Propagation of Rayleigh waves of $SV$ type in transversely isotropic elastic media

The asymptotics of high-frequency surface waves in elastic media is studied for a special case of anisotropy, namely, for transversely isotropic media (where the parameters of elasticity are invariant with respect to rotations about one of the coordinate axes). In the zeroth asymptotic approximation, the slow Rayleigh waves (of $SV$ type) under study are polarized in the plane of the normal section of the surface. The principal term of the asymptotics (which has the form of a space-time (caustic) expansion) is found, and calculations related to the necessity of introducing two additional faster waves with complex eikonals are carried out. The conditions on the elasticity parameters of the medium that insure the origination of the surface waves in question are obtained. Due to the specific structure of the elasticity tensor under consideration, the boundary of the medium is necesarily plane. For appropriate values of elastic parameters, the resulting formulas coincide with the corresponding expressions in the isotropic case. Bibl. 8 titles.