Hybrid Pseudospectral/Finite‐Difference Numerical Simulation and Stability Analysis of Pure P‐Wave Propagation in Vti Media

Abstract

AbstractThe attractive feature of pure P‐wave equations for anisotropic media is that it is completely free from shear‐wave artifacts, and can alleviate the numerical instabilities caused by anisotropy. We present the first‐order pure P‐wave velocity‐stress equation for transversely isotropic media with a vertical symmetry axis. Like most other pure acoustic anisotropic wave equations, our equation involves complicated pseudo‐differential operators in space, which cannot be solved with the finite‐difference method alone. For computational efficiency, we adopt an efficient hybrid pseudospectral (PS)/finite‐difference (FD) scheme to solve the pure P‐wave equation. The stability of the hybrid PS/FD scheme on central and staggered grids is investigated by von Neumann's method. Numerical tests on 2D synthetic examples demonstrate that the proposed pure P‐wave equation provides stable and kinetically accurate simulation results for complex anisotropic media.