Modeling 3D elastic VTI wave propagation using an optimal k-space operator-based temporal high-accuracy staggered-grid finite-difference scheme

Abstract

It is difficult to extend the present time-space-domain or temporal high-order finite-difference (FD) stencils to model anisotropic wave equations owing to anisotropy parameters and spatial derivatives are mutually coupled. Thus, high-order spatial and second-order temporal FDs are commonly used to discretize anisotropic wave equations. To improve temporal modeling accuracy, we develop an efficient temporal high-accuracy staggered-grid FD (SG-FD) scheme to solve the first-order elastic wave equations in 3D vertical transversely isotropic (VTI) media. Through combining the spatial dispersion relation of the original SG-FD stencil with the first-order k (wavenumber)-space operator, we construct a modified SG-FD dispersion relation and determine FD coefficients using least-squares (LS). We adopt the modified LS-based SG-FD scheme using k-space operator compensation to simulate 3D elastic VTI wave propagation. Dispersion analysis and numerical examples demonstrate that our optimal k-space operator-based SG-FD scheme can achieve high temporal accuracy without compromising spatial accuracy compared with the traditionally uncompensated Taylor-series expansion- and LS-based SG-FD methods. Moreover, the stability of our proposed FD scheme is superior to the conventional ones.