Seismic Crosswell Tomography: A Gauss-Newton Type Algorithm Based on B-splines for Velocity Field Parametrization. Part I: Fundamentals

A Gauss-Newton type method for seismic crosswell traveltime tomography based on B-splines products linear combinations for velocity field representation is presented. Knot points and order are estabilished through Dierckx approximation technique according to the initial guess model parameters. The Frechet derivatives are contour integrations along the rays and the regularization factor is estimated using the concepts of condition number and Backus-Gilbert spread factor for normalized resolution matrices. A numerical example demonstrates the robustness of the method.