On the inverse problem of the scattering of elastic waves by a thin foreign inclusion
The problem of the remote determination of the shape of an isolated scatterer is considered using longitudinal elastic waves. It is assumed that the scatterer is a thin elastic solid of revolution situated in an elastic space under conditions of rigid contact and that Poisson's ratios of the medium and the scatterer are the same. The use of multifrequency wave information is a special feature of the solution of the problem. The problems of the uniqueness and stability of the solution obtained are also studied. We mean by the inverse scattering problem the problem of determining the form of the scattering region by analyzing the scattered field. The problem, as a rule, is one of a number of ill-posed problems of mathematical physics. The present paper uses the method given by the author, ibid. 48(1985), 89-92 (1984; Zbl 0566.73026) to solve the problem of determining the form of a thin elastic solid of revolution using the experimentally known scattering amplitude of longitudinal displacement waves specified on a discrete set of the sounding frequencies in a fixed direction in space. It is assumed here that Poisson's ratios of the medium and the solid in question are the same, and the solid is in rigid contact with the elastic medium.
scientific article; zbMATH DE number 4009913