Ray tracing in azimuthally anisotropic media-II. Quasi-shear wave coupling

Quasi-shear wave polarizations typically twist along ray paths through gradient regions in anisotropic media, causing frequency dependent coupling between the qS-waves. This coupling is much stronger than the analogous coupling between P- and SV-waves in isotropic gradients because of the small difference between the qS-wave velocities. Geometrical ray theory is typically valid for qS-waves only at relatively high frequencies, and does not converge to the isotropic result in the limit of infinitely weak anisotropy. Using the plane-wave layered response, we show examples of this coupling and how it may cause frequency dependent shear-wave polarizations. We consider two special cases where the coupling is especially strong in hexagonally symmetric media: (i) intersection singularities where the slowness sheets cross, and (ii) kiss singularities where the slowness sheets touch at the symmetry axis. We show numerical and asymptotic solutions for the pulses generated in these situations. In some cases, far-field excitation of both quasi-shear waves (and shear-wave splitting) will result from an incident wave composed of only one of the quasi-shear waves.