired in March 2013 (Figure 4.1a).
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 138
with a magnitude of O(0.1) m s−1 in the upper 200 m. Flow reverses at 500 m depth. The magni-
tude and direction of calculated geostrophic currents are robust to the chosen level of no motion.
Thus, horizontal speeds measured along these seismic profile are consistent with similarly orien-
tated geostrophic currents providing confidence in this technique. Furthermore, average southward
advection of internal wave speed measurements, 0.01 m s−1, is equivalent to 8.64 km day−1, which
correlate well with large-scale advection of the frontal system observed in seismic images and sea-
surface temperature measurements. This correlation suggests that horizontally averaged internal
wave speed measurements are a reliable indicator of large-scale in-plane current flow. It is evident
that a similar flow field is measured across each seismic image. Moreover, each independently es-
timated flow field advects with thermohaline structure providing confidence in the scheme that is
used here to measure internal wave speeds and constrain large-scale currents (Figure 4.17).
A back-of-the-envelope calculation of volume flux is made using average estimated current speeds.
The volume flux, fV , of water through the seismic survey region is calculated using the average
velocity across the entire depth of the water column (v = 0.01 m s−1 southwestward; Figure
4.16b). fV =
∫
vdA, where v is the speed and A is the area water fluxes through. Integrating
gives fV = v
∫
dA = v × A in m3 s−1. Along-front thermohaline structure is consistent within
each three-dimensional swath, therefore is is reasonable to assume that the current speed is also
constant in this direction (i.e. ∼SW–NE). Clearly the calculated flux is dependent upon A, which
is based upon the interpretation of current location. Here, the simple assumption is made that
measured currents are consistent across the seismic survey box and that the horizontally averaged
currents as representative of the current profile as a function of depth (Figure 4.17). Given A ≈
160× 3 = 480 km2 = 4.8× 108 m2, and using v = 0.01 m s−1 southwestward, the flux through the
seismic survey during 10th–17th February 2013 is 4.8 Sv southwards. The energetic Brazil Current
transports up to 4–6 Sv between 10 and 20 ◦S, but increases to 20 Sv at 38 ◦S (Stramma et al., 1990;
Peterson & Stramma, 1991; Piola & Matano, 2017). The transport calculated here is comparable
to these results.
4.5 Discussion
4.5.1 Slope of Frontal Interface
Seismic images are presented which show continuous sets of dipping (≤ 2◦) reflectivity that are
interpreted as a frontal interface within the Brazil-Falkland Confluence. These seismic images
Time-lapse Imaging of the Brazil-Falkland Confluence 139
yield useful physical oceanographic insights to the nature of this front. Assuming that the front is
in geostrophic balance, it is possible to compare the observed slope of the front with predictions of
slope based on the thermal wind equation. This relationship states that if density (i.e. temperature
and/or salinity) varies in the horizontal then geostrophic currents will vary in the vertical. It is
possible to relate the thermal wind equation to the Margules formula for the slope of a front
(Margules, 1906). The thermal wind equation for an incompressible fluid, such as water, is
∂ug
∂z
=
g
f
(−α∇T + β∇S)xˆ, (4.1)
where ug is geostrophic velocity, z is depth, f is the Coriolis frequency and g is gravitational
acceleration. α is the thermal expansion coefficient. By taking the x component of Equation 4.1,
it is possible to consider thermal wind balance in a two-dimensional plane. Here the x direction
is along-front (NE–SW). For two fluids of different densities, the discrete relationship between
temperature and current speed is given by,
u2 − u1
z2 − z1 =
g
f
−α(T2 − T1) + β(S2 − S1)
x2 − x1 , (4.2)
where subscripts 1 and 2 denote in-plane properties of light and dense fluids. Equation 4.2 is
rearranged to give
u2 − u1 = g
f
[−α(T2 − T1) + β(S2 − S1)] ∆z
∆x
. (4.3)
Finally, the Margules formula for frontal slope is given by
u2 − u1 = g
f
[−α(T2 − T1) + β(S2 − S1)] tan γ, (4.4)
since ∆z/∆x = tan γ, where γ is the slope of the front from the sea-surface. Equation 4.4 is
essentially a discrete version of the thermal wind equation and can be used to relate the change
in temperature and geostrophic current across a frontal interface to its slope. Based on the ob-
servations presented here, Equation 4.4 is solved using T1 = 15
◦C, T2 = 7.5◦C, S1 = 35.5 psu,
S2 = 34 psu and γ = 0.5
◦ measured at 500 m depth from converted temperature distributions and
seismic imagery (Figures 4.7 and 4.15a). f = 2 × 10−4 s−1, g = 9.81 m2 s−1, α = 10−4 1/C and
β = 10−4 1/psu. These values give |u2 − u1| ≈ 0.5 m s−1. Since the fastest currents in the ocean
are of order O(1) m s−1 this estimate is reasonable and implies that the flow may be in geostrophic
balance (Vallis, 2006). Nevertheless, fronts are often associated with quasi-geostrophic flows. Fur-
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 140
thermore, the steep slope of the frontal interface implies that the dip of the frontal interface may
be adjusted by frontogenic processes.
4.5.2 Frontogenesis
Large-scale confluent flow, such as in the Brazil-Falkland Confluence, causes geostrophic defor-
mation whereby pre-existing gradients are amplified, driving the flow away from geostrophic bal-
ance. The change in pressure gradient induces a secondary, ageostrophic circulation. The induced
mesoscale vertical velocity, w, attempts to restore geostrophic and thermal balance (Hoskins &
Bretherton, 1972). However, the imposed force continually pushes the system away from geostrophic
balance and the secondary circulation acts to restore it. This so-called ‘forced’ frontogenesis may
be considered one of continuous geostrophic adjustment (Shakespeare & Taylor, 2013). Thus the
system remains close to a balanced state and it is possible to use the balanced (i.e. primitive) equa-
tions to examine its dynamics. Quasi-geostrophic theory can be used to describe this near-balanced
flow (Hoskins & Bretherton, 1972). The omega equation, ω, is a diagnostic equation that solves
for vertical velocity, w, induced as part of the secondary ageostrophic circulation. w is difficult
to measure directly due to its small magnitude (scale analysis of the momentum equation yield
values O(10−5–10−3) m s−1 that border state of the are instrument precisions). However, it is
possible to infer the ageostrophic velocity field from synoptic density and geostrophic field using ω.
Although estimates of these fields are available, it is not appropriate to calculate vertical velocity
for the data presented here since the fields of density and currents must be well-constrained at
the smallest scales. The solution to the ω equation requires second-order derivatives, which will
significantly enhance noise. Although it is not possible to quantify the magnitude of ageostrophic
flow, qualitative assessments are made and the implications of secondary circulation discussed.
The classic work of Hoskins & Bretherton (1972) identified the connection between frontogenesis,
steepening isopycnals and modifications in stratification. They demonstrated that frontogenetic
confluent flow, such as that seen in the Brazil-Falkland Confluence, will always drive a thermally
direct (i.e. warm/cold water rises/sinks) ageostrophic secondary circulation. This ageostrophic
flow is upward (downward) on the light (dense) side of the front (Hoskins & Bretherton, 1972).
Palla`s-Sanz et al. (2010a) investigate the three-dynamical nature of a shallow front in the California
Current system. Hydrographic surveys reveal that when the front is straight, ageostrophic circu-
lation is thermally direct. Sea-surface temperature measurements across the seismic survey region
indicate that the front is straight and is orientated almost perpendicular to acquired seismic lines
Time-lapse Imaging of the Brazil-Falkland Confluence 141
(Figure 4.9). The observation of Palla`s-Sanz et al. (2010a) supports the inference that ageostrophic
circulation upwells (downwells) on the light (dense) side of the front acoustically imaged here.
Frontogenesis refers to the intensification of gradients at a front due to direction and speed changes
in the forcing field (Petterssen, 1936; Miller, 1948; Hoskins & Bretherton, 1972; Spall, 1995) . It is
likely that the observed steep slope of the frontal interface is a direct effect of induced secondary
circulation, whereby horizontal flows near the surface move water from the light to dense side
of the front and act to steepen isopycnals. Seismic imagery reveal that the steepest and brightest
reflections outcrop at the sea-surface indicating the presence of sharp temperature gradients (Figure
4.7). Furthermore, vertical upward flows on the light side of the front act to squeeze isopycnals
together thereby re-stratifying water (Hoskins & Bretherton, 1972). The opposite is true for the
dense side of the front. Lapeyre et al. (2006) use numerical simulations to show that surface
frontogenesis increases stratification in the upper 2000 m of the water column through efficient
stirring of density fronts near the surface. Seismic images reveal long continuous reflections on
the light side of the front and more chaotic reflectivity on the dense side. Long and continuous
reflections indicate stratified fluid since they tend to track isopycnals (Holbrook et al., 2013).
Thus it is possible that the characteristic reflectivity on either side of the front is a consequence
of induced secondary circulation. Furthermore, calculated buoyancy frequency distributions reveal
high stratification that tracks the deepening frontal interface, consistent with the induced secondary
circulation stratification. Furthermore, restratification caused by frontogenesis is maximum at the
surface and decreases with depth resulting in an exponential profile of N2 as a function of depth
(Lapeyre et al., 2006). A similar exponential trend in buoyancy frequency measurements is observed
here (Figure 4.2h and 4.15e).
Thomas & Ferrari (2008) investigated the relative importance of stratification modification induced
by frontogenesis or friction in the mixed layer (i.e. upper ∼100 m). Frictional forces can be induced
by external wind stress or spindown of the current itself. Thomas & Ferrari (2008) find that for
typical wind stress magnitudes of 0.1 N m−2, mixed layer depths, and cross-front density gradients,
friction dominates frontogenesis in the modification of stratification near the surface. Frictional
forces may modify stratification by inducing Ekman flow that differentially advects density. Friction
can either stratify or de-stratify the fluid depending upon the orientation of forces, lateral buoyancy
gradient and geostrophic flow. If winds are orientated in the same direction as the frontal jet then
Ekman flow will advect dense water to the light side of the front. The induced Ekman flow causes
convection and stratification to be reduced (Thomas & Lee, 2005; Thomas & Ferrari, 2008; D’Asaro
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 142
et al., 2011). Average wind stress during the seismic survey was 0.08 Pa orientated down-front,
suggesting that stratification may be reduced. Close inspection of seismic images reveals patches
of low amplitude reflectivity on the dense side of the front that may be indicative of reduced
stratification caused by Ekman flow (e.g. Figure 4.5iii; 44–50 km range, 100–200 m depth). It is
possible to test this hypothesis by calculating the depth and speed of wind induced currents. The
depth of the Ekman layer, δE , scales with the latitude and magnitude of the mixing coefficient,
given by δE =
√
2K/f . Using K ∼ 1 m2 s−1 and f ∼ 2 × 10−4 s−1 gives δE ≈ 100 m. This
estimate gives an indication of the penetration depth of wind-induced currents. Thomas & Lee
(2005) provide a scaling argument for the relative contribution of mixed layer restratification by
frontogenesis and frictionally induced flows,
γ ≡ ∆vwind
∆vfront
≈ uw∗
∆ugRo
(4.5)
where v is the horizontal flow caused induced by wind and frontogenesis effects. uw∗ is the friction
velocity caused by wind stress, τ , at the sea-surface, given by uw∗ =
√
τ/ρ. At the time of seismic
acquisition τ = 0.08 Pa toward the east. In the upper 200 m of the water column, where ρ varies
between 1025 and 1026 kg m−3, uw∗ = 8×10−3 m s−1. In the upper 100 m, ∆ug is 0.2 m s−1 (Figure
4.15i). Taking a typical value of Ro = 0.1, γ is 0.4 suggesting that the stratification modification
from frictional processes is less critical than that of frontogenic processes. This disparity is probably
due to the fast NW–SE frontal jet that reaches 1 m s−1 in the upper few hundred metres, and
dominates any Ekman induced flow (Figure 4.15i). Furthermore, the mixed layer depth, δML,
scales with δE as δML ≈ 0.44δE . Therefore the thin mixed layer effects are unlikely to be the
dominant player in this region.
4.5.3 Time-lapse Imaging of Deep Eddy
The Brazil-Falkland Confluence zone hosts an energetic eddy field that occupies a range of scales.
Here, lens-shaped sets of reflectivity that are indicative of eddies are observed at all depths with
variable dimensions. For example, a lens of 20 km length and 200 m thickness is observed at 1200 m
depth (Figure 4.13a). Several eddies are observed within the thermocline. For example, between
200 and 700 m a warm-core eddy is observed that extends 22 km horizontally (Figure 4.14c). An
unusual eddy is observed that lies on the dense side of the front, reaches lengths of 30 km and
thickness of 500 m, and rapidly grows and decays. The uniqueness of this lens plus its proximity to
the frontal interface requires further investigation. Rapid evolution of the deep eddy and adjacent
Time-lapse Imaging of the Brazil-Falkland Confluence 143
frontal interface is tracked using the four-dimensional nature of these seismic data. A 50× 1.7 km
window around the structure is extracted from each profile in Set A and B (Figures 4.18 and C.6).
Each window shows a snapshot of these structures between 10th and 17th February 2013. The
windows are shown in sequential order, each separated by approximately 14 km and 12 hours.
Qualitative assessment of the seismic profiles presented here suggest that there are significant
changes in the cross-sectional area of the deep eddy (Figure 4.18a–d). Spatial observations are
used to quantitatively constrain these changes. First, an ellipse is fit to the interpreted position
and shape of each eddy (Figure 4.18e–h). The cross-sectional area of the ellipse, A, is calculated
using A = pilh, where l and h are the horizontal and vertical radius of the eddy, respectively. Error
in cross-sectional area is calculated by propagating errors in l and h. Secondly, a straight line is
fit to the clearest frontal interface reflection that lies above each eddy (Figure 4.18e–h). The angle
from horizontal is calculated for these best-fit lines. Measured values of cross-sectional area and
tilt are shown in Figures 4.18i,j and C.6i,j. Error propagation is used to relate the uncertainties in
measured radial distances (dl and dh) into these estimates. The vertical and horizontal resolution
of these seismic images is calculated using Equations (2.24) and (2.25), respectively, and assuming
that the dominant wavelength is 38 m (based on dominant source frequency of 40 Hz and average
sound speed of 1530 m s−1). Calculated resolutions are 10 m vertically and 120 m horizontally.
To account for subjectivity of interpretation, 50 m is added to both of these values based on the
vertical thickness of reflections.
Between the 11th and 13th February, the cross sectional area of the eddy increases by an order
of magnitude to 14 km2. After the 13th February the cross-sectional area decreases to <1.2 km2
(Figures 4.18i and C.6i). Tilt is inversely related to the eddy size (Figures 4.18j and C.6j). Large
cross-sectional areas correspond to small tilts, suggesting that as the eddy grows in size it deflects the
frontal interface upwards, forcing the plane closer to horizontal. Before considering the dynamical
implications of this structure, its shape and transient (or non-transient) nature must be established.
Since these seismic profiles were not acquired simultaneously, there are three possible explanations
for the apparent change in area. First, the eddy may advect across the seismic survey. Secondly,
two small eddies are imaged at each location of Set A and B. Finally, it is hypothesised that the
eddy rapidly evolves over time yet remains coincident with the front.
First, it is assumed that the eddy advects across the survey in a direction perpendicular to the
main current flow (i.e. 131). Assuming that the eddy shape is consistent over this period of time,
the apparent change in cross-sectional area is due to imaging different portions of the lens (Figure
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 144
Figure 4.18: Temporal evolution of frontal interface and deep eddy. Images separated by ∼1 day
and 1 km with acquisition date annotated. Windows are 50 km × 1.7 km. (a) Profile 1. (b) Profile
2. (c) Profile 3. (d) Profile 4. (e–h) Interpretation of panels (a–d). Black polygon = identifiable
eddy structures; red ellipse = best-fitting ellipses to observed eddies; red line = best-fitting line
to clearest frontal interface reflection close to eddy. (i) Black circles = cross-sectional area, A, as
function of time calculated using, A = pilh, for ellipses shown in (e–h). (j) Black circles = tilt of
clearest frontal reflection close to eddy calculated from straight lines shown in (e–h).
Time-lapse Imaging of the Brazil-Falkland Confluence 145
4.19b). Figure 4.15g shows geostrophic currents that have been calculated perpendicular to the
frontal interface. These currents suggest a southeastward jet of up to 0.8 m s−1 that is focused on
the light side of the front and decreases with depth. The seismically imaged eddy in this profile is
located at 60 km range and 800 m depth. The geostrophic current at this depth is 0.2 m s−1 (Figure
4.15g). Assuming the eddy is embedded in the southeastward geostrophic flow and speed remains
constant, the eddy will travel 121 km in 7 days. This distance is one order of magnitude greater
than the distance between Set A and B (i.e. 14 km). If the eddy were embedded in the eastward
geostrophic flow of 0.2 m s−1, and assuming it is approximately 20 km in diameter, its entire body
would advect past the area imaged by Set A and B in 1.2 days. Since these observations are spread
over 1 week, the eddy would not be observed multiple times suggesting that this hypothesis is
unlikely.
Secondly, it is assumed that an eddy has been imaged at each location of the fours profiles that
comprise Set A and B (Figure 4.19a). In this way, Set A images a single eddy at four locations
across the lens (Figure 4.19c). This hypothesis implies that eddies advect in the along-front direction
coincident with the front. Furthermore, the two eddies are less than 20 km in width. In this way,
each two-dimensional profile within a set of four captures a different portion of the ellipsoid, creating
apparent variations in the cross-sectional area (i.e. large and small cross-sectional areas cut across
the centre and edge of the eddy, respectively). To test this hypothesis it is assumed that the eddy
is an oblate spheroid and each seismic profile has imaged the eddy parallel to its semi-major axis,
therefore each eddy cross-section can be described by the equation for an ellipse. Assuming that
the largest cross-section is an ellipse centred on x- and y-coordinates of (0,0) where x and y are the
horizontal and vertical axes, it is possible to extract the radii along these axes, a and b, from the
seismic image. From Figure 4.18b a = 15 km and b = 0.4 km. In Cartesian coordinates where the
origin is the centre, the equation of an ellipse is given by
x2
a2
+
y2
b2
= 1. (4.6)
Given a = 15 km, b = 0.4 km, y is calculated for the eddy that is seismically imaged 1 km away
from the center, i.e. x = 1 km . Using these values, y = 0.4 km. The observed value of y is 100 m,
which 75% less than the modelled value of y (Figure 4.18c). This large mismatch in the observed
and modelled area suggest that this hypothesis is also unlikely. Furthermore, for such a dramatic
change in y, the eddies would need to be closer to prolate rather than oblate, which is dynamically
unlikely.
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 146
Figure 4.19: Three hypotheses for cross-sectional area change of eddy. (a) Cartoon showing
racetrack acquisition configuration of three-dimensional seismic data. Black dashed lines = path of
seismic vessel; thick coloured lines = three-dimensional swath of ocean collected during each pass
coloured by time of acquisition; arrows = direction of acquisition; thick black line = orientation of
four cross-sections shown in (b–d) at t1, t2, t3 and t4. (b) A single eddy advects southeastward (i.e.
cross-front). (c) Edge and centre portions of a single eddy are imaged as lens advects southeastward
(i.e. along-front). (d) A single eddy is imaged which grows and decays during observation period
whilst advecting southeastward (i.e. along-front). Boxes orientated perpendicular to seismic profile
(NW–SE); black ellipses = eddy; coloured dashed line = vertical cross-section of water column
imaged by central profile of each seismic swath coloured by time of acquisition; thick line = imaged
portion of eddy that produces characteristic acoustic blank patch coloured by time of acquisition;
black arrows = cross-front advection; cross surrounded by circle = along-front advection (i.e. motion
out of page).
Time-lapse Imaging of the Brazil-Falkland Confluence 147
Finally, it is hypothesised that the structure does not move spatially, apart from to advect in the
along-front direction, but evolves rapidly with time (Figure 4.19d). A set of 8 seismic profiles
acquired two months after Set A and B, during April 2013, revealed a strikingly similar set of
dipping reflectivity that was also paired with a lens (Figure C.1 and C.2). These acoustic patterns
are interpreted as a second independent observation of a frontal interface and deep eddy and imply
that the eddy and front are dynamically linked. This eddy is of similar length scales (∼20 km length
and ∼400 m thickness). Set C and D seismic profiles show a disrupted patch of reflectivity on the
dense side of the front that appears to coalesce into a well-resolved lens in two days (Figure 4.11).
This rapid development is strikingly similar to the growth and decay of the deep eddy of O(3) days
observed in seismic profiles Set A and B. It is well known that the Brazil-Falkland Confluence
region is rich in eddies, however it is unlikely that sixteen seismic profiles spaced two months apart
have captured a chance meeting of an eddy and frontal interface twice. It is more likely that the
deep eddy is intrinsically linked to the frontal interface. This conclusion is summarised along with
others made in this Chapter in Figure 4.20.
The rapid growth and decay of O(3) days is compared to an estimate of frictional spin-down given
by Pedlosky (1987) as
τ =
h√
2K|f | , (4.7)
where h ∼ 200 m is vertical scale of motion, f ∼2×10−4 s−1 is Coriolis frequency and K is diapycnal
diffusivity of an eddy. K is measured by applying spectral methods to tracked seismic reflection,
yielding a value of 10−3 m2 s−1 in the vicinity of the deep eddy (Chapter 4). These values yield
τ = 3.4 days. This estimate implies that the observed eddy decays in ∼3 days, and is consistent
with seismic observations of rapid growth and decay. It is possible to conclude that these seismic
images have captured rapid growth and decay of a deep eddy that advects with the frontal interface.
This conclusion suggests that the eddy and front are dynamically linked and may be ubiquitous
features of this frontal region. The maximum horizontal length of the eddy if ∼30 km, which is of
the same order as the separation between Set A and B. Therefore, it is reasonable to assume the
eddy is symmetrical and ellipsoidal in shape. At its largest, 32 km diameter and 500 m height, the
volume of the eddy is >250 km3. The rapid generation and diffusion of this large structure raises
important questions about the dynamics controlling its formation.
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 148
4.5.4 Generation Mechanisms of Deep Eddy
The deep eddy has several key features that can be used to discern its dynamics. First, the
structure forms a lens-shape. The upper and lower boundary are convex and concave, respectively,
and surround an acoustically blank center. The lens is tilted along the frontal interface. Secondly,
the lens is repeatedly observed at the front and demonstrates similar behaviour at each observation.
These repeat observations suggest that fronts in this region have a common structure over time,
implying that the confluence is forced in similar ways during February and April 2013, at least.
Finally, the lifetime of the lens is evidently short.
Lenses of water with anomalous properties have been known to exist in the world’s oceans for
decades. Satellite imagery typically show that wavelike meanders of frontal interfaces are ubiquitous
features. Meander growth increases until a lens of water is cut off from the main front thereby
generating an eddy (Vallis, 2006). These eddies are persistent features in frontal regions and are
O(100) km diameter, with clear surface expressions in sea-surface temperature (e.g. Lee et al.,
1991; Adams et al., 2017). For example, satellite and hydrographic data acquired during 1984
across the southwest Atlantic Ocean reveal three large eddies of O(100) km. These eddies were
identified by sea-surface temperature measurements then targeted using hydrographic data acquired
by research vessel. Anomalous temperatures were clearly visible in surface water characteristics,
with magnitudes of ∼1◦C (Gordon, 1989). Since the eddy observed here lies at 800 m depth and has
no clear surface expression, it is possible to rule out frontal meandering as a generation mechanism.
Absence of anomalous patches of water in regional sea-surface temperature measurements that
were acquired during seismic surveying supports this inference (Figure 4.9). Abyssal eddies have
been observed in the southwest Atlantic Ocean between 2800 and 4800 m. This anticyclonic
eddy was observed at ∼46 ◦S, 53 ◦W, and was identified by its distortion of isopycnals. The
homogeneous core extended 77 km horizontally and 2 km vertically (Gordon & Greengrove, 1986).
Gordon & Greengrove (1986) suggest that this eddy is a product of local topography and circulation
interaction. It is unlikely that the eddy observed here is caused by topographic interactions since
its core is approximately 1 km above the seabed. Moreover, deep eddies that have rapid lifetimes
are observed in Set A/B and C/D which are acquired in areas of different bathymetry (Figures 4.7,
4.8, 4.11, 4.12). The maximum dip of the seafloor in Set A and B is 6◦, and is even less in Set C
and D. The distance between the eddy and seabed, plus smooth seafloor gradients, implies that
topographic interaction is not a likely generation mechanism. Furthermore, the diameter of this
eddy which is between 10 and 40 km distinguishes it as either small mesoscale to sub-mesoscale.
Time-lapse Imaging of the Brazil-Falkland Confluence 149
Sub-mesoscale lenses that lie in the stratified interior of the worlds ocean (>100 m depth) are
referred to as intra-thermocline eddies or sub-mesoscale coherent vortices (Dugan et al., 1982;
McWilliams, 1985). Intra-thermocline eddies are characterised by a central core with weak strat-
ification and anticyclonic circulation (Thomas & Ferrari, 2008). These lenses are azimuthally
symmetric and coherent. Finally, the horizontal width is small relative to the first baroclinic radius
of deformation (Thomas & Ferrari, 2008). The lens that is observed in seismic sections matches
all of the characteristics of an intra-thermocline eddy except the latter. The Rossby radius of
deformation is given by
LR =
Nh
npi|f | , (4.8)
where N is buoyancy frequency, h is characteristic height and n=1... represents the nth baroclinic
wave. The front is deeply penetrating suggesting h ∼ 2000 m. Average survey latitude is 37 ◦S
giving f ∼2×10−4 s−1. A background stratification of N = 1 × 10−5 s−1 is assumed based on
hydrographic measurements at depths of 800 m (Figure 4.2f). These values give LR ∼ 9 km. LR is
consistent with the numerical prediction of an intra-thermocline eddy which has a horizontal and
vertical radius of 6 km and 32 m shown by Thomas & Ferrari (2008). Yet, the deep eddy that
has been acoustically imaged here has a maximum horizontal and vertical length of >25 km and
200 m, which is one order of magnitude greater than LR and the modelled results of Thomas &
Ferrari (2008). However, N calculated from converted profiles of temperature and salinity suggest
that there is an area of highly stratified water that follows the frontal interface. This peak in N
is corroborated by near coeval hydrographic data that show strong stratification at similar depths
(Figure 4.15e,f). The distribution of N suggest that at the depth of the eddy, stratification is
much higher than the background field. Given N = 6× 10−5 s−1, LR ≈ 22 km. It is possible that
significant levels of stratification allow generation of large intra-thermocline eddies. Such large
values of N2 may be generated by the secondary ageostrophic circulation discussed above since this
induced circulation is known to restratify the water column (Lapeyre et al., 2006). The properties
of the deep eddy observed here share similarities with intra-thermocline eddies or sub-mesoscale
coherent vortices so the generation of these structures are now discussed.
Several mechanisms of generation have been proposed for intra-thermocline eddies that rely on the
creation of weak stratification and anticyclonic vorticity water masses. The mechanism must be
spatially intermittent so that the anomalous water becomes isolated. Thomas & Ferrari (2008)
propose mechanisms of intra-thermocline eddy generation at wind-driven upper ocean fronts. Me-
anders isolate anomalous water that then subducts along the frontal outcrop into the stratified
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 150
interior. This mechanism requires that the frontal interface outcrops in a region of strong baroclin-
icity and wind forcing that is orientated down-front. Although it does not appear that the front
observed here meanders at the surface, the region is characterised by down-front wind-forcing. The
mechanisms proposed by Thomas & Ferrari (2008) are similar to that of Spall (1995) who sug-
gested intra-thermocline eddies may be formed at meandering fronts that have an initial gradient
in physical properties. Alternative mechanisms include patchy diapycnal diffusivity that subse-
quently spins up anticyclonic vortices by geostrophic adjustment (McWilliams, 1985). D’Asaro
(1988) suggest that flow separation triggered by variations in bathymetry may drive formation of
coherent bodies. The key difference between the mechanisms listed above and the observations
presented here are threefold. First, the size of the eddy is mesoscale as opposed to sub-mesoscale.
Secondly, the eddy appears to be intrinsically linked to the front (i.e. it is not isolated). Thirdly,
the generation mechanisms proposed by Thomas & Ferrari (2008) require 10 inertial periods (ap-
proximately 7.8 days) for the the intra-thermocline eddy to form and subduct approximately 80 m.
Structures imaged here do not appear to change from an average depth of 800 m and, critically,
form and decay over 7 days. Finally, these eddies are restricted to the upper few hundred metres.
Deeper sub-thermocline eddies have been observed in the 300–800 m depth range in the northwest-
ern Pacific using 14 years of Argo Float data (Chang et al., 2016). 337 lenses that trap cold and
fresh water have vertical and horizontal scales between 100 and 200 m and 5–15 km. However,
an important characteristic of these eddies is that they are long-lived and carry anomalous water
properties thousands of kilometres away from their formation site (Chang et al., 2016). Observa-
tions presented here reveal a complete frictional spindown of the eddy within 3 days, suggesting
that these mechanisms do not describe the dynamics shown here.
An eddy is observed with horizontal and vertical length scales of up to 30 km and 500 m, respec-
tively, which is inconsistent with observations of surface and abyssal eddies in the southwest Atlantic
Ocean. Presented arguments imply that the rapid evolution of this eddy is caused by changes in
its size rather than location. Its observed scale and duration are inconsistent with previous analyt-
ical and numerical studies of intra-thermocline eddies. Modelled intra-thermocline eddies are less
than 10 km radius and consistent with the Rossby radius of deformation. Assuming a background
stratification, the observed eddy is far larger than LR of O(10) km. However, calculated buoyancy
frequencies reveal a band of stratification along the frontal interface that is six times greater than
background stratification. This band implies LR of O(20) km, which is consistent with acoustic
eddy observations. High stratification may be generated by frontogenically induced ageostrophic
circulation. Another important inconsistency between these observations and previous analytical
Time-lapse Imaging of the Brazil-Falkland Confluence 151
Figure 4.20: Idealised sketch of deep reaching front at Brazil-Falkland Confluence. Cartoon
shows the main components of frontal dynamics including frontal interface and deep eddy. Thick
black arrows = direction of confluent flow; thick white arrow = average wind stress direction; thin
solid black arrows = horizontally averaged current field from internal wave speed measurements
and calculated geostrophic currents; thin black dashed arrows = thermally direct ageostrophic
secondary circulation; curved arrows = rotation of eddy about a vertical plane; TW = Tropical
Water; SAAW = Sub-Antarctic Water; SACW = South Atlantic Central Water; AAIW = Antarctic
Intermediate Water; NADW = North Atlantic Deep Water; UCDW = Upper Circumpolar Deep
Water.
and numerical studies of intra-thermocline eddies is the lifetime of the structure. However, its du-
ration is consistent with scaling arguments of frictional spin-down (Pedlosky, 1987). Since studies
of fronts are generally restricted to the upper few hundred metres or have low spatial resolution,
it is possible that the dynamics creating the eddy here have not been observed previously. It is
also possible that the large depth extent of the front may affect the properties of generated ed-
dies. Nevertheless, the discrepancy between these observations and current models implies that the
processes captured here are not fully accounted for dynamically and warrant further investigation.
4.6 Conclusions
A three-dimensional seismic survey has been used to investigate the nature and dynamics of a
deep penetrating front in the southwest Atlantic Ocean (Figure 4.20). First, the frontal interface
is marked by bright dipping reflections that extend to 1800 m depth. Secondly, the front separates
K.L. Gunn, Ph.D. Dissertation
Time-lapse Imaging of the Brazil-Falkland Confluence 152
two distinct regions of the water column. In the northeast, the fairly quiescent warm Brazil Current
flows southwards. The vertical water structure is characterised by horizontally continuous reflec-
tions. The Falkland Current flows toward the north and appears to be significantly more energetic
due to the abundance of mesoscale to sub-mesoscale reflectivity patterns that evolve rapidly with
time. Thirdly, a lens-shaped pattern of reflectivity is observed on the dense flank of the front at
approximately 750 m depth. Numerous, sub-mesoscale reflective pattern are identified across all
profiles at all depths. Three-dimensional cross-sections reveal that the thermohaline structure is
homogeneous in the cross-front direction, NW–SE, and that there are significant gradients of phys-
ical properties in the along-front direction, NE–SW. The front is long-lived. These observations are
corroborated by regional sea-surface temperature variations. The front migrates southwards with
a speed of O(10) km day−1. Seismic images are converted into two-dimensional profiles of temper-
ature, salinity, potential density and buoyancy frequency. The long wavelength vertical structure
is well-recovered and match near-coeval hydrographic data well. Furthermore, the methodology
described here can be applied to any uncalibrated seismic survey, which means that substantial
archives of legacy surveys covering most continental margins can be exploited. The speed of inter-
nal waves across the frontal zone are measured from pre-stack seismic data. These measurements
constrain large-scale current flow and indicate convergence at the frontal interface as expected. The
nature and dynamics of a deep eddy are discussed. Its observed scale and duration are inconsistent
with analytical and numerical studies of intra-thermocline eddies suggesting that the processes
imaged here are not fully accounted for in models. Nevertheless, its duration is consistent with
scaling arguments of frictional spin-down.
Chapter 5
Estimating Diapycnal Diffusivity from Seismic
Images
5.1 Introduction
Renewal of deep water masses (i.e. overturning) plays a primary role on our climate, through
uptake, transport, and storage of heat and carbon in the ocean. Overturning circulation is fed by
waters that become dense enough to sink into the ocean abyss at high latitudes and return to the
surface through complex three-dimensional pathways (Vallis, 2006). While it is well established
that most sinking is confined to the Labrador and Greenland Seas in the North Atlantic and the
Weddell and Ross Seas around Antarctica, the return pathways are less constrained (Talley et al.,
2011). Upwelling is caused by energetic turbulence induced by breaking internal gravity waves,
which provide energy to lift dense water toward the surface. This vertical density flux leads to
mixing of the stably stratified ocean (Wunsch & Ferrari, 2004). Upwelled water ultimately flows
back to sinking regions, thereby completing the overturning loop. Gyres are a key component of
large-scale meridional overturning circulation since they connect tropical and polar waters. The
Brazil-Falkland Confluence is a region of subtropical-subantarctic water exchange and therefore is
likely to play a key role in the southern limb of Atlantic overturning (Jullion et al., 2010).
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 154
Munk (1966) presented the first basin-scale mixing estimates in the ocean. He assumed a uniform
upwelling of cold, deep water over the entire abyssal ocean. Energy required to maintain a steady
state against the resultant advected heat, or salt, is derived from the diffusive downward mixing
of surface warm, or salty, water, giving a steady-state advection-diffusion equation of the form,
w∂ρ/∂z = Kp∂ρ
2/∂z2, in which w is the speed of upwelling water and Kp is the diffusion coefficient
of mass. Where density variations are dominated by those of temperature, it is assumed that the
diffusion coefficient of mass, Kp, is equal to that of heat, Kt. Using w = 0.1 cm day
−1, estimated
from rates of high-latitude bottom water production, Kt is 10
−4 m2 s−1 (Munk, 1966; Munk &
Wunsch, 1998). Aside from assuming large-scale conservation principles, mixing rates in the ocean
can be inferred in a number of ways. Temporally averaged basin-wide mixing rates may be inferred
from tracking the spread of inert tracers (e.g. Ledwell et al., 1998). Direct measurements of
turbulent dissipation rates may be obtained by means of shear probes (e.g. Osborn, 1980). Finally,
shear and strain spectra computed from lowered ADCP and CTD profiles can be used to infer
mixing rates (e.g. Thompson et al., 2007). Rates of Kt measured within the thermocline are an
order of magnitude less (i.e. 10−5 m2 s−1) than this inferred whole ocean average (Gregg, 1989;
Ledwell et al., 1993). However, recent observations in the deep ocean have revealed that turbulence
is greatly enhanced (i.e. 10−4 m2 s−1) 1–2 km above the seafloor in regions of rough bottom
topography (e.g. Polzin et al., 1997; Ledwell et al., 2000). Today, it is thought that widespread
and small-scale mixing drives upwelling of the densest waters through internal wave impingement
on topography, enhanced atmospheric forcing, rough bathymetry and elevated eddy and internal
wave energy levels (e.g. Whalen et al., 2012; Kunze, 2017).
Frontal regions, such as the Brazil-Falkland Confluence, have been linked to enhanced turbulence
and energy dissipation (D’Asaro et al., 2011; Johnston et al., 2011). For example, mixing rates
exceeding the background value by a factors of 10-1000 are widespread in the fronts of the Southern
Ocean directly above rough bathymetry (Garabato, 2004). Quasi-geostrophic and semi-geostrophic
theory as well as numerical models indicate that vertical circulation is enhanced at frontal regions
due to baroclinic instabilities (Chapter 4). Downwelling is intensified on the dense side of the front
whilst more diffuse upwelling occurs on the light side of the front (Hoskins & Bretherton, 1972).
Strong downwelling may distort lateral buoyancy gradients and enhance mixing whilst upwelling
can restratify the water column (Lapeyre et al., 2006; Capet et al., 2008a,b; Nagai et al., 2012).
Although observational evidence of enhanced turbulence near fronts has increased, the detailed
mechanisms responsible for increased dissipation and their relative importance is still unclear (e.g.
Molemaker et al., 2005; Thomas & Ferrari, 2008; Taylor & Ferrari, 2009). Furthermore, increased
Estimating Diapycnal Diffusivity from Seismic Images 155
stratification (i.e. regions of low mixing) at fronts inhibit vertical motions and trigger enhancement
of primary production (Strass et al., 2002; Taylor & Ferrari, 2011). However, few observations have
both the spatial resolution and coverage to reveal the entire distribution of mixing surrounding
these ubiquitous features. Most investigations of mixing around fronts are constrained to the
upper ∼300 m of the water column (D’Asaro et al., 2011; Johnston et al., 2011; Nagai et al., 2012).
Thus, a technique that will reveal mixing distributions around fronts with large spatial coverage
whilst maintaining high resolutions will help to improve our understanding of large-scale circulation
and its link with climate, primary productivity and the dissipation of kinetic energy.
The patchiness of oceanic mixing leads to fundamental measurement and interpretation problems.
Mixing distributions are not well described by sparse ship based observations since the patterns
are both spatially and temporally intermittent (Whalen et al., 2012). Furthermore, since turbulent
mixing is small-scale it is represented in ocean models by a variety of parameterisations that
approximately reproduce observed water mass structures and mixing distributions (Marshall &
Zanna, 2014). Due to these observational constraints, the question of how much and where mixing
occurs is still debated (Ivey et al., 2008). As a result of the enhanced lateral resolution and large
spatial coverage provided by seismic reflection profiling, the resultant images provide an important
new tool with which to investigate spatial and temporal variability of kinetic energy dissipation.
Seismic datasets can span a few hundred kilometres in length, a few hundred meters in width, and
extend to abyssal depths. Moreover, fast imaging leads to near-instantaneous maps of temperature
gradients within the water column which can be used to infer mixing rates. Holbrook & Fer (2005)
first showed that horizontal wavenumber, kx, spectra of tracked seismic reflectors carry information
about the oceanic internal wave field. From these spectra, it is possible to estimate the turbulent
dissipation rate, ε, and diapycnal diffusivity, K, that are commonly used to quantify mixing.
Spectral analysis of processed seismic images reveals clear internal wave, turbulent, and noise sub-
ranges. Subsequent work has corroborated the sensitivity of the seismic method to internal waves,
although wavenumber spectra may be distorted in the presence of strong currents (Krahmann et al.,
2009; Vsemirnova et al., 2009). The wealth of seismic observations can be used to investigate the
spatial and temporal pattern of diapycnal diffusivity. This capacity is particularly important since
mounting evidence suggests that upwelling occurs in localised regions of high mixing (Kunze, 2017).
Here, seismic images from a three-dimensional survey across the Brazil-Falkland Confluence are
spectrally analysed. The aims of this chapter are threefold. First, it is shown how spectral analysis
of seismic imagery can be used to characterise the oceanic internal wavefield. Secondly, spatial and
temporal patterns of diapycnal diffusivity around the frontal region are presented and analysed.
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 156
Finally, possible mechanisms of mixing and their implications are discussed. A series of significant
parameters and equations will be introduced in the following sections and are summarised in Table
5.1.
5.2 Energy Density Spectra
Internal waves form in the ocean when its stratification is disturbed. Frequency, vertical and
horizontal wavenumber (kx) domain representations of internal wave energy reveal remarkably
uniform energy density spectra in the open ocean. These spectra mostly agree with the Garret-
Munk model spectrum, which has a power law of k−2x (Garrett & Munk, 1975; Gregg, 1989). The
spectrum is maintained by a cascade of energy from large-scale internal wave generating processes
such as winds and tides to small-scale turbulent motions. At these small length scales, turbulence
irreversibly converts kinetic energy. Small length scales correspond to high wavenumbers, and it is
these high wavenumbers that are dominated by turbulence. The spectral slopes exhibit Kolmogorov
behaviour characterised by k
−5/3
x . Typically, energy density spectra are calculated using in situ
hydrographic measurements, yet recent work has shown that acoustic imaging can be used to
quantify the oceanic internal wave and turbulent wavefields since energy density spectra are related
to vertical displacements of density that are manifest in seismic reflections. Holbrook & Fer (2005)
compare seismically inferred energy density spectra with the Garret-Munk spectrum from seismic
transects in the Norwegian Sea. Measurements from seismic images show a good match to the
Garrett-Munk spectrum (that has a power-law slope of −2), strongly suggesting that seismic images
are able to quantify the internal wave field. Krahmann et al. (2008) obtain spectra from the Iberian
Peninsula that show similar characteristics to those of Holbrook & Fer (2005). Seismic images have
been used in a variety of locations to identify internal wave and turbulent spectral sub-ranges in
order to quantify mixing rates. This methodology provides a significantly greater horizontal and
vertical coverage of diapycnal diffusivity when compared to towed instruments. Such estimates
reveal that mixing rates are spatially heterogeneous with hotspots of elevated mixing that can be
linked to specific generation mechanisms such as lee waves (Fortin et al., 2016; Dickinson et al.,
2017).
Following the method of Holbrook et al. (2013), the energy spectrum of the ocean is interrogated
by tracking and spectrally analysing reflections from stacked seismic images. To ensure spectra
are unaltered by seismic processing, no trace mixing nor deconvolution should be applied (Figure
Estimating Diapycnal Diffusivity from Seismic Images 157
5.1a,b). First, each trace of seismic amplitude is converted to the cosine of the instantaneous phase
angle; a seismic attribute used to emphasise the continuity of reflections which does not affect
the resolution of the image (Holbrook et al., 2013). Reflections can be tracked by contouring a
constant value of instantaneous phase. The choice of contour value does not affect the form of
tracked reflections, but may change the quantity (Dickinson et al., 2017). Secondly, midpoints of
tracked reflections are extracted, providing time series coordinates of kx. Midpoints of tracked
reflections now represent vertical density displacements (Figure 5.1c). Thirdly, power of vertical
displacement, Φξ, as a function of kx is calculated from each linearly detrended tracked reflection
using a multi-taper Fourier Transform, F (kx), where Φξ = |F (kx)|2 (Thomson, 1982). Φξ provides
a description of the power distribution of the decomposed signal as a funtcion of kx (Figure 5.1d).
Finally, horizontal wavenumber power spectra are converted to power spectra of the horizontal
gradient of vertical displacements, Φξx (i.e. slope spectra; Figure 5.1e). Horizontal wave number
spectra are multiplied by (2pikx)
2 to create Φξx , which highlights the transition between internal
wave and turbulent spectral sub-ranges (Klymak & Moum, 2007a,b). Before estimating diapycnal
diffusivity three preliminary steps are carried out to assess the suitability of each seismic image for
spectral analysis.
Table 5.1: Constants and variables used in mixing analysis. GM = Garrett-Munk.
Description Symbol Unit
Turbulent dissipation rate ε m2 s−3
Reference (GM) turbulent dissipation rate εr m
2 s−3
Turbulent flux coefficient Γ -
Diapycnal diffusivity K m2 s−1
Horizontal wavenumber kx cycle/m
Ozmidov length scale lO m
Buoyancy frequency N s−1
Local mean buoyancy frequency N s−1
Power spectrum of vertical displacement Φξ m
2 cpm−1
Slope spectrum Φξx cpm
−1
GM slope spectrum ΦGMξx cpm
−1
Density ρ kg m−3
Local shear-strain ratio Rω -
Shear-strain ratio of GM wavefield RωGM -
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 158
Figure 5.1: Estimating diapycnal diffusivity from seismic images. (a) Seismic reflection Profile 1
where red/blue stripes correspond to vertical displacements in density within water column. Thick
black box = zoomed portion shown in (b). (b) Zoomed portion of seismic reflection data. (c)
Black lines = tracked reflection midpoints; thick black line = spectrally analysed tracked reflection
shown in (d). (d) Φξ as function of kx calculated using multi-taper Fourier Transform from linearly
detrended tracked reflection shown in (c). Internal wave, turbulent and noise sub-ranges charac-
terised by −2, −5/3 and 0 spectral slopes, respectively. Vertical dashed line = white noise cutoff.
(e) Φξx as function of kx calculated by multiplying Φξ shown in (d) by (2pikx)
2. Internal wave,
turbulent and noise sub-ranges characterised by −1/2, +1/3 and +2 spectral slopes, respectively.
Thin black line = model fit to sub-ranges; blue portion of spectra = identified turbulent sub-range;
vertical dashed line = white noise cutoff.
Estimating Diapycnal Diffusivity from Seismic Images 159
5.3 Seismic Images
Seismic images that reveal the spatial and temporal nature of thermohaline structure around a
deeply penetrating front have been chosen to investigate the distribution of diapycnal diffusivity
(Chapter 4). The frontal interface extends to 1800 m depth and is long-lived. The reflectively
structure and thermohaline properties of the region have been previously discussed (Chapter 4).
5.3.1 Assessing Suitability for Spectral Analysis
First, direct data transforms are used to provide a preliminary assessment of the spectral content
of an acoustic image (Holbrook et al., 2013). At any given depth slice across the seismic image,
the kx spectrum of seismically observed amplitudes is calculated. Averaging spectra over a range
of depths and multiplication by (2pikx)
2 yields horizontal gradient spectra that reveal the oceanic
spectral content captured by that image. Direct data transforms provide a first-order assessment of
the horizontal wavenumber content of the seismic image. Secondly, the signal-to-noise ratio, SNR,
of the seismic image is calculated. The signal-to-noise ratio between two adjacent traces is defined
as
SNR =
√
|c|
|a− c| , (5.1)
where c is the maximum value of the cross correlation between these traces, and a is the value
of the zero-lag autocorrelation of the first trace (Holbrook et al., 2013). A lower threshold of 4 is
recommended to estimate robust values of diapycnal diffusivity (Holbrook et al., 2013). Finally,
average spectra are calculated from vertical displacement series using a Welch Transform (Welch,
1967). The Welch Fourier Transform splits the signal into half-overlapping segments. Each segment
is linearly detrended and windowed by multiplication with a Hanning window. The Hanning window
acts as a weighting function that removes edge effects caused by the application of any Fourier
Transform. The Fourier Transforms of all weighted segments along the split reflection are found
and averaged. The averaged values provide spectral density information for each tracked reflection
of a set length. The spectral density information for all reflections in a chosen window are averaged
together providing the final spectra. Since Welch’s method uses segments to calculate spectral
density information, kx are the same for each series of vertical displacement. In this way, the Welch
Transform allows spectra to be averaged at the same values of kx. Power is averaged in log(kx)–
log(Φξx) space since ε has a log-normal distribution. These spectra provide a final assessment of the
spectral content of the image, and are less affected than direct data transforms by image frequency
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 160
and amplitude content (Holbrook et al., 2013). Seismic images shown here have been assessed for
their suitability for spectral analysis using the preliminary diagnostics described above. Direct data
transforms, signal-to-noise ratio and average spectra for sub-regions across a representative seismic
image are shown in Figure 5.2.
Direct data transforms reveal a two-part spectrum composed of internal and turbulent sub-ranges.
In most cases these sub-ranges show slopes close to the predicted values of −1/2 and +1/3, respec-
tively (Figure 5.2a,d,g,j). There is a fairly sharp transition between the internal wave and turbulent
sub-range (e.g. Figure 5.2g; kx ∼ 10−2 cpm). The signal-to-noise ratio of each of the examples
shown in Figure 5.2 is above the value of 4 recommended by Holbrook et al. (2013). Spectra reveal
that the turbulent sub-range, with a slope of +1/3, can extend to the highest wavenumbers that
correspond to ∼15 m (Figure 5.2a,d,g,j; 10−1.2 cpm). However, sharp peaks in the amplitude of
spectra at wavenumbers of 10−1.7, 10−1.4, and 10−1.2 cpm show that harmonic noise disrupts this
portion of the spectra. This noise is an effect of seismic survey geometry that leads to harmonic
changes in the amplitude of incoming reflected energy.
Shot spacing, ∆s, creates harmonic noise spikes, ks, at integer multiples of the shot spacing
wavenumber, ks. ks is given by n/∆s where n is any integer (Holbrook et al., 2013). ks is the
wavenumber at which recorded traces have identical ray geometry and therefore will constructively
stack with an abnormally high amplitude. In this survey, CMP spacing is 6.25 m and shot spacing is
∆s = 50 m. Therefore harmonic noise spikes occur at |ks| =0.02, 0.04 and 0.06 cmp, corresponding
to kx =10
−1.7, 10−1.4 and 10−1.2 cpm (Figure 5.2a,d,g,j). Though present at all depths, harmonic
noise weakens as depth increases since raypaths for adjacent CMPs become more similar (Holbrook
et al., 2013). It is possible to remove harmonic noise spikes following the method of Holbrook et al.
(2013). First, data are transformed into the two-dimensional Fourier domain. For each wavenum-
ber, the sum of all frequencies is plotted revealing sharp spikes in amplitudes (Figure 5.2b,e,h,k).
Noise spikes at kx = ks are attenuated using a bandstop notch filter centred over the spikes in the
kx domain. This filtering technique was applied to the Uruguay dataset, yet was found to enhance
rather than suppress harmonic noise. Holbrook et al. (2013) use bandstop notch filtering to remove
sharp noise spikes across a two-dimensional seismic dataset. The maximum width of these spikes
is ∼0.0005 cpm. kx spectra from the Uruguay survey reveal harmonic spikes of 0.01 cpm width
(Figure 5.2b,e,h,k). These wide harmonic noise spikes are the result of binning three-dimensional
seismic data. Here, along-swath stacks are extracted whereby CMPs are stacked from subsurface
points acquired in the same areal bin. Since three-dimensional surveys are exposed to feathering,
Estimating Diapycnal Diffusivity from Seismic Images 161
Figure 5.2: Assessing suitability of seismic images for spectral analysis. Direct data transforms,
wavenumber spectra and tracked reflection spectra shown for four zoomed portions of Profile 2
(see Figure 4.3 for location). Zooms are 20 × 0.15 km starting at 75, 300, 535 and 765 m depth
and 60 km range. (a) Direct data transform of zoomed portion of seismic profile at 75–225 m
depth. Amplitude plotted as function of kx. Grey reticule = slopes of representative internal wave,
turbulent and noise sub-ranges with spectral gradients of −0.5, +1/3 and +2, respectively; black
arrows = noise spikes at kx = 10
−1.7, 10−1.4 and 10−1.2 cpm caused by harmonic noise. SNR
annotated top left. (b) kx spectrum of zoomed portion of seismic profile at 75–225 m depth. Black
arrows = noise spikes at |kx| = 0.02, 0.04 and 0.06 cpm caused by harmonic noise. (c) Spectra
calculated from tracked reflections across zoomed portion of seismic profile at 75–225 m depth.
Grey lines = individual reflection spectra; black line = averaged spectra. SNR annotated top left.
(d-f) Same as (a-c) for 300–450 m depth. (g-i) Same as (a-c) for 535–685 m depth. (j-l) Same as
(a-c) for 765–915 m depth.
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 162
harmonic noise will be smeared across multiple CMPs. Along two-dimensional seismic lines CMPs
are composed of traces from planned subsurface locations thereby ensuring harmonic noise is at
ks. Thus, the application of a sharp notch filter is not effective on these data and conversely, filter
edge effects strengthen harmonic noise spikes.
Average spectra suggest that the entire spectrum is dominated by turbulence (Figure 5.2c,f,i,l;
spectral slope of +1/3). However, comparison with spectra from individual reflection tracked
reflections reveal a three-component spectra (Figure 5.2c,f,i,l). Individual spectra show that the
internal wave sub-range is highly variable. Since Welch spectra are averages, the internal wave
sub-range appears to smooth out. Furthermore, average spectra lie higher in amplitude on the
power spectra of the horizontal gradient of isopycnal displacement axis, Φξx . This is due to the fact
that higher amplitude reflections will contribute more to the final average. Nevertheless, both types
of spectra show that the effect of harmonic noise is much less when spectra are calculated from
tracked reflections. Holbrook et al. (2013) note that direct data transforms are strongly dependent
upon the frequency band of seismic images and that this dependency is significantly reduced when
spectra are calculated from tracked reflections. Holbrook et al. (2013) go on to say that tracked
reflections are less affected by harmonic noise than direct data transforms.
Finally, the implicit assumption that tracked reflections follow isopycnals is considered. This state-
ment implies that displacements in reflections represent vertical perturbations of density that are
caused by diapycnal diffusivity. Permanent thermohaline features will in general follow isopycnals
however on shorter timescales, reflections may not honour this assumption (Ruddick, 1992; Hol-
brook et al., 2013). This assumption is assessed using potential density, ρθ, distributions that have
been calculated from inverted temperature and salinity profiles (Figure 4.15c). Isopycnals reveal
that, overall, seismic reflections follow lines of equal ρθ except at sub-mesoscales. In this region the
contribution of temperature to observed reflectivity is estimated as 91% (Chapter 2). Calculated
temperature profiles show a clear correlation between reflectivity and isotherms providing confi-
dence in this estimate (Figure 4.14). It is important to make this distinction as diffusion rates for
heat and salt are different. Hence, diapycnal diffusivity that is calculated from tracked reflections is
strictly a measure of thermal diffusivity. Henceforth these values are called diapycnal diffusivity, K.
Due to the correlation of reflections with isopycnals and isotherms, it is reasonable to assume that
the perturbations in reflections tracks are caused by the oceanic internal wavefield, and therefore
can be used to estimate K.
Although direct data transforms reveal clear harmonic noise spikes, these peaks are not prevalent
Estimating Diapycnal Diffusivity from Seismic Images 163
in average and tracked spectra. Furthermore, the effect of harmonic noise is greatly reduced as
depth increases. However, the effect of harmonic noise is important to mitigate as it may act to
disrupt the slope that is fit to the turbulent sub-range. Since notch filtering is not effective here,
models are fit to each spectra using robust nonlinear regression that reduces the contribution of
outliers such as harmonic spikes. Nevertheless, observed harmonic noise in the turbulent sub-range
suggests that caution should be taken when interpreting diapycnal diffusivity at shallow depths of
<225 m. These conclusions combined with the high signal-to-noise ratios of >4 suggest that these
seismic profiles are suitable for spectral analysis.
5.3.2 Power Spectra of Horizontal Gradient of Vertical Displacements
Following the method of Holbrook et al. (2013), power spectra of horizontal gradient of vertical
displacements (i.e. slope spectra, Φξx) are calculated. Slope spectra reveal that the internal wave
and turbulent components of the oceanic energy spectrum possess distinctive regimes with unique
spectral slopes. 20 example spectra clearly reveal the unique distribution of kinetic energy for each
sub-range, thus, it is possible to classify sub-ranges of the oceanic energy spectrum (Figure 5.3).
Spectral characteristics match predicted slopes for both internal waves and turbulence well. The
internal wave regime exists at low wavenumbers, 10−3 < kx <10−2 cpm, corresponding to length
scales of >100–1000 m (Figure 5.1d and 5.3). The spectrum is red, with a slope of ∼ −0.5 and is
described well by the semi-empirical Garrett-Munk spectrum (Garrett & Munk, 1975; Holbrook &
Fer, 2005; Krahmann et al., 2008). At higher wavenumbers, kx >10
−2 cpm, internal waves break and
there is a clear transition into the turbulent regime. The spectral slope of this regime matches the
Kolmogorov exponent, −5/3 (Kolmogorov, 1941). When multiplied by (2pikx)2 to create horizontal
gradient spectra, the slope becomes +1/3. In this way, the transition from negative internal wave
slope to positive turbulent slope is highlighted (Figure 5.1d–e). White noise appears at the highest
wavenumbers with an gradient of +2 (Figure 5.1d and 5.3). These example spectra suggest that
seismic imagery can be used to recover distinct sub-ranges of energy spectra.
The Ozmidov length scale, lO, is generally interpreted as the largest vertical scale that can overturn
(Ozmidov, 1965). lO is typically 0.01–1 m, which corresponds to kx of 10
2–100 cpm. The vertical
resolution of seismic images does not generally extend higher than 10 m, therefore it is not expected
that seismic imagery will resolve vertical displacements in density that occur over lO. At vertical
length scales greater than lO (i.e. >1 m), significant density variations occur. In a strongly stratified
fluid, vertical motions are suppressed by the stabilising buoyancy force, however horizontal flow
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 164
Figure 5.3: Suite of 20 horizontal gradient spectra calculated from tracked seismic reflections.
Red/blue/black lines = identified internal wave/turbulent/noise sub-ranges; grey reticule = slopes
of representative internal wave and turbulent sub-ranges with spectral gradients of −0.5 and +1/3,
respectively.
is unconstrained. Energy will therefore be dissipated anisotropically by a preferentially horizontal
turbulence cascade (Lindborg, 2006). At vertical length scales smaller than lO density variation
is negligible, therefore an increasingly isotropic form of turbulence is expected to dominate (e.g.
Batchelor et al., 1959). Since these seismic images have a maximum vertical resolution of O(10) m,
energy is expected to dissipate in the turbulence sub-range anisotropically (Figure 5.3).
5.3.3 Diapycnal Diffusivity
For each seismic image over 20,000 reflections ≥250 m in length are tracked (Figure 5.4). Choosing
a lower limit of 250 m ensures that reflections are well within the horizontal resolution limits of
the seismic image. Slope spectra are calculated and the internal wave, turbulent and noise sub-
Estimating Diapycnal Diffusivity from Seismic Images 165
ranges are identified by fitting a model to these spectra in log(kx)–log(Φξx) space. Of the original
tracked reflections, over ∼1000 spectra fit strict quality control criteria (Figure 5.4b). The criteria
ensure that the length of each sub-range is statistically significant, the fit model is within error
of expected spectral slopes and the model is not dominated by noise. The spectra reveal a clear
three-component model containing internal wave, turbulent and noise sub-ranges.
It is possible to estimate K using both the internal wave and turbulent sub-ranges. The physics of
the energy cascade is well-constrained during turbulence and ε can be directly estimated from this
sub-range. Φξx is related to ε by a simplified version of the Batchelor et al. (1959) model,
Φξx =
4piΓ
N2
CT ε
2
3 (2pikx)
1
3 (5.2)
where CT and Γ are constants given by 0.4 and 0.2, respectively. Γ is the dissipation flux coefficient
(i.e. mixing efficiency) and is generally assumed to be 0.2, although it is recognised that this value
is likely to vary both spatially and temporally (Osborn, 1980; Mashayek et al., 2017).
The logarithm of Equation (5.2) yields a straight line relationship of the form y = mx+c. Now it is
possible to fit a straight line to the coordinates of log(Φξx) and log(kx). Due to the onset of noise at
high wavenumbers, a clear turbulent sub-range is apparent in the majority of slope spectra (Figure
5.3 and 5.4c–g). Using the straight line fit to the turbulent sub-range it is possible to extract c
which contains ε. Diapycnal diffusivity is related to ε through the Osborn (1980) relation, given
by
K =
Γε
N2
. (5.3)
N is the buoyancy frequency at the average depth of each tracked reflection, obtained from an
averaged regional profile (Figure 4.2f). Finally, each reflection is coloured by its estimated value
of log(K) and overlain onto the seismic image, thereby revealing spatial patterns of diapycnal
diffusivity (Figure 5.4h).
The physics underpinning breakdown of energy in the internal wave sub-range is less well un-
derstood. The most commonly used approach to relate energy of the internal wave field to ε
is based upon the theoretical and numerical analysis of Henyey et al. (1986). They infer that
ε depends quadratically on the energy of the internal wave field and N . ε also has a weak de-
pendence on latitude (Gregg et al., 2003). Their analysis predicts that internal wave spectra, at
10−3 < kx < 10−2 cpm, can be approximated by a power law of the form Φξx ∝ kpx, where p is
between -1 and 0. Average spectral slopes from low wavenumber sub-ranges for seismic data shown
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 166
Estimating Diapycnal Diffusivity from Seismic Images 167
Figure 5.4 (previous page): Distribution of K estimated from seismic imagery. (a) Stacked
seismic section. (b) Black lines = tracked reflections of length >250 m used in spectral analysis;
labelled red lines = example tracked reflections shown in spectral domain in (c–g). (c–g) Slope spec-
tra. Red/blue/black lines = identified internal wave/turbulent/noise sub-ranges; coloured dashed
lines = straight line fits to sub-ranges; grey reticule = slopes of representative internal wave and
turbulent sub-ranges with spectral gradients of −0.5 and +1/3, respectively. Diapycnal diffusiv-
ity calculated from turbulent sub-range, KT , annotated. (h) Seismic image shown in (a) overlain
with estimated distribution of K. Coloured lines = tracked reflections coloured by estimated K
according to scale at right. All K given as log(K).
here is p = -0.6±0.3, suggesting that this region is indeed characterised by internal waves. The
analysis of Henyey et al. (1986) is based upon towed instrument measurements of the horizontal
wavenumber spectra (e.g. Zenk & Katz, 1975) and a semi-empirical model developed by Garrett &
Munk (1975). This model follows internal wave theory which describes how the speed of propaga-
tion of internal waves depends upon the density difference across the boundary of a stratified fluid
that is disturbed. If buoyancy is known it is possible to predict internal wave normal modes that
act to restore the imbalance. Henyey et al. (1986) used numerical simulations to investigate how
energy is transferred between the low and high wavenumber regimes (i.e. internal wave breaking)
which provided a numerical scaling of the first order effects on ε from the internal wave spectrum.
Since 1986, various modifications have been made to this parameterisation (e.g. Gregg, 1989).
Gregg (2015) detail a history of the study of mixing and the development of this approach.
Estimates of ε are determined by reference to the dissipation rate of the Garrett-Munk spectrum,
εr, at a specified buoyancy frequency, Nr, at a given latitude with Coriolis parameter, fr (Henyey
et al., 1986; Gregg, 1989; Gregg et al., 2003). The equation is given by
ε = εr
(
N
Nr
)2
farccosh(N/f)
frarccosh(Nr/fr)
RωGM
Rω
Rω + 1
RωGM + 1
√
RωGM − 1
Rω − 1 Eˆ
2, (5.4)
where N is the local mean stable stratification, f is the local Coriolis parameter, Rω is the local
shear-strain ration, RωGM = 3 is the shear-strain ratio of the GM wave field, and Eˆ is a measure
of the energy of the observed wavefield (Polzin et al., 2014). Eˆ is evaluated in terms of horizontal
gradient spectra using
Eˆ =
Rω
RωGM
〈Φξx〉
〈ΦGMξx 〉
, (5.5)
where ΦGMξx is the GM spectrum for the local value of buoyancy frequency, N . Angular brackets
denote integration over the wavenumber range of the internal wave sub-range. Due to the lack of
local measurement of Rω, the globally averaged value of 7±3 is used (Kunze et al., 2006). f is
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 168
assumed to be constant and is calculated using the latitude at the centre of the seismic survey,
36.6 ◦S. N is taken as the buoyancy frequency at the average depth of each tracked reflection,
obtained from an averaged regional profile. Following Gregg et al. (2003), observed dissipation
rates are compared with those predicted by the Garrett & Munk (1975) model at 30◦N latitude
with Nr = 3 cph. This model is chosen as the reference spectrum with a mode number scale j∗ = 4
and a high wave number saturated sub-range in the vertical spectra for vertical wavenumbers
kz > 0.1 cpm. The reference spectrum gives ε = 7.2 × 10−10 m2 s−3. The Garrett & Munk
(1975) spectrum is a good first-order approximation to the characteristics of most internal waves
(Dickinson et al., 2017).
5.3.4 Comparing Internal Wave and Turbulent Estimates of K
Diapycnal diffusivity measurements based on the internal wave, KIW , and turbulent, KT , sub-
ranges are qualitatively compared (Figure 5.5). Tracked reflections are spectrally analysed for
Profile 2, which is representative of the thermohaline structure of the deep penetrating front.
Distribution of estimated mixing rates are shown for KIW (Figure 5.5a) and KT (Figure 5.5b).
These images clearly demonstrate that relative patterns of diapycnal diffusivity are reproduced
by both sub-ranges. To first-order, mixing rates are enhanced and suppressed on the dense (i.e.
∼0–40 km range) and light side of the front, respectively. This mirrored pattern of diapycnal
diffusivity provides confidence that diapycnal diffusivity measurements can be accurately recovered
from seismic images using either the internal wave or turbulent sub-ranges. It is possible to conclude
that the relative distribution of diapycnal diffusivity is faithfully recovered by either sub-range.
However, individual spectra reveal that absolute values of estimated K are not consistent between
these two sub-ranges (Figure 5.5c–g). This inconsistency is probably due to the well-constrained
physics in place at higher wavenumbers (i.e. turbulent sub-range). First, less assumptions are
required to estimate KT than KIW . Secondly, the spectral slope of turbulence is +1/3, however
the exponent for low wavenumbers ranges between -1 and 0. Here, KIW is estimated using the
Henyey et al. (1986) and Garrett-Munk model which assume a power law exponent of −1/2 at the
limit of high wavenumbers (kx ≤10−2 cmp). However, since the spectral slope of internal wave
sub-ranges can vary it is likely that in some cases this sub-range is not well-described by this
parameterisation. This hypothesis is corroborated by spectra shown here. When the internal wave
sub-range has a slope close to −1/2, KIW and KT are within error (e.g. Figure 5.5c). However,
when the internal wave sub-range has significantly steeper or shallower slopes, KIW is not within
Estimating Diapycnal Diffusivity from Seismic Images 169
Figure 5.5: Spatial pattern of K estimated using internal wave and turbulent spectral sub-
regions (Profile 2; Figure 4.7b). Tracked reflections coloured by estimated K according to scales
at right. (a) Spatial distribution of KIW . (b) Spatial distribution of KT . (c–g) Slope spectra
of highlighted reflections shown in (a) and (b). Red/blue/black dashed line = identified internal
wave/turbulent/noise sub-ranges; coloured dashed lines = straight line fits to sub-ranges; grey
reticule = slopes of representative internal wave and turbulent sub-ranges with spectral gradients
of −0.5 and +1/3, respectively. KT and KIW annotated. All K given as log(K).
error of KT (e.g. Figure 5.5g). Furthermore, a model is fit to each spectra that is based on
prescribed turbulent and internal wave spectral slopes of +1/3 and −1/2, respectively. Although
these slopes are allowed to vary it is possible that in some cases the line fit to the internal wave
spectra does not accurately represent this sub-range.
Figure 5.6 quantitatively compares KIW and KT . Estimates of diapycnal diffusivity are similar,
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 170
Figure 5.6: Correlation of diapycnal diffusivity estimated from internal wave and turbulent sub-
ranges. Coloured points = KIW against KT for 307 reflection shaded by N according to scale at
right. Pearson’s correlation coefficient annotated top left.
KIW = 10−6.7–10−1.3 m2 s−1 and KT = 10−5.6–10−2.2 m2 s−1, although the range of KIW is larger.
The Pearson correlation coefficient between KIW and KT is 0.77 suggesting that both internal
wave and turbulent sub-ranges can be used to identify diapycnal diffusivity (Figure 5.6). Similar
comparisons of KIW and KT have previously been published. For example, Sheen et al. (2009)
calculated mixing rates from both the turbulent and internal wave regimes from a seismic image
near the Falkland Islands. Their mean estimates of mixing rates are similar, KIW = 10−4.6±0.7 and
KT = 10−4.2±0.4 m2 s−1. Klymak & Moum (2007a) estimate KIW and KT using a towed vehicle
deployed near Hawaii and compare these values to turbulent dissipation rates measured from shear
probes. They find that the correlation coefficient of KIW has near-zero correlation (i.e. 0.08) with
shear-probes estimates. This value is contrasted by the correlation coefficient between shear probes
measurements and turbulence sub-range estimates of 0.84. Klymak & Moum (2007a) found that
internal wave amplitudes have a weaker dependence on wave energy and therefore cannot be reliably
deduced from horizontal measurements alone. They conclude that mixing rates are more reliably
measured from the turbulent sub-range. Sheen et al. (2009) also conclude that KT is probably more
robust than KIW . It is likely that the applicability of estimating K from internal wave sub-range
using the Garret-Munk method is spatially variable, which is probably due to the fact that the
Estimating Diapycnal Diffusivity from Seismic Images 171
Garrett-Munk spectrum is based on open ocean data which prescribes a spectral slope (Garrett &
Munk, 1975). In the region surveyed by seismic profiles presented here, bathymetry varies between
2500 and 3000 m. In contrast, Klymak & Moum (2007a) compare estimates from horizontally
towed vehicles with shear probe data acquired in the Kauai Channel, which is characterised by
bathymetry that ranges between ∼600 and 2000 m depth, which may explain the low correlation
they find. Dickinson et al. (2017) calculate K from the internal sub-range of seismically inferred
spectra. A weighted histogram of the fitted gradients to the low wavenumber spectral sub-range
reveals a prominent peak at −0.2 ± 0.6 consistent with internal wave field regime. For the 307
estimates of K shown in Figure 5.6 the average spectral slope of the internal wave is −0.6 ± 0.3,
implying that the observed spectral sub-ranges at low wavenumbers corresponds to the internal
wave field. Finally, the correlation between KIW and KT appears to vary slightly with buoyancy
frequency, N (i.e. depth). Nevertheless, r is >0.73 at all depths. The high correlation and average
spectral slope of -0.6 suggests that this area is well-constrained by the open-ocean assumptions of
the Garrett-Munk spectrum. However, further estimates of K presented here are from the turbulent
sub-range only due to the robustness of the estimates obtained from this portion of the spectra.
Figure 5.6 also highlights diapycnal diffusivity measurements that are in excess of 10−3 m2 s−1
which are considered extremely high. KIW exceeds 10−2 m2 s−1, yet the highest estimate KT is
10−2.2 m2 s−1. Nevertheless, KT often exceed 10−3 m2 s−1 suggesting vigorous mixing. High values
of K that have been estimated from both the turbulent and internal wave sub-ranges are shown
in Figure 5.7. Figure 5.7 shows that values of K in excess of 10−3 m2 s−1 are patchy across the
frontal zone. Spectra reveal clear sub-ranges suggesting that these high estimates are not in error
(Figure 5.7b–f). Although hotspots of vigorous mixing are believed to drive meridional overturning,
diapycnal diffusivities greater than 10−3 m2 s−1 are not often observed. MacKinnon et al. (2008)
inferred a mean diapycnal diffusivity in excess of 10−2 m2 s−1 several hundred meters from the
seabed using LADCP and CTD data in the southwest Indian ridge. They found turbulent diffusivity
within a deep jet to be over two orders of magnitude grater than typical deep ocean measurements of
O(10−5) m2 s−1. MacKinnon et al. (2008) infer that the reliability of K that exceed 10−2 m2 s−1
inferred at ≥5000 m are questionable due to the extremely weak stratification at these depths.
Other similarly high values of K have been observed in western boundary currents. For example,
Tsutsumi et al. (2017) measured spatial and temporal variability of diapycnal diffusivity in the
Kuroshio Current. They measure strong eddy diffusivities of O(10−2) m2 s−1 downstream of a
seamount. A one-dimensional vertical diffusion model suggest that turbulent mixing may be a
large as O(10−1) m2 s−1 in the vicinity of the seamount. Tsutsumi et al. (2017) conclude that
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 172
F
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5
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Estimating Diapycnal Diffusivity from Seismic Images 173
the strong turbulent mixing is mainly due to interaction of the Kuroshio with topography. Other
studies have reported strong mixing in ares of topographically generated hydraulic jumps. For
example, Nishina et al. (2016) observe K > 10−1 m2 s−1 generated by lee waves in the wake of sills
in the Kerama Gap, Philippine Sea. Sill amplitude is ∼600 m. An overflow from the Philippine
Sea into the Okinawa Trough is concentrated in a narrow, near-bottom current of up to 0.5 m s−1
above the sill. Furthermore, fronts are areas associated with elevated mixing. Johnston et al. (2011)
measured eddy diffusivity in the California Current front system and observe K ≤ 10−3 m2 s−1
within 10-20 km of the frontal interface. D’Asaro et al. (2011) observe rates of energy dissipation
that are enhanced by over two orders of magnitude in the mixed layer. They attribute these
enhanced values to a frontal jet along a front in the Kuroshio Current that leads to energetic
instabilities. It is reasonable to conclude that high values of K that are estimated here are not in
error. It appears that KIW tend to over- or under-estimate diapycnal diffusivity (e.g. Figure 5.7f)
which is probably due to the variability in spectral slope and extra assumptions required to extract
these values. For this reason, absolute values of KIW are treated with caution.
5.3.5 Spatial and Temporal Variation of Diapycnal Diffusivity
The spatial distribution of K across a front in the Brazil-Falkland Confluence is investigated (Fig-
ure 5.8). Calculated diapycnal diffusivity varies by up to 4 orders of magnitude, 10−6 < K <
10−2 m2 s−1, with a mean of O(10−3) m2 s−1. This elevated mean is similar to high rates of mix-
ing observed within the vicinity of the Brazil-Falkland Confluence (St. Laurent & Schmitt, 1999;
Bianchi et al., 2002). Across sub-mesoscales, O(1) km, diffusivity is patchy. Intermittent mixing
has been observed by previous seismic oceanography studies and is believed to be ubiquitous across
the oceans (e.g. Sheen et al., 2009; Dickinson et al., 2017). However, at length scales >O(1) km
there is a clear spatial pattern of diapycnal diffusivity.
In general, the dense (i.e. southern) side of the front is characterised by short disrupted reflectively
that reveal diapycnal diffusivities greater than 10−3 m2 s−1, implying that this area experiences
enhanced mixing. These elevated K often reach 10−2 m2 s−1 (e.g. Figure 5.8c; 0–40 km range).
Conversely, lower values, 10−5 < K < 10−4 m2 s−1, are observed on the light side of the front
(e.g. Figure 5.8c; 100-120 km range). Within ∼50 km of the light side of the frontal interface
mixing rates are particularly low (Figure 5.8e; 40–100 km range, 500–1000 m depth). Low mixing
rates are estimated for long dipping reflections that mark the frontal interface. These values of
K < 10−4 m2 s−1 suggest that vertical motions are inhibited. This inference is supported by
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 174
buoyancy frequency distributions that have been calculated from seismic imagery which reveal a
band of high stratification along the frontal interface (Figure 4.15e). Vertical circulations are often
induced at fronts as they try to maintain equilibrium, and this ageostrophic circulation distorts
buoyancy gradients. Strong downwelling on the dense side of the front has been observed to enhance
kinetic energy dissipation whilst upwelling on the light side of the front is known to suppress mixing
(Capet et al., 2008a; Johnston et al., 2011; Nagai et al., 2012). These observations are consistent
with the results presented here. Suppressed mixing on the light side is probably due to strong
stratification induced by ageostrophic currents. Lapeyre et al. (2006) use numerical simulations
to show that frontogenesis increases stratification in the upper 2000 m of the water column which
can lead to suppressed mixing. Notably, the lowest values of K follow long reflections whilst
short disrupted reflections generally indicate areas of enhanced vertical motion. This correlation
of reflectively and K suggests that fine-structure in seismic images may be a useful indicator of
turbulence levels. This inference is consistent with similar conclusions made by Holbrook et al.
(2013). Figure 5.5 reveals that some long dipping reflections only exhibit an internal wave spectral
sub-range, implying that these continuous strands are dominated by internal waves rather than
turbulence. As the frontal interface splits into fingers at mid- and abyssal depths, K maintains
its low values (e.g. Figure 5.8a; 90–101 km range, 500–900 m depth). Deep regions of suppressed
mixing are focused around long continuous reflectively, which has previously been interpreted as
the frontal interface (e.g. Figure 5.8c; 125–140 km range, 1500–1700 m depth). This observation
implies that the front is affecting dissipation of kinetic energy at abyssal depths. At shallow
depths, high mixing is observed on both the light and dense side of the front within 10 km of
outcropping reflections. This observation is consistent with Palla`s-Sanz et al. (2010a). They use
microstructure observations in the California Current System to show strong turbulent dissipation
near the surface at the location of the outcropping frontal interface. Nagai et al. (2012) also observed
similar patterns in their microstructure observation near the Kuroshio Front. These studies are
both limited to 250 m depth and the high levels of mixing are attributed to interaction of the wind
and frontal jet.
Horizontally averaged profiles of K show decreasing mixing rates with depth (Figure 5.8d,b,f,h). K
is generally less than 10−3.5 m2 s−1 at depths over 2000 m and in some profiles K decreases by up
to half an order of magnitude (e.g. Figure 5.8d). This trend is perhaps surprising as traditionally
mixing rates are believed to increase toward the the seabed (Waterhouse et al., 2014). Nevertheless,
horizontally averaged values of K close to the seafloor are higher than 10−4 m2 s−1 which constitutes
elevated mixing rates. Furthermore, towards the more southerly part of each section, K appears to
Estimating Diapycnal Diffusivity from Seismic Images 175
increase slightly over rougher bathymetry. It appears that in this region, although K is high close to
the seabed, the majority of mixing is in the upper 1000 m of the water column and is controlled by
the frontal thermohaline structure. Bianchi et al. (2002) surveyed the Brazil-Falkland Confluence
in September 1991 and estimated vertical thermal diffusivity. Their survey consisted of ten CTD
profiles along a section of 30 km, that extended to 500 m depth. High values of 10−4 m2 s−1 were
found. These values match similarly large diffusivity results of the North Atlantic Tracer Release
Experiment St. Laurent & Schmitt (1999). Coincident measurements of diapycnal diffusivity are
not available. However, to test these spectral results, fine-scale strain parameterisations of CTD
casts acquired along WOCE transects A10 and A11 are performed. These results, although not
coincident in time or space, are used to benchmark seismically estimated values of K. 18 CTD
casts are of sufficiently high quality to be used for this parameterisation. Temperature and salinity
profiles are used to calculate buoyancy frequency, N . Strain (i.e. the vertical gradient of vertical
displacements, ξZ) is given by
ξZ =
N2 −N2S
N2S
, (5.6)
where N2S is the stable buoyancy profiles. N
2
S is estimated using adiabatic levelling calculated over
a pressure range of 400 dbar (Polzin et al., 2014). The upper 100 m is discarded and strain profiles
are divided into half-overlapping segments of 100 m in order to avoid contamination from rapidly
varying near-surface thermohaline properties. ε and K are calculated using Equation (5.4) and the
Osborn (1980) relation. Diapycnal diffusivity estimated from strain spectra ranges between 10−5.5
and 10−1.2 m2 s−1 and is in good agreement with the magnitude of K estimated from seismic
images (Figure 5.8d,b,f,h). These estimates do not reveal a clear trend which is probably due to
the extended time of acquisition (i.e. austral winter 1992 austral winter 2002). The distribution
of energy dissipation computed from CTD casts cannot be compared in detail with the seismically
recovered estimates since the two datasets are acquired ≥10 years apart. Unfortunately, no other
near-coeval measurements are available that are suitable for this analysis. Nevertheless, these
two methodologies yield estimates that broadly agree at large-scales and provide confidence in
seismically recovered distributions of K.
Deep eddies are characterised by elevated turbulence on the southern and shallowest corner of the
lens, K > 10−3 m2 s−1. Low values of K, 10−5 m2 s−1, are found along the upper and lower
boundaries (e.g. Figure 5.8a; 68–85 km range, 400–800 m depth). In some places, discontinuous,
short reflections tracked within the lens reveal high diapycnal diffusivity, ≤ 10−2 m2 s−1 (e.g.
Figure 5.8c; 50 km range, 700 m depth). A shallow eddy is observed in Profiles 3 and 6 (Figure
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 176
Figure 5.8: Seismic reflection profiles from Set A overlain with spatial pattern of K (see Figure 4.3
for location). Tracked reflections coloured by K according to scale at bottom. (a) Profile 1.
(b) White circles = horizontally averaged K as function of depth in 50 m vertical bins; grey
circles = estimates of K from strain spectra calculated from 18 CTD casts. (c) Profile 2. (d) Same
as (b) for (c). (e) Profile 3. (f) Same as (b) for (e). (g) Profile 4. (h) Same as (b) for (g). All K
values given as log(K)
Estimating Diapycnal Diffusivity from Seismic Images 177
4.7e; range 105–130 km and Figure 4.7f; range 50–70 km). In Chapter 4, this eddy is interpreted
as a lens of warm-core SACW that translates southwestward. This intra-thermocline eddy reveals
the same pattern of diapycnal diffusivity as the deep eddy observed on the dense side of the front.
Specifically, suppressed K on the curved upper and lower boundaries of the lens and enhanced K
at the corners and within the eddy centre. Acoustical blank centres indicate either high levels of
mixing that have resulted in diffuse physical properties gradients or an absence of mixing due to
an homogenised water mass. Elevated mixing seen within the core of eddies suggests that these
cores are undergoing vigorous mixing. These observations are in direct contrasts with mixing rates
seismically and hydrographically inferred around Meddies. Song et al. (2011) report that mixing is
virtually absent with the core but is anomalously high at the top and bottom. Sheen et al. (2015)
used hydrographic, current velocity, and microstructure measurements, to investigate the effect of
an eddy on local turbulent dissipation rates in the Southern Ocean. They also conclude that the
eddy suppresses turbulent kinetic energy dissipation within the eddy core while enhancing turbulent
dissipation rates near the eddy upper and lower boundaries. High K observed at the edges of the
eddy is generally consistent with high mixing rates inferred at the boundaries of eddies by Song
et al. (2011) and Sheen et al. (2015). However, the suppressed mixing observed at the upper and
lower curved boundaries of these eddies is not consistent. It is hypothesised that suppressed mixing
is caused by distortions of the lateral buoyancy gradient due to these anomalous patches of water.
Figure 5.8 shows distributions of K that are separated by ∼1 km and ∼1 day. These profiles reveal
a clear spatial distribution of K that is strongly correlated to the thermohaline structure of the
Brazil-Falkland Current. Despite a clear translation of the K field with the front, the distribution
appears to be fairly consistent (i.e. there little temporal variability of K). However, there is one key
difference between these transects that appears to be related to the evolution of the deep eddy. As
the eddy grows and dies with increasing time, there is an increase in the number of reflections that
yield suppressed mixing estimates (e.g. compare Figures 5.8a and 5.8c). One possible cause for this
change in behaviour is internal waves that can be generated at the frontal interface then propagate
away. Such waves may act to restratify the water column and have important implications for
the oceanic internal wavefield and its mixing (Alford et al., 2013). It is beyond the scope of this
study to model the generation of these waves and their effect on the water column, however it is
hoped that these speculative observations may lead to further efforts in this area. Nevertheless,
seismic images are presented that span one week and reveal a long-lived distribution of diapycnal
diffusivity. This observation is consistent with measurements of turbulent kinetic variability along
the A25 Greenland-Portugal transect (Ferron et al., 2016). CTD and ADCP measurements were
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 178
used to parameterise turbulent kinetic energy from 2002–2012. Ferron et al. (2016) found that
the inter-annual variability of the transect was remarkably small with a small number of unusual
dissipation events.
5.4 Discussion
In the analysis presented here the value for stratification used in Equations (5.2) and (5.3) is a
depth-dependent regional average profile of N . However, diapycnal diffusivity estimated using
the spectral method described here calculates mixing rates across a large range of scales. Mixing
estimates calculated for reflections that lie close to or within eddies may be associated with a
different value of N than the regional average. Therefore, calculated values of K are likely to
include some uncertainty. Ideally, Equations (5.2) and (5.3) would be solved using local buoyancy
frequency values extracted from a coeval, two-dimensional profile of N . Here, by replacing the
depth-dependent regional average profile ofN with the distribution of stratification that is extracted
using the adapted inversion procedure (i.e. Figure 4.15e), it would be possible to further constrain
the presented estimates of K. However, this substitution is likely to introduce its own error since
salinity is difficult to constrain using a local T -S-z relationship. In most cases this local field
is unavailable which necessarily limits the calculation of diffusivity to the method described and
implemented in this chapter. Here, a regional profile of N has been chosen since it is difficult to
quantify stratification locally and also to maintain consistency with previously published spectral
analysis methods. Consequently, anomalously high or low values of eddy diffusivity may be related
to the use of a regional average of N . Therefore the results presented here must be interpreted
with this caveat in mind.
5.4.1 Mixing Mechanisms
Southern hemisphere western boundary currents distribute a large amount of heat, salt and nutri-
ents from mid to low latitudes. Subsequent flow generated by this confluence sweeps out into the
southwest Atlantic. Turbulent mixing along these pathways may modify temperature and salinity
of advected water masses, distribute nutrients and matter. These modifications underpin physi-
cal and biological processes. Since this frontal region is an area of particularly elevated mixing,
∼ 10−6 < K < 10−2 m2 s−1, it is important to identify the location and mechanisms by which
Estimating Diapycnal Diffusivity from Seismic Images 179
turbulent mixing is generated. Eddy diffusivity is enhanced across the entire seismic survey, with
mean K of O(10−3) m2 s−1.
Several mechanisms are likely to result in elevated mixing; internal wave impingement on topogra-
phy, enhanced atmospheric forcing, rough bathymetry, or elevated eddy and internal wave energy
levels. Since it is well-known that mixing is enhanced near the seafloor (e.g. Waterhouse et al.,
2014), the relationship of K as a function of depth is assessed. Scatter-plots of K against depth
are shown from 9 sub-regions across a representative seismic section (Profile 2; Figure 5.9). The
correlation between K and depth is quantified using Pearson’s correlation coefficient. In all cases
r is less than 0.5. It is possible to conclude that there is no clear relationship between depth
and diapycnal diffusivity across this frontal zone (Figure 5.9b–j). This conclusion is robust to the
size and position of sub-ranges. The relationship of K with reflection dip, perpendicular distance
from frontal interface and azimuthal distance from the centre of the deep eddy have been simi-
larly analysed. No clear relationships were found. Although there is likely to be a component of
topographically driven elevated mixing, this is unlikely to be the main generation mechanism for
mixing for three reasons. First, high mixing is not constrained to abyssal depths. Horizontally
averaged profiles show that K decreases with depth. Secondly, bathymetry is not characterised by
sharp transitions such as seamounts. The submarine canyons here have a slope of ∼6◦, whereas
seamounts typically have slope that are one order of magnitude greater. Finally, there is no signif-
icant upstream topographic obstacle. The Rio Grande Rise is >1000 km further north. It is more
reasonable to assume that elevated mixing is caused by the front and its dynamics.
Spatial patterns of diapycnal diffusivity follow the passage of the confluence over a period of at
least 1 week, suggesting that the front is an important control on the oceanic internal wavefield sup-
porting the above conclusion that there is a strong relationship between mixing and thermohaline
structure of the frontal region. Clear southward migration of the frontal interface has been observed
from seismic images and sea-surface temperature measurements. Based on the known position of
the confluence and the four-dimensional nature of the seismic survey it is possible to investigate
distributions of diapycnal diffusivity before, during and after the passage of the front through the
seismic survey. It is important to note that the frontal interface does not pass through the water
masses that define the southwest Atlantic Ocean, rather there is a solid body translation of the en-
tire confluence (Chapter 4). In other words, the frontal interface represents the boundary between
the Falkland and Brazil Current and the entire system migrates southwestward over the period of
seismic surveying. The observed migration implies that before (after) the front translates south-
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 180
Figure 5.9: Relationship between K and depth. (a) Stacked seismic section overlain with K.
Black boxes = sub-regions shown in (b)–(j). (b–j) Scatter-plots of K against depth within each
sub-region shown in (a). Pearson correlation coefficient, r, given for each region.
Estimating Diapycnal Diffusivity from Seismic Images 181
Figure 5.10: Spatial and temporal variation of diapycnal diffusivity across front. Three distri-
butions of diapycnal diffusivity are shown that typify water column structure before, during and
after advection of confluence through seismic survey (see Figure 4.3 for locations). (a) Profile 17
representing water mass conditions 10 days before confluence reaches seismic survey. (b) Horizon-
tally averaged K as a function of depth. K shown in 50 m vertical bins. (c) Profile 2 representing
water mass conditions during confluence. (d) Same as (b) for (c). (e) Profile 19 representing wa-
ter mass distributions 1 month after advection of confluence. (f) Same as (b) for (e). Coloured
lines = tracked reflections coloured by estimated K according to scale at bottom. All K values
given as log(K)
K.L. Gunn, Ph.D. Dissertation
Estimating Diapycnal Diffusivity from Seismic Images 182
wards the water column represents the Falkland (Brazil) Current. Spatial and temporal variations
of diapycnal diffusivity before, during and after the advection of the Brazil-Falkland Confluence
are shown in Figure 5.10. Before the confluence passes through the seismic survey region, vertical
water mass structure is characterised by multiple sub-mesoscale structures and appears energetic.
In general, the highest values of K are observed at mid-depths where most disrupted reflectively
occurs (Figure 5.10a). Low diapycnal diffusivity, K < 10−4 m s−1, are observed within 500 m of
the sea-surface and seabed. Figure 5.10c reveals the classic pattern of diapycnal diffusivity that
is revealed by images of the confluence. 1 month after the confluence passes through the seismic
survey region, spatial patterns of diapycnal diffusivity are characterised by K < 10−4 m s−1 in
the upper 1000 m (Figure 5.10e). At greater depths, intermittent patches of high K are observed.
The dominance of suppressed mixing is likely related to the higher stratification present in the
Brazil Current. Furthermore, long, continuous reflections suggest that this current is fairly quies-
cent compared to the Falkland Current (Chapter 4). The two-dimensional patterns of reflectively
that characterise each stage are revealed by horizontally averaged profiles of diapycnal diffusivity
(Figure 5.10b,d,f). Although the frontal interface is a dominant feature of Figure 5.10c it does not
appear to significantly change long wavelength patterns of diapycnal diffusivity either side of the
front. However, the region surrounding the deep eddy does appear to be affected. Since this region
is interpreted as being under frontogenetic processes it is likely that frontogenesis is the generation
mechanisms for these locally altered diapycnal diffusivities (i.e. enhanced and suppressed mixing
on the light and dense side of the front are observed within the vicinity of the deep eddy, respec-
tively). These patterns are apparent in the higher mixing rates at the southern, shallow corner of
the eddy and upper boundary that aligns with the frontal interface. The rapid lifetime of this eddy
may be linked to the mixing patterns described here. Bianchi et al. (1993) described intensification
of fine-structure in the frontal zone and estimated a vertical diffusivity of 10−4 m2 s−1. Bianchi
et al. (1993) also considered the role of elevated diffusivities in dissipating intrusive lenses found
near the front. A lens of 70 m thick × 7 km diameter had an estimated lifetime of 1 week. These
observations are comparable with those presented here. Conversely, eddies that were generated by
detachment from a meander of order 100 km, had lifetimes of 6 months.
5.5 Conclusions
In this chapter, diapycnal diffusivity estimates from seismic images are presented. Spectra of the
horizontal gradient of vertical displacement are constructed from automatically tracked seismic re-
Estimating Diapycnal Diffusivity from Seismic Images 183
flections. Acoustically imaged reflections track vertical displacements of isopycnals. The internal
wave, turbulent and noise regimes are carefully isolated, a model is fit, and K is estimated. Seismic
imagery records oceanic fine-structure with resolutions of up to 10 m and these profiles cover large
regions. In this way, seismically inferred diapycnal diffusivity distributions yield detailed distri-
butions of K across a range of spatial and temporal scales and complement other methodologies
of estimating mixing rates that do not have both the spatial resolution and coverage of this tech-
nique. This approach is applied to a three-dimensional seismic survey acquired in the path of the
Brazil-Falkland Confluence. The confluence is marked by diffusivity that ranges four orders of mag-
nitude, 10−5 < K < 10−2 m2 s−1. Estimated mixing rates are compared to published values and
diffusivity calculated from hydrographic data acquired in the region. Seismically inferred mixing
rates are consistent with these estimates of K. The frontal interface is characterised by a distinct
spatial pattern in diapycnal diffusivity. There is a clear spatial and temporal variation in K that is
attributed to the migration of the confluence across the seismic survey. Localised enhancement and
suppression of mixing is likely caused by secondary ageostrophic circulation at the frontal interface.
K.L. Gunn, Ph.D. Dissertation

Chapter 6
Conclusions and Further Work
6.1 Summary
Since 2003, low frequency acoustic profiling has been used to image vertical temperature variations
across the world’s oceans. This tool has three key advantages over hydrographic techniques. First,
high resolution profiles cover large areas. Secondly, these records are acquired rapidly in either two-
or three-dimensions. For example, a three-dimensional survey of length 140 km and width 600 m
which extends several kilometres beneath the sea-surface can be acquired in several hours. Thirdly,
there is a wealth of legacy seismic reflection datasets that represent an untapped resource. Here, the
seismic reflection profiling methodology has been employed to constrain mesoscale to sub-mesoscale
thermohaline structure and processes in the Bellingshausen Sea and southwest Atlantic Ocean. In
both areas, the advantage of resolution and coverage yielded by this technique allows quantification
of the size and properties of an eddy field and a deep-reaching front. Such observations are a
challenge to make using standard hydrographic methods.
In Chapter 2, the history of seismic exploration is outlined. Acquisition and processing techniques
of two- and three-dimensional seismic datasets are demonstrated with the aid of an academic- and
industry-standard seismic survey, respectively. The principles of acquisition are largely the same;
however, the experiment configurations are distinct. Two-dimensional seismic surveys acquire
K.L. Gunn, Ph.D. Dissertation
Conclusions and Further Work 186
single vertical cross-sections whilst three-dimensional experiments simultaneously collect multiple
sections. Furthermore, these two datasets highlight the improved imaging capabilities of industry-
standard surveys compared with academic experiments as a result of the increased size and higher
quality of acquisition equipment. A typical three-stage processing flow is described that outlines
the core techniques of a seismic oceanography study. The contribution of sound speed and density
variations to recorded reflectivity, which are controlled by temperature and salinity, are calculated.
Changes in acoustic impedance, which are captured by seismic imagery, are controlled by changes
in sound speed that is in turn dominated by temperature contrasts.
In Chapter 3 a set of seismic images from the Bellingshausen Sea of the Southern Ocean are pre-
sented and analysed. These are the first seismic reflection images of the Antarctic water column.
These images reveal a pattern of large-scale reflectivity that is consistent across the entire seismic
survey and is probably typical of that expected during the austral summer. At smaller scales
large numbers of lens-shaped reflectivity patterns are observed which have lengths and thickness
of 2–12 km and a few hundred metres, respectively. These distinctive structures are interpreted as
eddies. Since seismic reflections from the water column are caused by changes in temperature and
salinity, acoustic images contain information about the ocean’s physical properties. An iterative
inversion procedure is adapted from the method of Papenberg et al. (2010). Application of this
procedure is limited in the absence of in situ sound speed measurements which are required to
provide a long wavelength background model. In the adapted inversion developed here, long wave-
length sound speed information is extracted directly from seismic observations, yielding reliable
background models of sound speed. This adaptation is valuable since it obviates the need for large
amounts of coeval hydrographic observations, which are often unavailable. The resultant temper-
ature distributions for seismic images across the Bellingshausen Sea demonstrate that lens-shaped
reflectivity surrounds anomalously warm patches of water. Pre-stack seismic data are used to con-
strain the direction of ocean currents. These measurements indicate that flow is toward the shelf,
and is of O(0.1) m s−1, consistent with previous hydrographic observations. The shape and tem-
perature anomalies of the lens-shaped seismic reflections indicate that they are warm-core eddies.
These eddies are observed in the vicinity of the Marguerite and Belgica Troughs on the shelf edge
of the west Antarctic Peninsula and Bellingshausen Sea. They are therefore likely mechanisms for
warm-water intrusion which contribute to rapid melt rates on the basal side of ice shelves. The num-
ber of observed eddies suggests that warm-water transport across the shelf has been significantly
underestimated. A direct consequence of this underestimate is the potential impact upon basal
melting of ice shelves. A set of sloping reflections are observed offshore of Belgica Trough. Due to
Conclusions and Further Work 187
the location and form of these reflections, they are interpreted as the Antarctic Slope Front. This
interpretation places the circumpolar influence of the front within the Bellingshausen Sea which
is further east than previously suggested. Finally, a substantial warm-core anticyclonic circulation
feature is observed above the Alexander Island Drift. Scaling analysis suggests that a combination
of local bathymetry and circulation are conducive to the formation of a stratified Taylor column in
this location.
In Chapters 4 and 5, a three-dimensional industry standard survey is presented and analysed. The
southwest Atlantic Ocean is dominated by the confluent flow of the Brazil and Falkland Currents
which creates a complex frontal system that sweeps eastward across the ocean. 20 seismic profiles
have been extracted from this survey and are used to investigate the nature and dynamics of a deep
reaching front, which forms part of the Brazil-Falkland Confluence. The frontal interface is marked
by bright, dipping reflections that extend to 1800 m depth, and separates two distinct regions of
the water column. In the northeast, the fairly quiescent warm Brazil Current flows southwards and
is characterized by near-horizontal continuous reflections. The Falkland Current flows toward the
north and has a more disrupted thermohaline structure. Spatial and temporal variation of thermo-
haline structure is investigated using the three-dimensional aspect of this dataset. Thermohaline
structure is homogeneous in the cross-front direction (NW–SE). There are significant gradients
of physical properties in the along-front direction (NE–SW). The front is observed at 8 locations
over a 1 week period at 12 hour intervals. These cross-sections reveal that the front migrates
southwestwards at speeds of O(10) km day−1. The overall reflective structure does not change
significantly, suggesting that the front is long-lived. A front of similar characteristics is observed
approximately two months later and 30 km eastward of the front observed during February 2013.
The similarities of the thermohaline structure of two fronts observed in February and April 2013
implies that fronts in this region may have similar characteristics over time and space. Numer-
ous, sub-mesoscale reflectivity patterns are identified across all profiles and depths. A prominent
lens-shaped pattern of reflectivity is observed on the dense flank of the front at ∼750 m depth.
This structure is interpreted as an eddy and has an extremely short lifetime, which is consistent
with a frictional spin-down estimate of 3 days (Pedlosky, 1987). Several generation mechanisms for
this structure are discussed. High resolution seismic observations span the extensive spatial and
temporal scales of frontal systems which are difficult to constrain using traditional hydrographic
data. Here, these observation have been used to constrain a front to a depth of 1800 m.
In Chapter 5, spatial distributions of mixing are calculated from the seismic images presented
K.L. Gunn, Ph.D. Dissertation
Conclusions and Further Work 188
in Chapter 4. Diapycnal diffusivity has been estimated from the turbulent and internal wave
sub-ranges of spectra extracted from seismic images. Spectra of the horizontal gradient of verti-
cal displacement are constructed from automatically tracked seismic reflections. Acoustically im-
aged reflections track vertical displacements of isopycnals. The internal wave, turbulent and noise
regimes are carefully isolated, model spectra are fit, and K is estimated. Internal wave, turbulent
and noise sub-range power laws of ∼-1/2, +1/3 and +2 are observed as expected. Seismic images
record detailed thermohaline fine-structure with resolutions of up to 10 m and cover a large spatial
area. In this way, these images are able to bridge observational gaps when investigating patchy and
intermittent diapycnal diffusivity in the ocean and complement standard techniques. The conflu-
ence is marked by diffusivity that ranges over four orders of magnitude, 10−5 < K < 10−2 m s−1.
These extremely high estimates of kinetic energy dissipation are compared with published results
and found to be reasonable. Strain spectra from nearby CTD casts yield diapycnal diffusivity
estimated of the same magnitude. These elevated mixing rates imply that this area is a region of
enhanced mixing. The frontal interface is characterised by a distinct spatial pattern in diapycnal
diffusivity. There is a clear spatial and temporal variation in K which is attributed to the migration
of the confluence across the seismic survey. Since there is no clear correlation between mixing rates
and depth, reflection dip, or distance from the frontal interface, seismic images that typify the
water mass structure before, during and after the confluence advects across the survey are spec-
trally analysed. Analysis of the temporal variation of mixing implies that the Falkland and Brazil
Currents are mostly unaffected by the frontal interface. Instead, enhancement and suppression of
mixing is localised near the deep eddy. This modification is likely caused by secondary ageostrophic
circulation at the frontal interface.
6.2 Further Work
Chapter 2 outlines the core principles of acquisition and processing that underpin seismic oceanog-
raphy studies. Nevertheless, it is possible to improve seismic processing techniques as each flow can
be tailored to the seismic dataset, which will be exposed to a variety of noise sources. Furthermore,
this work presents a first step in application of deconvolution and migration, but much remains to
be done. Further studies would benefit from a detailed analysis of the affects of deconvolution and
migration on the final seismic image. More sophisticated and standardised methods may increase
the accuracy of deconvolved amplitudes and adjusted reflection positions. Velocity picking is a sub-
jective and time-consuming task. Due to the low signal-to-noise ratio of water column reflections,
Conclusions and Further Work 189
noise is often misrepresented as signal during semblance analysis. Therefore, automatic velocity
picking algorithms produce physically unrealistic sound speed models (e.g. 50 m s−1 change across
vertical distances of a few tens of metres). Such profiles are unlikely in the ocean since density
and sound speed vary smoothly in both vertical and horizontal directions. For this reason, velocity
profiles are manually picked, which typically takes 3–5 hours for a seismic lines that extends 140 km
in length. Since velocity picking is particularly important for extracting physical property distribu-
tions, this stage could be improved by accelerating the process and reducing its subjectivity. Long
wavelength vertical profiles of sound speed are fairly well-known due to the variety of global hy-
drographic datasets. Significant improvement could be make to this procedure by inserting guides
into automatic picking algorithms. A guide could be derived from hydrographic measurements of
sound speed that were, ideally, coevally acquired. By limiting the automatic algorithm to a band
around the guide, realistic sound speed profiles could be generated in a matter of a few minutes.
Furthermore, this would release velocity picking from its subjective nature.
In Chapter 3 and 4 a technique is presented which constrains current speeds using pre-stack seismic
data. This technique identifies internal waves in moved-out CMP gathers and tracks their movement
in space and time, thereby providing an estimate of internal wave speed. However, since no direct
current measurements were taken at the time of either seismic survey, these measurements have been
compared to near-coeval hydrographic data or estimates of geostrophic currents. This technique
should be employed in an area in which simultaneous current measurements are collected in order
to further constrain its accuracy. Here, measurement errors have been estimated based upon the
straight line fit to extracted time and position coordinates. However, these errors are likely to
be relative rather than absolute since a true representation of the error will require consideration
of blurring of reflections caused by acquisition and processing. Comparison with coeval current
measurements will make it possible to determine an absolute error on these measurements. Once
the errors have been further constrained, a clear avenue of future work would be to expand this
technique to investigate current velocity in three-dimensions.
Extracting mixing rates from seismic imagery can be refined in a number of ways. First, K is
calculated using the Osborn relation which requires an assumption to be made about the dissipation
flux coefficient and buoyancy frequency. The dissipation flux coefficient is commonly assumed to
have a value of 0.2, however, this value varies both spatially and temporally. Perhaps of more
concern is the value of buoyancy frequency which significantly varies in both space and time. Here,
an average profile of buoyancy is use to provide a value at the reflector depth. By replacing
K.L. Gunn, Ph.D. Dissertation
Conclusions and Further Work 190
maps of K with ε, a level of uncertainty is removed. Secondly, there is a paucity of near-coeval
hydrographic data surrounding the Uruguay survey. Comparison with calculated mixing rates that
have been estimated from nearby CTDs suggests that the seismic method faithfully reproduces the
distribution of diapycnal diffusivity. To unambiguously link K estimated from seismic imagery to
K directly inferred from shear probes, it would be sensible to deploy a large-scale experiment that
collected these types of data simultaneously.
Many of the ideas discussed above could be tested by a joint seismic oceanography and hydrographic
research cruise. ADCPs, shear probes and gliders could be deployed to collect coeval profiles
of water column properties. Direct comparison between measurements of current speed, mixing
and physical properties with the equivalent values estimated from seismic imagery will allow a
quantifiable estimate of the accuracy of seismic images for recovering these properties. One further
consideration is the resolution of seismic images. Here, the classic equations (used in the solid
Earth) are adopted to estimate the resolution of water column seismic imagery. These equations
do not consider the effect of reflector movement and gradational boundaries.
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Appendix A
Seismic Processing Flow
K.L. Gunn, Ph.D. Dissertation
Seismic Processing Flow 204
Figure A.1: Processing flow applied to two- and three-dimensional seismic datasets discussed in
this dissertation. Processing carried out using Omega2 software, except when tables are generated
for trace position, seabed muting and receiver array directivity corrections. Omega2 modules
capitalised. Black arrows = stages applied to all seismic datasets; grey arrows = stages applied at
user discretion.
Appendix B
JR298 Seismic Survey
Acquisition details of the entire JR298 seismic survey are given (Table B.1). Images have been
processed using the flow described in Chapter 2 and are grouped by survey (Figures B.1–B.7).
K.L. Gunn, Ph.D. Dissertation
JR298 Seismic Survey 206
T
a
b
le
B
.1
:
S
eism
ic
refl
ection
p
rofi
les
a
cq
u
ired
d
u
rin
g
cru
ise
J
R
298.
S
y
m
b
ols
*,
†,
‡
in
d
icate
sim
u
ltan
eou
sly
acq
u
ired
h
y
d
rograp
h
ic,
ech
o-
sou
n
d
er
an
d
A
D
C
P
o
b
servation
s,
resp
ectiv
ely.
B
iT
=
B
isco
e
T
rou
gh
;
T
ID
=
T
h
u
rston
Islan
d
D
rift;
B
eT
=
B
elgica
T
rou
gh
;
A
ID
=
A
lex
an
d
er
Isla
n
d
D
rift;
M
T
=
M
argu
erite
T
ro
u
g
h
;
S
O
L
=
start
of
lin
e;
E
O
L
=
en
d
of
lin
e.
S
ite
area
L
in
e
n
u
m
b
er
D
ate,
d
d
/m
m
/y
y
y
y
D
irection
S
O
L
, ◦S
S
O
L
, ◦W
E
O
L
, ◦S
E
O
L
, ◦W
L
in
e
len
gth
,
k
m
B
iT
3
9 ‡
02
/02/2015
N
–S
64.498
69.535
65.170
68.270
112.5
4
0 ‡
03
/02/2015
W
–E
65.170
68.270
64.561
68.193
26.75
4
1 ‡
03
/02/2015
S
–N
64.935
68.193
64.700
68.620
36.55
4
2 ‡
03
/02/2015
E
–W
64.718
68.672
65.192
69.667
77.3
T
ID
43 †‡
07
/02/2015
E
–W
69.372
93.468
69.389
95.251
75
44 †‡
08
/02/2015
N
–S
69.389
95.267
69.582
95.332
20.675
45 †‡
08
/02/2015
W
–E
69.582
95.332
69.520
94.560
31.525
46 †‡
08
/02/2015
N
–S
69.520
94.560
69.213
94.489
33.5
47 †‡
08
/02/2015
N
W
–S
E
69.240
94.576
69.561
93.566
48.55
48 †‡
08
/02/2015
E
–W
69.533
93.525
69.535
94.608
37.9
B
eT
4
9 †
11
/02/2015
W
–E
69.115
87.170
69.955
84.505
97.2
5
0 †
11
/02/2015
S
–N
68.935
84.498
68.651
84.658
31.275
5
1
11
/02/2015
E
–W
68.648
84.658
68.723
86.028
52.075
5
2
12
/02/2015
N
–S
68.725
86.040
70.251
86.000
158.65
A
ID
53 †‡
17
/02/2015
N
E
–S
W
67.720
75.890
68.132
76.636
61
54 †‡
18
/02/2015
S
W
–S
E
68.132
76.636
67.993
76.011
29.525
5
5* †‡
18/
02/2015
S
E
–N
W
67.991
76.119
67.501
77.714
95.025
56 †‡
18
/02/2015
N
E
–S
W
67.513
77.760
67.746
77.552
28.85
57 †‡
18
/02/2015
S
W
–N
E
67.752
77.498
67.448
77.660
96.4
58 †‡
19
/02/2015
N
E
–S
W
67.420
75.703
68.075
77.363
107.65
59 †‡
19
/02/2015
N
W
–S
E
68.103
77.312
67.865
74.932
117.975
6
0 ‡
20
/02/2015
S
W
–N
E
67.865
74.930
67.448
74.315
57.975
M
T
61
*
2
2/02/2015
N
W
–S
E
66.086
72.348
66.580
71.283
75
6
2
* †
22/
02/2015
S
W
–N
E
66.575
71.261
66.372
70.692
36.65
6
3
22
/02/2015
S
–N
66.360
70.683
66.000
71.355
60.225
6
4
23
/02/2015
N
E
–S
W
65.999
71.371
66.476
72.260
71.125
6
5 †
23
/02/2015
S
W
–N
E
66.500
72.208
66.180
71.540
50.75
6
6 †
23
/02/2015
N
–S
66.173
71.530
66.435
71.758
38.55
6
7 †
23
/02/2015
S
E
–N
W
66.438
71.758
66.208
72.030
38.85
6
8 †
24
/02/2015
N
E
–S
W
66.205
72.040
66.276
72.272
14.825
6
9 †
24
/02/2015
S
W
–N
E
66.280
72.281
65.852
71.256
77.525
7
0 †
24
/02/2015
N
E
–S
W
65.830
71.321
66.375
73.869
152.275
JR298 Seismic Survey 207
F
ig
u
re
B
.1
:
B
is
co
e
T
ro
u
g
h
se
is
m
ic
re
fl
ec
ti
on
p
ro
fi
le
s.
(a
)
L
in
e
39
.
(b
)
L
in
e
40
.
(c
)
L
in
e
41
.
(d
)
L
in
e
42
.
S
ol
id
an
d
d
ot
te
d
b
la
ck
li
n
e
=
se
a
b
ed
.
K.L. Gunn, Ph.D. Dissertation
JR298 Seismic Survey 208
F
ig
u
re
B
.2
:
T
h
u
rston
Islan
d
D
rift
seism
ic
refl
ection
p
rofi
les.
(a)
L
in
e
43.
(b
)
L
in
e
44.
(c)
L
in
e
45.
(d
)
L
in
e
46.
(e)
L
in
e
47.
(f)
L
in
e
48.
JR298 Seismic Survey 209
F
ig
u
re
B
.3
:
B
el
g
ic
a
T
ro
u
gh
se
is
m
ic
re
fl
ec
ti
on
p
ro
fi
le
s.
(a
)
L
in
e
49
.
(b
)
L
in
e
50
.
(c
)
L
in
e
51
.
(d
)
L
in
e
52
.
K.L. Gunn, Ph.D. Dissertation
JR298 Seismic Survey 210
F
ig
u
re
B
.4
:
A
lex
a
n
d
er
Isla
n
d
D
rift
seism
ic
refl
ection
p
rofi
les.
(a)
L
in
e
53.
(b
)
L
in
e
54.
(c)
L
in
e
55.
(d
)
L
in
e
56.
JR298 Seismic Survey 211
F
ig
u
re
B
.5
:
A
le
x
an
d
er
Is
la
n
d
D
ri
ft
se
is
m
ic
re
fl
ec
ti
on
p
ro
fi
le
s.
(a
)
L
in
e
57
.
(b
)
L
in
e
58
.
(c
)
L
in
e
59
.
(d
)
L
in
e
60
.
K.L. Gunn, Ph.D. Dissertation
JR298 Seismic Survey 212
F
ig
u
re
B
.6
:
M
a
rg
u
erite
T
ro
u
gh
seism
ic
refl
ection
p
rofi
les.
(a)
L
in
e
61.
(b
)
L
in
e
62.
(c)
L
in
e
63.
(d
)
L
in
e
64.
(e)
L
in
e
65.
S
olid
an
d
d
otted
b
lack
lin
e
=
sea
b
ed
.
JR298 Seismic Survey 213
F
ig
u
re
B
.7
:
M
ar
gu
er
it
e
T
ro
u
gh
se
is
m
ic
re
fl
ec
ti
on
p
ro
fi
le
s.
(a
)
L
in
e
66
.
(b
)
L
in
e
67
.
(c
)
L
in
e
68
.
(d
)
L
in
e
69
.
(e
)
L
in
e
70
.
K.L. Gunn, Ph.D. Dissertation

Appendix C
Uruguay Seismic Survey
K.L. Gunn, Ph.D. Dissertation
Uruguay Seismic Survey 216
Figure C.1: Seismic reflection profiles from Set C. Red/blue stripes correspond to posi-
tive/negative acoustic impedance contrasts caused by temperature and/or salinity variations within
water column (see Figure 4.3c for location). (a) Profile 9. (b) Profile 10. (c) Profile 11. (d) Profile
12.
Uruguay Seismic Survey 217
Figure C.2: Seismic reflection profiles from Set D (see Figure 4.3c for location). (a) Profile 13.
(b) Profile 14. (c) Profile 15. (d) Profile 16.
K.L. Gunn, Ph.D. Dissertation
Uruguay Seismic Survey 218
Figure C.3: Seismic reflection profiles from Set E (see Figure 4.3c for location). (a) Profile 17.
(b) Profile 18. (c) Profile 19. (d) Profile 20.
Uruguay Seismic Survey 219
Figure C.4: Seismic reflection profiles from Set A converted into temperature using iterative
inversion procedure. Blue/red colours = colder/warmer temperature according to scale at bottom..
(a) Profile 1. (b) Profile 2. (c) Profile 3. (d) Profile 4.
K.L. Gunn, Ph.D. Dissertation
Uruguay Seismic Survey 220
Figure C.5: Set B Seismic reflection profiles converted into temperature using iterative inversion
procedure. (a) Profile 5. (b) Profile 6. (c) Profile 7. (d) Profile 8.
Uruguay Seismic Survey 221
Figure C.6: Zoom of seismic imagery around frontal interface and deep eddy highlighting temporal
variation. Images separated by ∼1 day and 1 km with acquisition date annotated. Windows are
50 km × 1.7 km. (a) Profile 5. (b) Profile 6. (c) Profile 7. (d) Profile 8. (e–h) Interpretation
of panels (a–d). Black polygon = identifiable eddy structures; red ellipse = best-fitting ellipses to
observed eddies; red line = best-fitting line to clearest frontal interface reflection close to eddy. (i)
Black circles = cross-sectional area, A, as function of time calculated using, A = pilh, for ellipses
shown in (e–h). (j) Black circles = tilt of clearest frontal reflection close to eddy calculated from
straight lines shown in (e–h).
K.L. Gunn, Ph.D. Dissertation