Near-field influence on shear wave splitting and traveltime sensitivity kernels

In the last few years, Frechet (or sensitivity) kernels for seismic traveltimes have become important tools for mantle tomography. Sensitivity kernels for splitting intensity have been introduced recently for a better interpretation of shear wave splitting measurements. All ray-based sensitivity kernels studies relied so far on a far-field approximation of the Green's tensor. Under this approximation, the sensitivity kernels for splitting intensity do not accurately describe shear wave splitting at shallow depth. Here, we investigate the influence of near-field terms of the Green's tensor on the sensitivity kernels for both splitting intensity and traveltimes. Using the Born approximation, we derive analytical expressions for the complete sensitivity kernels. In contrast to the kernels obtained from the far-field Green's tensor, the sensitivity kernels based upon the complete Green's tensor are no longer zero on the ray path and show a complicated structure near the receiver. The results show that the near-field terms are needed to get accurate kernels at shallow depth. Using the complete Green's tensor, we define the normalized depth interval where near-field terms are important.