QS-waves in a vicinity of the axis of symmetry of homogeneous transversely isotropic media

Abstract

We study propagation of the SV and SH waves, generated by a concentrated force in unbounded transversely isotropic (TI) homogeneous media acting in orthogonal to the symmetry axis direction, in a vicinity of this axis. This problem is known in geophysics as the problem of kiss singularity. Our approach is based on application of the high-frequency asymptotics of the SV and SH waves in TI media in a vicinity of the axis of symmetry obtained earlier in [M.M. Popov, Asymptotics of the wave field in a vicinity of the axis of symmetry of a transversely isotropic homogeneous medium, Zap. Nauchn. Semin. POMI, 275 (2001) 199–211 (in Russian) [Engl. Trans.: J. Math. Sci. 117 (2) (2003) 4001–4007]. These formulas provide smooth transition of the qS-wave field from the vicinity of the axis, where the ray method fails, to the ray formulas for the SV and SH waves which are valid at some distance from the axis. We present time pulse propagation of the coupled SV and SH waves and their splitting with the increasing distance to the symmetry axis. A distortion of the initial time pulse and evolution of the wave field polarization are discussed.