Abstract:
A three-dimensional inverse scattering problem for the acoustic wave equation is studied. The task is to determine the density and acoustic impedance of a medium. A necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law. The interpretation of the solution to the inverse problem and the construction of medium images are discussed.
Key words:acoustic impedance, Galerkin method, acoustic, eikonal, Klein–Gordon, Schrödinger, and Riccati equations, Dirac system, Volterra and Gelfand–Levitan integral equations, tensor field.
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