Nonlinear inversion of a buried object in transverse electric scattering

A method for reconstructing the material properties of a buried bounded inh omogeneous object from measured scattered held data at the surface of the E arth's interface is presented. This work extends the method previously deve loped for the homogeneous transverse electric (TE) case to the more complic ated case of a buried object. In the TE case, the magnetic field is polariz ed along the axis of an inhomogeneous cylinder of arbitrary cross section, and the corresponding integral equation contains derivatives of both the ba ckground Green's function and the field. The nonlinear inversion, however, can be formulated from an electric held integral equation for the two trans versal components of the electric field. The integrand is a product of the background Green's function, the contrast, and the electric field vector; h owever, in the case of a buried object the background Green's function is t he one pertaining to a two-media configuration. The derivatives are operati ve outside the integral. In this paper the latter formulation will be taken as the point of departure to develop a nonlinear inversion scheme based up on the modified gradient method. In the inversion scheme the positivity of the material parameters has to be ensured in order to obtain a convergent i nversion scheme. Numerical results are presented in which the reconstructio n of the contrast is shown and compared in the case of TE excitation as wel l as transverse magnetic (TM) excitation.