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arXiv · 2212.11494

Dispersion relation and wave equation for attenuative elliptically anisotropic media

Qi Hao·Ilya Tsvankin
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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.

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Qi Hao, Ilya Tsvankin. 2022-12-22. Dispersion relation and wave equation for attenuative elliptically anisotropic media. https://arxiv.org/abs/2212.11494

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