Volume 12, Issue 4
A Strong Stability-preserving Predictor-corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media

D. H. Yang, N. Wang & E. Liu

Commun. Comput. Phys., 12 (2012), pp. 1006-1032.

Published online: 2012-12

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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 accuracyandthe validityof theSSPCmethod. Furthermore,severalnumericalexperiments 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 effectivenessin suppressing numerical dispersion even in the situations such as coarse grids, strong interfaces, or high frequencies.


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@Article{CiCP-12-1006, author = {D. H. Yang, N. Wang and E. Liu}, title = {A Strong Stability-preserving Predictor-corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {4}, pages = {1006--1032}, 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 accuracyandthe validityof theSSPCmethod. Furthermore,severalnumericalexperiments 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 effectivenessin suppressing numerical dispersion even in the situations such as coarse grids, strong interfaces, or high frequencies.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.010111.230911a}, url = {http://global-sci.org/intro/article_detail/cicp/7322.html} }
TY - JOUR T1 - A Strong Stability-preserving Predictor-corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media AU - D. H. Yang, N. Wang & E. Liu JO - Communications in Computational Physics VL - 4 SP - 1006 EP - 1032 PY - 2012 DA - 2012/12 SN - 12 DO - http://dor.org/10.4208/cicp.010111.230911a UR - https://global-sci.org/intro/cicp/7322.html KW - AB -

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 accuracyandthe validityof theSSPCmethod. Furthermore,severalnumericalexperiments 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 effectivenessin suppressing numerical dispersion even in the situations such as coarse grids, strong interfaces, or high frequencies.


D. H. Yang, N. Wang & E. Liu. (1970). A Strong Stability-preserving Predictor-corrector Method for the Simulation of Elastic Wave Propagation in Anisotropic Media. Communications in Computational Physics. 12 (4). 1006-1032. doi:10.4208/cicp.010111.230911a
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