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Discontinuous Galerkin method for solving 2D dissipative seismic wave equations

XIJUN HE1 ,  CHUJUN QIU2 ,  JIANQIANG SUN3
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1 School of Mathematics and Statistics, Beijing Technology and Business University (BTBU), Beijing 100048, P.R. China.,
2 Department of Mathematical Sciences, Tsinghua University, Beijing 100000, P.R. China.,
3 Department of Mathematical Sciences, Hainan University, Haikou 100000, P.R. China.,
JSE 2022, 31(2), 153–176;
Submitted: 8 July 2021 | Accepted: 16 January 2022 | Published: 1 April 2022
© 2022 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

He, X.J., Qui, C.J. and Sun, J.Q., 2022. Discontinuous Galerkin method for solving 2D dissipative seismic wave equations. Journal of Seismic Exploration, 31: 153-176. Seismic dissipation widely exists in underground media. To develop a detailed understanding of wave propagation in dissipative media, in this study, we introduce a discontinuous Galerkin (DG) method for solving acoustic and elastic wave equations in D’Alembert media. This method uses the numerical flux-based DG formulations with the explicit 3rd-order total variation diminishing (TVD) time discretization. We first derive an empirical formula for numerical stability conditions, which shows that the relative error of the Courant-Friedrichs-Lewy (CFL) condition numbers between the actual the numerical cases does not exceed 3%. The analyses also show that both the dispersion and dissipation in D’Alembert media are frequency dependent, and have a strong correlation with the dissipation factor. Finally, we present some numerical experiments. The quantitative comparisons of the attenuation ratios of the waveforms show that they are close to the theoretical ones, verifying the findings of the analyses. In particular, for elastic waves, the relative errors between the numerical attenuation ratios and the theoretical ones do not exceed 4%. The simulation of dissipative elastic wave propagation in a model with surface topography indicates our method is capable of dealing with complex geometry.

Keywords
discontinuous Galerkin method
D’Alembert media
dispersion
dissipation
numerical modelling
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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