High-Accuracy Modelling of 3D Frequency-Domain Elastic-Wave Equation Based on One-Direction Composition of the Average-Derivative Optimal Method

Abstract

Accurate simulation of seismic waves is essential for achieving high-precision full-waveform inversion (FWI). Within the Cartesian coordinate system-based frequency-domain finite-difference (FDFD) framework, we propose a one-direction composition average-derivative optimal method for the 3D heterogeneous isotropic elastic-wave equation, referred to as the 45-point scheme. The results of dispersion analysis and weighted coefficient optimization demonstrate that the 45-point scheme achieves higher dispersion accuracy than the existing 27-point average-derivative scheme. More importantly, by constructing the impedance matrix along the ‘composition’ direction, the bandwidth of the sparse impedance matrix increases only slightly, with nonzero elements compactly distributed in strips. On the basis of the multifrontal massively parallel sparse direct solver (MUMPS) on a supercomputer platform, the 45-point scheme does not significantly increase computational complexity compared to the 27-point scheme. To further test the performance of the 45-point scheme, we provide several numerical experiments, including simple homogeneous and complex SEG/EAGE overthrust models. In comparison with the 27-point scheme, the 45-point scheme yields a notable improvement in computational accuracy, particularly for large grid ratios, while imposing only a modest increase in computational cost. These findings thus strongly suggest that the 45-point scheme holds promise as a viable option for the forward part of frequency-domain FWI in practical high-accuracy seismic imaging applications.