An accurate and stable wave equation for pure acoustic TTI modeling

Abstract

One fundamental shortcoming of the conventional pseudoacoustic approximation is that it only prevents shear wave propagation along the symmetry axis of anisotropy and not in other directions. This problem leads to the presence of unwanted shear waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudo-acoustic wave equations become unstable for anisotropy parameters e < δ and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely de-couple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems. In this work, we propose a new pure acoustic TTI wave equation and compare it with the conventional coupled pseudo-acoustic wave equation. We derive finite difference solutions to this new equation and use numerical examples to demonstrate that it produces highly accurate P-wave results, very close to results produced by coupled pseudo-acoustic wave equations, but completely free from shear wave artifacts.