Recently, scholars have proposed various methods to enhance the simulation accuracy of the staggered grid finite difference (SGFD) for the elastic wave equation. While these methods have significantly improved simulation precision, they inevitably face challenges related to simulation stability. The maximum Courant-Friedrichs-Lewy (CFL) number imposes certain constraints on simulation stability. It has been found that if the CFL number, calculated based on the temporal sampling interval, spatial sampling interval, and model velocity, exceeds the maximum CFL number that the chosen SGFD method can attain, the simulation becomes unstable. To address this issue, we introduce a new SGFD method that enhances the maximum CFL number by controlling the dispersion relation. This improvement allows us to surpass the limits of the maximum CFL number achievable by conventional methods, enabling simulations with larger temporal sampling intervals or smaller spatial sampling intervals. Stability analysis and numerical simulations validate that our new method exhibits superior stability and efficiency while maintaining simulation accuracy. This presents a viable solution for the efficient simulation of the elastic wave equation.
Ren et al. (Thu,) studied this question.