Ill-Posedness and Nonlinearity

The direct scattering problem consists of the calculation of the scattered field if we know the underground scenario, whereas the inverse scattering problem consists in the reconstruction of the underground scenario if we know the scattered field. In both the direct and the inverse problem the characteristics of the antennas and of the soil are assumed to be known. Customarily the inverse problems present some additional difficulties with respect to the corresponding direct ones. In particular, unlike the direct ones, the inverse problems are usually ill-posed. Moreover, if the direct problem is nonlinear, also the corresponding inverse problem is nonlinear. In particular, the electromagnetic inverse scattering problem is both ill-posed and nonlinear.