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An inverse scattering problem for the 3D acoustic equation in time domain isconsidered. The unknown spatially distributed speed of sound is the subject ofthe solution of this problem. A single location of the point source is used.Using a Carleman Weight Function, a globally strictly convex cost functional isconstructed. A new Carleman estimate is proven. Global convergence of thegradient projection method is proven. Numerical experiments are conducted.

Convexification for the inversion of a time dependent wave front in a heterogeneous medium