We propose a shape optimization algorithm to reconstruct sharp interfaces in time-domain FWI. The interface of a salt domain is considered as the variable of a tracking-type cost functional. A damping term in the neighborhood of the boundary is used to model an unbounded domain. Using a Lagrangian approach, we compute the shape derivative of the cost functional. The shape derivative depends on an adjoint state, which is the solution of a wave equation with the residual on the right-hand side. The interface evolution is performed using a level set method. Using synthetic measurements, we show the efficiency of the method through several examples of reconstruction.


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