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Recovering multiscale buried anomalies in a two-layered medium. (English) Zbl 1330.78012

Summary: We develop an inverse scattering scheme of recovering impenetrable anomalies buried in a two-layered medium. The recovery scheme works in a rather general setting and possesses several salient features. It makes use of a single far-field measurement in the half-space above the anomalies, and works independently of the physical properties of the anomalies. There might be anomalous components of multiscale sizes presented simultaneously. Moreover, the proposed scheme is of a totally direct nature without any inversion involved, and hence it is very fast and robust against measurement noise. Both theoretical foundation and numerical experiments are presented. This extends related results in the literature on recovering multiscale scatterers located in a homogeneous space.

MSC:

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P25 Scattering theory for PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78M25 Numerical methods in optics (MSC2010)
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