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A Strong Stability-Preserving Predictor-Corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media

Published online by Cambridge University Press:  20 August 2015

D. H. Yang ,
N. Wang  and
E. Liu
D. H. Yang*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
N. Wang*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China
E. Liu*
Affiliation:
Department of Geophysics, China University of Mining and Technology, Xuzhou, Jiangsu Province, P. R. China
*
Corresponding author.Email:dhyang@math.tsinghua.edu.cn
Email:happyxiaoxi114@163.com
Email:eliu0103@hotmail.com(E.Liu)
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Abstract

In this paper, we propose a strong stability-preserving predictor-corrector (SSPC) method based on an implicit Runge-Kutta method to solve the acoustic- and elastic-wave equations. We first transform the wave equations into a system of ordinary differential equations (ODEs) and apply the local extrapolation method to discretize the spatial high-order derivatives, resulting in a system of semi-discrete ODEs. Then we use the SSPC method based on an implicit Runge-Kutta method to solve the semi-discrete ODEs and introduce a weighting parameter into the SSPC method. On top of such a structure, we develop a robust numerical algorithm to effectively suppress the numerical dispersion, which is usually caused by the discretization of wave equations when coarse grids are used or geological models have large velocity contrasts between adjacent layers. Meanwhile, we investigate the performance of the SSPC method including numerical errors and convergence rate, numerical dispersion, and stability criteria with different choices of the weighting parameter to solve 1-D and 2-D acoustic- and elastic-wave equations. When the SSPC is applied to seismic simulations, the computational efficiency is also investigated by comparing the SSPC, the fourth-order Lax-Wendroff correction (LWC) method, and the staggered-grid (SG) finite difference method. Comparisons of synthetic waveforms computed by the SSPC and analytic solutions for acoustic and elastic models are given to illustrate the accuracy and the validity of the SSPC method. Furthermore, several numerical experiments are conducted for the geological models including a 2-D homogeneous transversely isotropic (TI) medium, a two-layer elastic model, and the 2-D SEG/EAGE salt model. The results show that the SSPC can be used as a practical tool for large-scale seismic simulation because of its effectiveness in suppressing numerical dispersion even in the situations such as coarse grids, strong interfaces, or high frequencies.

Keywords

65M0665M1286-0886A15SSPC methodseismic wavefield modelinganisotropynumerical dispersionshear-wave splitting
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 4 , October 2012 , pp. 1006 - 1032
Copyright
Copyright © Global Science Press Limited 2012

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