Identification of acoustic point sources in a two-layered medium from multi-frequency sparse far field patterns

Abstract

We consider the reconstruction of point sources in a two layered medium from the multi-frequency sparse far field patterns taken on the upper half sphere. The point sources are located in both the upper half space and the lower half space, and consequently bring difficulty for the inverse problem because of the combination of two different types of far field patterns. After establishing the uniqueness of the point sources by the multi-frequency far field patterns at properly chosen sparse observation directions, we introduce a multi-step numerical scheme for identifying all the points sources. Numerical examples show that the proposed sampling methods work very well for locating the positions and the formulas for determining the corresponding scattering strengths are valid and stable with respect to the noises.