| 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- andelastic-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 solvethe 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 effectivelysuppress the numerical dispersion, which is usually caused by the discretization ofwave equations when coarse grids are used or geological models have large velocitycontrasts between adjacent layers. Meanwhile, we investigate the performance of theSSPC method including numerical errors and convergence rate, numerical dispersion,and stability criteria with different choices of the weighting parameter to solve 1-Dand 2-D acoustic- and elastic-wave equations. When the SSPC is applied to seismicsimulations, 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 SSPCand analytic solutions for acoustic and elastic models are given to illustrate the accuracy and the validity of the SSPC method. Furthermore, several numerical experimentsare conducted for the geological models including a 2-D homogeneous transverselyisotropic (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 seismicsimulation because of its effectiveness in suppressing numerical dispersion even in thesituations such as coarse grids, strong interfaces, or high frequencies. |
