Temporal High-Order Time–Space Domain Finite-Difference Methods for Modeling 3D Acoustic Wave Equations on General Cuboid Grids

Finite-difference (FD) methods are popularly utilized to achieve precise and efficient simulations of acoustic wavefields in large-scale 3D seismic inversion and imaging. General cuboid grid (i.e., different grid spacings in different spatial directions)-based space-domain FD is only second-order accurate. The standard time–space-domain FD is based on cubic grids (i.e., the same spacing for all directions), and only achieves high-order accuracy along 48 propagation directions. We developed two novel cuboid grid-based high-order time–space FD for 3D acoustic modeling. Two new stencils containing grid points both on and off the axis are developed to achieve fourth- and sixth-order discretization, respectively, for solving second-order temporal derivatives on general cuboid grids. The joint time–space dispersion relations for wave extrapolation using the proposed temporal FD and spatial central FD are derived by plane-wave analysis, and the analytical expressions for the coefficients used are derived by Taylor expansion. The two schemes yield arbitrary even-order accuracy in space and fourth- or sixth-order accuracy in time. Dispersion analysis, stability analysis, and numerical examples on cuboid grids confirm that the two schemes have better accuracy and stability than both the space-domain FD and the Lax–Wendroff FD. Because they allow for larger time steps, the two schemes are more efficient. They show superiority over the standard time–space-domain FD as well when cubic grids are used. Our new methods thus provide more general and effective tools for studying 3D acoustic wave propagation.