Sensitivity kernels for shear wave splitting in transverse isotropic media

Shear wave splitting observations are often used to constrain upper-mantle anisotropy. However, their interpretation, which is still controversial, always implicitly relies on geometric ray theory. This high-frequency approximation does not take the finite frequency of the shear wavefield into account. In this paper, the effects of transverse isotropic perturbations of the elastic parameters on shear wave splitting are investigated. The theory, based on the first-order Born approximation, allows the derivation of 2-D and 3-D Frechet or sensitivity kernels for a new seismic observable called the splitting intensity. It is shown that the splitting intensity measured at the surface can be written to first order as a weighted average of two anisotropic perturbation parameters gamma(c) and gamma(s) related to the anisotropic parameter gamma introduced by Mensch & Rasolofosaon. We also demonstrate, using a stationary-phase approximation, that the volume integral of the sensitivity kernels for a homogeneous transverse isotropic medium leads to the ray theoretical prediction for the splitting intensity. A numerical experiment on a two-block model demonstrates that lateral variations of anisotropy in the upper mantle introduce complicated and counterintuitive effects on shear wave splitting observed at the surface.