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Validation of a fast semi-analytic method for surface-wave propagation in layered media

Brissaud, Quentin and Tsai, Victor C. (2019) Validation of a fast semi-analytic method for surface-wave propagation in layered media. Geophysical Journal International, 219 (2). pp. 1405-1420. ISSN 0956-540X. doi:10.1093/gji/ggz351.

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Green’s functions provide an efficient way to model surface-wave propagation and estimate physical quantities for near-surface processes. Several surface-wave Green’s function approximations (far-field, no mode conversions and no higher mode surface waves) have been employed for numerous applications such as estimating sediment flux in rivers, determining the properties of landslides, identifying the seismic signature of debris flows or to study seismic noise through cross-correlations. Based on those approximations, simple empirical scalings exist to derive phase velocities and amplitudes for pure power-law velocity structures providing an exact relationship between the velocity model and the Green’s functions. However, no quantitative estimates of the accuracy of these simple scalings have been reported for impulsive sources in complex velocity structures. In this paper, we address this gap by comparing the theoretical predictions to high-order numerical solutions for the vertical component of the wavefield. The Green’s functions computation shows that attenuation-induced dispersion of phase and group velocity plays an important role and should be carefully taken into account to correctly describe how surface-wave amplitudes decay with distance. The comparisons confirm the general reliability of the semi-analytic model for power-law and realistic shear velocity structures to describe fundamental-mode Rayleigh waves in terms of characteristic frequencies, amplitudes and envelopes. At short distances from the source, and for large near-surface velocity gradients or high Q values, the low-frequency energy can be dominated by higher mode surface waves that can be captured by introducing additional higher mode Rayleigh-wave power-law scalings. We also find that the energy spectral density for realistic shear-velocity models close to piecewise power-law models can be accurately modelled using the same non-dimensional scalings. The frequency range of validity of each power-law scaling can be derived from the corresponding phase velocities. Finally, highly discontinuous near-surface velocity profiles can also be approximated by a combination of power-law scalings. Analytical Green’s functions derived from the non-dimensionalization provide a good estimate of the amplitude and variations of the energy distribution, although the predictions are quite poor around the frequency bounds of each power-law scaling.

Item Type:Article
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URLURL TypeDescription
Brissaud, Quentin0000-0001-8189-4699
Tsai, Victor C.0000-0003-1809-6672
Additional Information:© The Author(s) 2019. Published by Oxford University Press on behalf of The Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2019 September 2. Received 2019 May 17; in original form 2019 January 30. Published: 05 September 2019. The authors would like to thank the two anonymous reviewers that greatly helped improving the paper.
Group:Seismological Laboratory
Subject Keywords:Numerical approximations and analysis, Seismic noise, Surface waves and free oscillations, Wave propagation
Issue or Number:2
Record Number:CaltechAUTHORS:20191031-104134697
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Official Citation:Quentin Brissaud, Victor C Tsai, Validation of a fast semi-analytic method for surface-wave propagation in layered media, Geophysical Journal International, Volume 219, Issue 2, November 2019, Pages 1405–1420,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99581
Deposited By: Tony Diaz
Deposited On:31 Oct 2019 17:46
Last Modified:16 Nov 2021 17:47

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