Imaging the Earth Using Time‐Domain Surface‐Wave Measurements: Evaluation and Correction of the Finite‐Frequency Phase Shift
Publication Date
2022-05-12Journal Title
Journal of Geophysical Research: Solid Earth
ISSN
2169-9313
Volume
127
Issue
5
Language
en
Type
Article
This Version
AO
VoR
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Xu, Y., Lebedev, S., & Meier, T. (2022). Imaging the Earth Using Time‐Domain Surface‐Wave Measurements: Evaluation and Correction of the Finite‐Frequency Phase Shift. Journal of Geophysical Research: Solid Earth, 127 (5) https://doi.org/10.1029/2021jb023701
Abstract
Abstract: Surface waves propagating from earthquakes, active sources or within the ambient noise wavefield are widely used to image Earth structure at various scales, from centimeters to hundreds of kilometers. The accuracy of surface‐wave, phase‐velocity measurements is essential for the accuracy of the Earth models they constrain. Here, we identify a finite‐frequency phase shift in the phase travel time that causes systematic errors in time‐domain, phase‐velocity measurements. The phase shift arises from the approximation of monochromatic surface waves with narrow‐band filtered surface waves. We derive an explicit formula of the finite‐frequency phase shift and present a numerical method for its evaluation and for the correction of the measurements. Applications to high‐frequency and long‐period examples show that the phase shift is typically around π/60‐π/16 for the common settings of ambient‐noise imaging studies, which translates to 0.2%–0.8% phase‐velocity measurement errors. The finite‐frequency phase shift depends on the (a) second derivative of the wavenumber with respect to frequency; (b) width of the narrow‐band filter; (c) epicentral or interstation distance; and (d) center frequency of the filter. In conversion to phase velocity, the last two factors cancel out. Frequency‐domain methods for phase‐velocity measurements have the advantage of not producing the finite‐frequency phase shift. Both time‐ and frequency‐domain measurements, however, can be impacted by a break‐down of the far‐field approximation (near‐field phase shift), which our calculations also show. Our method offers an effective means of improving the accuracy of the widely used time‐domain, phase‐velocity measurements via the evaluation of and corrections for the finite‐frequency phase shift.
Keywords
Seismology, SEISMOLOGY, Surface waves and free oscillations, Research Article, surface wave, phase shift, phase velocity measurement, noise interferometry
Sponsorship
European Commission ‐ Horizon2020 (776622)
Identifiers
jgrb55632, 2021jb023701
External DOI: https://doi.org/10.1029/2021jb023701
This record's URL: https://www.repository.cam.ac.uk/handle/1810/337071
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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