Abstract of the paper ``Global extrema in traveltime tomography''

In acoustics of inhomogeneous media, Fermat's principle of least time is fundamental to forward modeling; it is the basis of the bending methods of ray tracing often used to find acoustic ray paths. Fermat's principle plays an equally important role in the traveltime inversion problem, {\it i.e.}, the problem of attempting to estimate the wave velocities in the medium through which a sound pulse has traveled in a measured time from known source to receiver. Since measured first-arrival traveltimes are necessarily the minimum traveltimes through the medium whose sound velocity profile is to be reconstructed, Fermat's principle allows us to assign all possible wave-speed profiles to one of two classes: a model is either infeasible or feasible depending on whether or not there are paths from source to receiver that have less traveltime than that measured. The feasible set of models is convex and furthermore an exact solution to the inversion problem (if any) must lie on the boundary between the feasible and infeasible sets. Thus, Fermat's principle permits a convexification of the nonlinear traveltime inversion problem, so the only extrema are global extrema.

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