Perturbation of Rayleigh waves in anisotropic media

Abstract

Herein we consider Rayleigh waves propagating along the traction-free surface of a homogeneous anisotropic elastic half-space. We investigate the perturbation of the phase velocity and of the polarization of Rayleigh waves, i.e., the shift of phase velocity and the shift of polarization of Rayleigh waves from their respective value pertaining to a comparative isotropic state of the elastic medium, as caused by the anisotropic part of the elasticity tensor. With the help of the Stroh formalism, we derive first-order perturbation formulas for these shifts. We also discuss the problem of determining elastic constants of a weakly anisotropic elastic medium by making measurements of Rayleigh waves propagating in all the directions on the traction-free surface.