@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.010111.230911a},
url = {http://global-sci.org/intro/article_detail/cicp/7322.html}
}