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

Abstract

The 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.