Simulation of Scalar Wave Propagation with High-Order Temporal and Spatial Accuracy by a New Multi-Axial Staggered-Grid Finite-Difference Scheme

Abstract

ABSTRACT Staggered-grid finite-difference (SFD) stencils are extensively applied for scalar wavefield simulations and inversions in seismology because of their easy implementation and effectiveness of propagating the wave in heterogeneous media. The conventional SFD (CSFD) stencil adopts second-order temporal and high-order spatial finite-difference operators to approximate the partial derivatives inside the wave equation. The spatial SFD operator only adopts grid points along one orthogonally axial direction to approximate the spatial partial derivative along that direction. Therefore, increasing the number of grid points along the axis will not improve the temporal accuracy. To simultaneously enhance the temporal and spatial accuracy, we propose a new multi-axial SFD (MASFD) stencil, which consists of grid points along three directions for each partial derivative in space. The MASFD weightings (coefficients) are derived by preserving the dispersion relation of the scalar wave in the frequency–wavenumber domain. We prove that increasing the number of the grid points of the new stencil can simultaneously reach high-order accuracy in time and space. The performance of the new MASFD scheme is compared with the CSFD schemes by quantitative dispersion analyses, stability analyses, and numerical examples. Our comprehensive comparisons demonstrate that the MASFD scheme can be more accurate than the CSFD ones because of improved temporal accuracy. Under comparable accuracy, the MASFD scheme can be more efficient than the CSFD ones because the MASFD scheme can adopt larger time steps to perform stable wave extrapolation.