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An algorithm for parameter estimation in multidimensional media

We present the mathematical basis for an algorithm based on the adjoint method to locate points that provide an approximate solution to the parameter estimation problem for the acoustic model. The parameter belongs to infinite-dimensional sets. We state conditions under which the existence of the directional derivative of the solution with respect to the parameter exists in some dense set of directions of the set of parameters. This derivative is the solution of a differential boundary value problem. The adjoint problem is presented. We state a result on the convergence of the iterations.