Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

Abstract

Herein we derive an explicit first-order perturbation formula for the phase velocity of Rayleigh waves that propagate along the free surface of a homogeneous pre-stressed half-space, the incremental elasticity tensor L of which has a principal part C that is orthorhombic (with two of the axes of two-fold rotational symmetry being normal to the free surface and being the propagation direction, respectively) or transversely isotropic (with the ∞-axis being normal to the free surface). The remaining (perturbative) part A of the incremental elasticity tensor can be arbitrarily anisotropic. As an application of the perturbation formula, we consider the case where C is transversely isotropic and A is given by a contraction of the sixth-order acoustoelastic tensor with the pre-stress, and we examine the possibility of and the problems and issues about determination of the pre-stress by boundary measurement of phase velocities of Rayleigh waves.