Avalanching on dunes and its effects: Size statistics, stratification, & seismic surveys
University of Cambridge
Applied Mathematics and Theoretical Physics
Doctor of Philosophy (PhD)
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Arran, M. I. (2018). Avalanching on dunes and its effects: Size statistics, stratification, & seismic surveys (Doctoral thesis). https://doi.org/10.17863/CAM.26140
Geophysical research has long been interdisciplinary, with many phenomena on the Earth's surface involving multiple, linked processes that are best understood using a combination of techniques. This is particularly true in the case of grain flows on sand dunes, in which the sedimentary stratification with which geologists are concerned arises from the granular processes investigated by physicists and engineers, and the water permeation that interests hydrologists and soil scientists determines the seismic velocities of concern to exploration geophysicists. In this dissertation, I describe four projects conducted for the degree of Doctor of Philosophy, using a combination of laboratory experimentation, fieldwork, numerical simulation, and mathematical modelling to link avalanching on dunes to its effects on stratification, on the permeation of water, and on seismic surveys. Firstly, I describe experiments on erodible, unbounded, grain piles in a channel, slowly supplied with additional grains, and I demonstrate that the behaviour of the consequent, discrete avalanches alternates between two regimes, typified by their size statistics. Reconciling the `self-organised criticality' that several authors have predicted for such a system with the hysteretic behaviour that others have observed, the system exhibits quasi-periodic, system-spanning avalanches in one regime, while in the other avalanches pass at irregular intervals and have a power-law size distribution. Secondly, I link this power-law size distribution to the strata emplaced by avalanches on bounded grain piles. A low inflow rate of grains into an experimental channel develops a pile, composed of strata in which blue-dyed, coarser grains overlie finer grains. Associating stopped avalanche fronts with the `trapped kinks' described by previous authors, I show that, in sufficiently large grain piles, mean stratum width increases linearly with distance downslope. This implies the possibility of interpreting paleodune height from the strata of aeolian sandstones, and makes predictions for the structure of avalanche-associated strata within active dunes. Thirdly, I discuss investigations of these strata within active, Qatari barchan dunes, using dye-infiltration to image strata in the field and extracting samples across individual strata with sub-centimetre resolution. Downslope increases in mean stratum width are evident, while measurements of particle size distributions demonstrate preferential permeation of water along substrata composed of finer particles, explaining the strata-associated, localised regions of high water content discovered by other work on the same dunes. Finally, I consider the effect of these within-dune variations in water content on seismic surveys for oil and gas. Having used high performance computing to simulate elastic wave propagation in the vicinity of an isolated, barchan sand dune, I demonstrate that such a dune acts as a resonator, absorbing energy from Rayleigh waves and reemitting it over an extensive period of time. I derive and validate a mathematical framework that uses bulk properties of the dune to predict quantitative properties of the emitted waves, and I demonstrate the importance of internal variations in seismic velocity, resulting from variations in water content.
Avalanches, Granular flow, Size distribution, Intermittency, Erodible bed, Granular segregation, Stratification, Sandflow cross-strata, Dunes, Water permeation, Seismic surveys, Ground-roll, Rayleigh-wave scattering, Internal structure, Particle-size distributions
This work was supported by a PhD studentship within the Cambridge Earth Systems Science Doctoral Training Partnership (ESS DTP), funded by the National Environmental Research Council, grant number NE/L002507/1. Additional support was provided by Schlumberger Cambridge Research (SCR), through a CASE studentship.
This record's DOI: https://doi.org/10.17863/CAM.26140
Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), The Intellectual Property of chapter 5 was transferred from Schlumberger Cambridge Research Ltd.