New formulae for linear travel time inversion in 2-d heterogeneous media. Theory and results.

Abstract

Reliable formulae for the computation of travel time residuals and partial derivatives for the inverse problem in two dimensions based on ray tracing are developed. The partial derivatives are completely determined by the path and the travel time residuals are as accurate as the observed travel times; it is not necessary to solve the traditional fixed ends problem'. A new kind of inversion is introduced that operates directly on the shape of the isovelocity lines, making possible the immediate visual inspection of the results of an iteration. The formulae were checked against synthetic data corresponding to a variety of models. The way to approach a particular problem depends both on the available data and the structure.