Stable iterative reconstruction algorithm for nonlinear traveltime tomography

Abstract

Reconstruction of acoustic, seismic, or electromagnetic wave-speed distributions from first arrival traveltime data is the goal of traveltime tomography. The reconstruction problem is nonlinear, because the ray paths that should be used for tomographic backprojection techniques can depend strongly on the unknown wave speeds. In the author's analysis, Fermat's principle is used to show that trial wave-speed models which produce any ray paths with traveltime smaller than the measured traveltime are not feasible models. Furthermore, for a given set of trial ray paths, non-feasible models can be classified by their total number of 'feasibility violations', i.e. the number of ray paths with traveltime less than that measured. Fermat's principle is subsequently used to convexify the fully nonlinear traveltime tomography problem.