Applying an advanced temporal and spatial high-order finite-difference stencil to 3D seismic wave modeling

Abstract

Present finite-difference (FD) algorithms for modeling seismic wave propagation in 3D acoustic media are mainly based on the traditional orthogonal stencil and can achieve spatial high-order but temporal second-order accuracy. Therefore, these approaches may result in visible temporal dispersion and even instability for relatively large time sampling intervals. In this paper, we develop an advanced FD stencil with temporal and spatial arbitrary even-order accuracy to solve the 3D acoustic wave equation. The temporal derivative is approximated by an octahedron stencil with the operator length N together with the traditional second-order FD. Meanwhile, the spatial derivatives are calculated by the orthogonal stencil with the operator length M. The plane-wave theory is introduced to derive the time-space-domain dispersion relation and estimate the corresponding high-order FD coefficients by Taylor expansion. To achieve higher accuracy, we further optimize FD coefficients by applying least-squares (LS) to minimize the relative error of the time-space-domain dispersion relation. Dispersion and stability analyses show that our new schemes have higher modeling accuracy and propagation stability than the conventional method. Numerical examples demonstrate that the proposed FDs can generate greater temporal accuracy on the prerequisite of preserving satisfactory spatial accuracy. Our new temporal high-order FD stencil by incorporating larger time step, shorter operator lengths, LS-based coefficients and variable-length operators can be regarded as a kind of accurate and efficient tool for seismic wave modeling.