Asymptotic expansion of SV type surface waves for singular propagation directions in transversely isotropic elastic media

The general scheme of constructing the uniform asymptotics of SV type surface modes as the sum of space-time (ST) caustic expansion and two correction ST ray series (with complex eikonals) is applied to an inhomogeneous transversely isotropic elastic medium. The case is considered where at certain points on the boundary surface S (or at a curve which lies on S) the phase velocities of two quasi-shear elastic waves turn out to be identical. Here, on S, the elasticity tensor depends on four material parameters rather then five parameters as is commonly the case with transversely isotropic media.