Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model

We study wave propagation in anisotropic inhomogeneous media. Specifically, we formulate and analytically solve the ray-tracing equations for the factorized model with wavefront velocity increasing linearly with depth and depending elliptically on direction. We obtain explicit expressions for traveltime, wavefront (phase) angle, and ray (group) velocity and angle, and study these seismological quantities for a model that successfully describes field measurements in the Western Canada Basin. By considering numerical examples, we also show that the difference between the wavefront and ray velocities depends only slightly on the anisotropy parameter, whereas the difference between the wavefront and ray angles is, in a first-order approximation, linear in the anisotropy parameter.