Elastic-wave-equation numerical simulation using a time–space domain dispersion-relation-based staggered-grid finite-difference method

Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can suppress the numerical dispersion more efficiently to achieve higher modeling accuracy when applied to numerically solving the velocity–stress acoustic equation. The enhanced modeling accuracy of TS-SFD is attributed to the difference-coefficient calculation approach based on the time–space domain dispersion relation, which makes the difference coefficients change adaptively with the propagation velocity of seismic waves in the medium. However, when numerical simulation of the velocity–stress elastic wave equation is conducted with TS-SFD, if the difference coefficients are calculated based on the time–space domain P-wave dispersion relation, the modeling accuracy of P-wave is high, while that of S-wave is low and vice versa . To address the limitation of TS-SFD in ensuring high modeling accuracy for both P- and S-wave, in this article, we propose a novel strategy to conduct elastic wave numerical simulation with TS-SFD, in which the decoupled P- and S-wave elastic wave equations are numerically solved with TS-SFD, and the difference coefficients are calculated based on the time–space domain P- and S-wave dispersion relations, respectively. Numerical dispersion analysis and numerical simulation examples show that the simulation strategy proposed in this article can ensure high simulation accuracy for both P- and S-wave. Stability analysis shows that this simulation strategy can effectively improve the stability of elastic wave numerical simulation with TS-SFD. In addition, the simulation strategy has the additional advantage of automatically separating the P- and S-wave, which provides a solid foundation for the subsequent analysis of P- and S-wave propagation characteristics in elastic media and elastic wave reverse time migration.