Nonlinear inversion of a buried object in transverse electric scattering
Résumé
A method for reconstructing the material properties of a buried bounded inhomogeneous object from measured scattered field data at the surface of the Earth's interface is presented. This work extends the method previously developed for the homogeneous transverse electric (TE) case to the more complicated case of a buried object. In the TE case, the magnetic field is polarized along the axis of an inhomogeneous cylinder of arbitrary cross section, and the corresponding integral equation contains derivatives of both the background Green's function and the field. The nonlinear inversion, however, can be formulated from an electric field integral equation for the two transversal components of the electric field. The integrand is a product of the background Green's function, the contrast, and the electric field vector; however, in the case of a buried object the background Green's function is the one pertaining to a two-media configuration. The derivatives are operative outside the integral. In this paper the latter formulation will be taken as the point of departure to develop a nonlinear inversion scheme based upon the modified gradient method. In the inversion scheme the positivity of the material parameters has to be ensured in order to obtain a convergent inversion scheme. Numerical results are presented in which the reconstruction of the contrast is shown and compared in the case of TE excitation as well as transverse magnetic (TM) excitation.