Features of the Solution of Direct and Inverse Scattering Problems for Inhomogeneities with a Small Wave Size

An acoustic field scattered by a single inhomogeneity consists of components of different orders of multipolarity. For symmetric or weak-contrast inhomogeneities of a small wave size, these components are related to multipole components of an initial incident field by a set of scattering coefficients. It is established that the admissible range of each of these coefficients on the complex plane is a circle in the presence of absorption in the inhomogeneity and a circumference in the absence of absorption. The solution of the inverse problem for the purpose of reconstructing the mentioned inhomogeneity may encounter difficulties, since the spatial spectrum of the secondary sources is excessively expanded due to the multiple scattering, and an error is introduced into the reconstruction results. Sets of values of the monopole scattering coefficient are established on the complex plane for which this effect manifests itself to the greatest extent.