A Quadratic Model for Electromagnetic Subsurface Prospecting

Abstract

Abstract In this paper a quadratic model for the reconstruction of objects embedded in a lossy half space from scattered field data is introduced in a two dimensional and scalar geometry. It is shown that the present approach allows to reconstruct permittivity profiles that are not retrievable within a simpler linear model. This is due to the non-linearity of the quadratic approach, that allows to take into account for multiple scattering phenomena neglected by a linear approach. To perform the inversion, the object to be retrieved is projected within a finite dimensional subspace depending on the geometry of the problem, the electromagnetic properties of the half space, the configuration of the source and of the measurements. This step allows to regularize suitably the inverse problem. Furthermore, an appropriate choice of such a subspace and the use of a two step minimization procedure, with different solution spaces with progressively enlarged number of unknowns, allows to counteract the problem of local minima and to perform a computationally viable inversion.