Elastic wave propagation with high-order temporal and spatial accuracy by a new multi-axial staggered-grid finite-difference scheme

Staggered-grid finite-difference (SFD) scheme has become a cornerstone in numerical simulations of elastic wave phenomena, particularly valued for its enhanced precision and stability in wave equation solutions compared to conventional centered-grid approaches, effectiveness of describing the material heterogeneity and easy implementation. However, when adopting the elastic classical SFD (ECSFD) scheme to propagate the waves, the simulated wavefield is prone to temporal and spatial dispersion errors with a coarse grid configuration. While the issue could be ameliorated by tunable spatial finite-difference (FD) approximation, the non-adjustable second-order temporal FD makes ECSFD scheme vulnerable to the accumulated errors for wave propagation in a long-time or long-distance simulation scenario. To tackle the issue, we design an elastic multi-axial SFD (EMASFD) scheme, featuring the innovative EMASFD stencil and coefficients, to accurately and efficiently propagate the elastic waves. Unlike the ECSFD stencil, the EMASFD stencil consists of grid points not only in an axial direction, but also in two additional diagonal directions. To simultaneously reach high-order spatial and temporal accuracy, the SFD coefficients of the EMASFD stencil are derived by fitting the high-order terms of the k-t domain operators, which are related to the wave modes of the compressional and shear components. Using dispersion curves, stability analyses, and numerical examples, we have established that the EMASFD scheme exhibits superior stability and accuracy compared to the ECSFD scheme. Thanks to the improved temporal accuracy, the EMASFD scheme permits a larger stable time-stepping intervals to perform elastic wave propagation, translating to efficiency gains in large-scale elastic wave modeling applications.