Reflection Ray Tomography in case of Curved Reflector

The inverse problem has one of its manifestations in the seismic problem of the determination of reflector depth and seismic velocity above it from reflection traveltime data. Reflection ray tomography is an effort to solve this seismic problem. The work is based on the solution of the least-square linearized problem. The input data are synthetic traveltimes obtained doing a ray-tracing in a target model that has a polynomial parametrization. The system of observation, the conversion of units and normalization of the cummt model playa important role in the effort to get a sufficiently small condition number (CN) of the matriz AtA. This CN tells us about stability of the inversion in each iteration. We have observed that the number of rays, isolately, doesn't improve the situation of stability. Inversions are done in a very good condition of stability, some of them reach the target model begining in a very distant initial model. The reference model in each iteration has a parabolic reflector and a constant slowness field above it. The analytical derivatives are saving a lot of the computational time. A rather satisfactory result is gotten by adding random noise to the synthetic data for severals signal-naise ratios. key word.: Inverse problem, stability, parametrization, traveltime, curved reflector, tomogrophy.