Higher-Order Asymptotic Approximations for Surface Love Waves of SH Type in Tranversely Isotropic Elastic Media

Abstract

A uniform asymptotics of the surface Love modes for a special case of anisotropy (tranverse isotropy) of an elastic media is obtained. In constructing the asymptotics of surface waves, the space-time (ST) ray method is employed. The wave field of each Love mode is represented as the sum of the ST caustic expansion involving the Airy functions with a real eikonal and two correction terms that are ST ray solutions, which in fact are inhomogeneous waves with complex eikonals. The eikonals and coefficients of the caustic and ray series are sought in the form of expansions in powers of two variables. The first variable is the distance from the surface, whereas the other characterizes the proximity of the caustic of a ray field to the boundary surface. Thanks to the specific structure of the elasticity tensor for a transversely isotropic medium, the boundary surface is necessarily a plane. A recursion process of computation of higher terms of the asymptotic expansion allows one to trace the conversion of the formulas obtained to the known ray solutions for isotropic elastic media. Relations between the elasticity parameters of a medium are obtained that ensure the existence of SH Love waves in a transversely isotropic medium and that are consistent with the conditions of the positiveness of the elastic energy of deformation. Bibliography: 6 titles.