Tomographic Inversion of Travel Time Data for Estimating VelocityStructure and Discontinuities

We present a method to invert travel time data for determining the velocity structure and geometry of discontinuities in 2-D laterally varying media. The algorithm is based in the construction of a matrix of partial derivatives of travel times where the parameters may be either the velocity or the depth, or both, and SVD. The partial derivatives are computed using previous formulae for derivatives with respect to the velocity developed by Madrid (1986), and a ray tracing technique based on the partition of a medium in triangular regions wherein the gradient of velocity is constant. This kind of parameterization allows us to implement specific constrictions on the variations of depth parameters that are adequate in the search of discontinuities. The method is tested with synthetic data in the presence of noise. A simple real example is included.