Sensitivity kernels for time-distance inversion

Inversion of local-area helioseismic time-distance data has so far only been done in the ray approximation (Kosovichev, 1996). Since this is a high-frequency approximation its applicability can be questioned for the solar case. Bogdan (1997) showed that for a simple solar model the localized wave packets do follow, but are not confined to, the ray path. We use an approximation based on the first Fresnel zone that has been developed in geophysics by Snieder and Lomax (1996) to go beyond the ray approximation in the inversions. We have calculated sensitivity kernels using both approximations. To test them we use a finite-difference forward modeling of the whole wave field in an acoustic medium reminiscent of the Sun. We use the finite-difference modeling to calculate sensitivity kernels for the full wave field and compare this with the other kernels. The results show that the Fresnel-zone-based kernels are in good agreement with the sensitivity obtained from the modeling. Thus these new kernels represent a significant step forward in the inversion of time-distance data.