Bayesian Methods for a Particular Inverse Problem: Seismic Tomography

Abstract

We propose a stochastic technique to solve the problem inverse of seismic tomography in heterogeneous media with known and unknown reflector depths. This technique combines a Bayesian algorithm with simulated annealing. The advantage of this technique is that it allows to reconstruct a velocity-depth model that minimizes the travel times error, keeping in view the physical restrictions imposed by the properties of the model. Instead of working directly in an infinite dimensional frame, we discretize the problem. Hence, at step n the inverse problem is to estimate the amplitude values of the unknown velocity at n sites. The main result is that asymptotically, the Bayesian procedure is equivalent to selecting a quasi solution of original inverse problem that maximizes a convex criterion.