Optimal Fourth-order Staggered-grid Finite-difference Scheme for 3D Frequency-domain Viscoelastic Wave Modeling

Abstract

Frequency-domain seismic wave modeling has been extensively investigated and applied within the framework of seismic imaging techniques, such as the full waveform inversion (FWI) and the reverse time migration (RTM). Among different discretization approaches, finite-difference schemes has been gaining popularity due to its simplicity and computational efficiency. We investigate an optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling. The finite-difference coefficients and the anti-lumped mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity. Numerical dispersion analysis shows that the optimal fourth-order scheme presents less dispersion and anisotropy with respect to different propagation angles, and requires only 4 gridpoints per minimum shear wavelength to keep the error of the group velocities below 1%. Elastic wave modeling in a 3D homogeneous medium at different frequencies are conducted with the optimal fourth-order scheme.