Sensitivity kernels for time-distance inversion based on the Rytov approximation

The study of the solar convection zone has been given a new impetus with what promises to be a very powerful new tool in time-distance helioseismology (Duvall et al. 1993). Using data obtained with this technique, it has become possible to do a tomographic reconstruction of structures in the convection zone. Most of the work done on inversion of these data has relied on the ray approximation to deliver sensitivity kernels for the inversion procedures (Kosovichev 1996). Inversions using non ray-theoretical kernels were shown by Jensen et al. (2001). In this paper we go beyond the ray approximation and derive sensitivity kernels based on the Rytov approximation and Greenʹs function theory. We derive an expression for the sensitivity kernel using ray-based Greenʹs functions and show how further approximations can be done to increase the computational efficiency.