An application of the reciprocity gap functional to inverse scattering theory

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.