Abstract
The problem of scattering of sound waves by a local inhomogeneity in an anisotropic medium with a spherical stratification is studied for a linear acoustic model. Natural oscillations of the external medium are considered with a help of intertwining operators for the differential operator of the basic equation. We show that there exist local inhomogeneities (domains) for which there is no scattered field, induced by a falling on these inhomogeneities acoustic field, created by external compactly distributed sources. It means that these inhomogeneities cannot be detected by the acoustic field generated by external compactly distributed sources. The main characteristics of these nonscattering inhomogeneities are studied.
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