A linearized group velocity approach for two point qP ray tracing in a layered orthorhombic medium

P.F. Daley

ABSTRACT

Using a linearized approximation for the quasi-compressional phase velocity, vqP in an orthorhombic anisotropic medium, which is a subset of the related quasicompressional ( qP ) wave propagation in a general 21 parameter anisotropic medium, a linearized compressional group velocity may be derived as a function of group angles only. In addition, linearized analytic expressions for the components of the slowness vector in terms of group velocities and angles are also obtained. These expressions are used to define two nonlinear equations which are a generalization of Snell's Law. The solutions of these are used to determine the propagation directions of the reflected and transmitted rays due to an incident ray at an interface between two orthorhombic media. The axes of anisotropy in both media are, in general, not aligned with the interface separating them. Computer code has been written to consider ray tracing in media defined by a type of large scale 3D finite element blocking (blocky structures). However, a plane parallel layered will be used in preliminary investigations. Additionally, in each of these elements (layers) the anisotropic parameters are initially assumed to be constant, although provisions for at least minimal spatial variations of the anisotropic parameters have been considered.

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