Snell's law in transversely isotropic media using linearized group velocities and related quantities

P. F. Daley

Using a linearized approximation for the quasi-compressional phase velocity, vqP(nk) in a transversely isotropic (TI) medium, which is a subset of the related quasicompressional (qP) wave propagation in an orthorhombic medium, a linearized compressional group velocity, vqP(Nk), is derived as a function of group angles only. In addition, analytic expressions for the components of the slowness vector in terms of group velocities and angles are also obtained. These expressions are used here to set up the generally nonlinear equations that are required to be solved for the reflected and transmitted rays due to an incident ray, at a plane interface between two transversely isotropic media, when the axes of anisotropy, in both media, are, in general, not aligned with the interface. The total medium is assumed to be composed of finite elements, specifically Delauney triangles, which are used to account for vertical and lateral inhomogeneities as well as anisotropy with arbitrary orientation.