On Elastic-wave Propagation in Anisotropic Media: Reflection/Refraction Laws, Raytracing, and Traveltime Inversion

Michael A. Slawinski


An analytic method relating incidence, reflection and transmission angles at an interface between anisotropic media is presented. The method relies on the continuity conditions relating tangential components of phase slowness across the interface, and on the fact that the ray is perpendicular to the phase-slowness surface. The rather familiar concepts of vector calculus are used in a template for calculating phase and group angles. The angles involved in wave propagation through layered anisotropic media are, at times, significantly different than their isotropic counterparts. Thus the trajectories derived in raytracing by the isotropic versus the anisotropic approach differ significantly.

This template is used to derive analytic expressions for phase and group angles, and to elaborate a raytracing scheme for qP, qSV and qSH waves using expressions for phase velocities under the assumption of weak anisotropy. The raytracing method can be used to calculate traveltimes for layered weakly anisotropic media composed of TI materials.

The results of a physical laboratory experiment, which involved propagation in the symmetry plane of an orthorhombic material with known characteristics, have been compared with theoretical calculations. The comparison indicates that the anisotropic approach predicts reasonably well the experimental results and yields a significantly better prediction than an isotropic one. It also suggests that weak-anisotropy assumptions can be useful in practical applications as long as one remains within the intended limits of approximation.

The analytical approach is further extended to provide a traveltime inversion scheme for the anisotropic parameter characterizing qSH waves. The inversion method can be used in multi-layer media and accounts for raybending at interfaces. It is, however, very sensitive to errors in input parameters.

The results of both theoretical and laboratory investigations indicate that ignoring anisotropic effects can, in certain cases, lead to significant errors. This dissertation offers an approach which might prove helpful in such circumstances. Also, I believe, the usefulness of the present work to lie in clearly relating mathematical analytical formulations to physical consequences, thus contributing to a more intuitive understanding of phenomena exhibited by wave propagation in anisotropic media.

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