Dispersion relation and wave equation for attenuative elliptically anisotropic media
Abstract
The P-wave slowness and group-velocity surfaces in elliptically anisotropic media are ellipsoids. Elliptical anisotropy is convenient to use as the reference medium in perturbation methods designed to solve P-wave wave-propagation problems for transverse isotropy (TI). Here, we make the elliptically anisotropic TI model attenuative and discuss the corresponding P-wave dispersion relation and the wave equation. Our analysis leads to two conditions in terms of the Thomsen-type parameters, which guarantee that the P-wave slowness surface and the dispersion relation satisfy elliptical equations. We also obtain the viscoacoustic wave equation for such elliptically anisotropic media and solve it for point-source radiation using the correspondence principle. Numerical examples validate the proposed elliptical conditions and illustrate the behavior of the P-wavefield in attenuative elliptical TI models.
Cite
@article{arxiv.2212.11494,
title = {Dispersion relation and wave equation for attenuative elliptically anisotropic media},
author = {Qi Hao and Ilya Tsvankin},
journal= {arXiv preprint arXiv:2212.11494},
year = {2022}
}