3D acoustic wave modeling with a time-space-domain temporal high-order finite-difference scheme

Abstract

Conventional finite-difference (FD) methods for 3D acoustic wave modeling generally adopt 1D FD stencil along each coordinate axis to discretize spatial derivatives of the Laplace operator. It has been proved that when (2M)th-order spatial and second-order temporal 1D FD stencils are directly used to numerically solve the 3D acoustic wave equation, the modeling accuracy is second-order. The accuracy can be increased to (2M)th-order along 48 propagation directions by using spatial FD coefficients based on the time-space-domain dispersion relation. To improve the accuracy further, we design a novel temporal high-order FD stencil, which is a combination of the orthogonality and octahedron stencils, to discretize the 3D spatial Laplace operator. Based on the time-space-domain dispersion relation, we derive the corresponding FD coefficients using a plane wave theory and Taylor-series expansion. This new FD scheme can simultaneously achieve (2M)th-order spatial and (2N)th-order temporal modeling accuracies. Moreover, we further adopt a graphic processing unit to address the extensive computational cost in the 3D case. Dispersion and stability analyses indicate that our proposed FD scheme is more accurate and more stable than the conventional one under the same operator length M. The accuracy and efficiency advantages are also demonstrated by two 3D modeling examples.