First-order perturbation method for anisotropic media

Abstract

The first-order perturbation method is used to evaluate approximate phase velocities and polarization vectors in elastic anisotropic media. Formulae are given which make possible computations of perturbations of these parameters for quasi-compressional as well as quasi-shear waves, no matter whether the unperturbed medium is isotropic or anisotropic. Approximate results for an extremely anisotropic material and relatively large deviations of parameters of unperturbed and perturbed media closely resemble the results computed exactly. It is, therefore, expected that the application of the perturbation method to realistic media with generally weaker anisotropy and for smaller deviations between unperturbed and perturbed medium parameters should give satisfactory results. The method will find the most important applications in the investigation of high-frequency wave propagation in inhomogeneous anisotropic media and in solving inverse problems for anisotropic structures. Several possible applications are listed and briefly discussed.