On the effects of a dipping axis of symmetry on shear wave splitting measurements in a transversely isotropic medium

We derive the explicit expressions for the phase velocities and polarizations of quasi-shear waves propagating in a transversely isotropic medium. The normal to the plane defined by the phase normal and the symmetry axis gives the exact polarization of S1, while the polarization of S2 also depends on the elastic parameters of the medium and is thus more complicated. Therefore, we propose that the polarization of the slow S1 wave, instead of the fast S2 wave, as is common practice, should be determined from seismic data. For a dipping fast axis of symmetry, a 360° periodic variation of the apparent slow axis is predicted, with an amplitude given by arctan(tan q/tanq0), where q is the incidence angle and q0 the angle between the symmetry axis and the vertical. For a significant dip of the symmetry axis (larger than 20°) and for large incidence angles these variations should be observable in shear wave splitting measurements. This suggests that SKKS, and S waves generated by deep earthquakes, which are characterized by larger incidence angles in comparison to SKS waves, should be able to constrain a possible dip of the symmetry axis. In contrast, constraining the dip of the symmetry axis from the delay times turns out to be much more difficult owing to their complicated (and non-linear) dependence on azimuth and on the elastic parameters.