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Numerical solution of differential and integral equations
The regularity of the forward map for acoustic wave equation is studied. Existence of its Frechet derivative with respect to wave propagation velocity is justified. This fact opens a possibility of linearization (Born's approach) of the forward map. The structure of this linearized map is studied and its property to be a compact map is proved. This property brings to the light the nature of the troubles with propagator recovery via L_2 inversion and points to the way to overcome it. The comparison of linearized inversion and prestack seismic depth migration is studied as well. It happened that migration procedure is nothing else but the first step of LSQR procedure for linear inversion. Results of numerical experiments for realistic media structure are presented and discussed.
Note. Abstracts are published in author's edition
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