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An application of the reciprocity gap functional to inverse scattering theory. (English) Zbl 1086.35129

Summary: A method is given for determining the shape of an object from the Cauchy data of the total field measured on the boundary of a domain containing the object in its interior. An application is given to the problem of determining the shape of an object buried in the earth from measurements on the surface of the earth. The advantages of the method are that (1) no a priori knowledge is needed of the physical properties of the scattering object and (2) there is no need to compute Green’s function for the background medium.

MSC:

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35P25 Scattering theory for PDEs
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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