Asymptotic Theory For Diffusive Electromagnetic Imaging

SUMMARY We propose an asymptotic theory for diffusive electromagnetic imaging. Three steps are required to perform this imaging. (1) A high-frequency solution is first constructed which mimics the one usually found in wave-propagation phenomena. (2) This solution, valid for a smooth continuous description of the resistivity in the medium, is used in a first-order Born approximation leading to a linear relation between the resistivity perturbation of the subsurface and the perturbation of the electric signal obtained at the free surface. (3) This linear relation is asymptotically inverted by using an iterative quasi-Newtonian inversion based on a least-squares criterion developed by Jin et al. (1992). Although the extension to smooth heterogeneous reference medium is possible, we have only tested the inversion scheme for homogeneous reference media as Zhdanov & Frenkel (1983) previously did with another method.