Acoustic Anisotropic Wavefields through Perturbation Theory

Abstract

Solving the anisotropic acoustic wave equation in a conventional manner (i.e. finite difference implementation) introduces a number of problems, and sets media restrictions, and it rarely contributes to our ability to resolve the anisotropic parameters. Utilizing perturbation theory in developing the solution of the anisotropic acoustic wave equation allows us direct access to the desired limitations-free solutions, that is solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation as we can isolate the wavefield dependency on the perturbed anisotropic parameters. As a result, I derive approximate phase operators for a spectral domain wavefield extrapolation in transversely isotropic media based on perturbations in the anisotropic parameters. The solutions of the perturbation equations represent the coefficients of a Taylor's series type expansion of the wavefield as a function of the perturbed parameter, which is in this case the anellipticity parameter and the symmetry axis. The accuracy is relatively high in even inhomogeneous media.