Regularized inversion of multi-frequency EM data in geophysical applications

The purpose of this work is to detect or infer, by non destructive investigation of soil properties, inhomogeneities in the ground or the presence of particular conductive substances such as metals, minerals and other geological structures. A nonlinear model is used to describe the interaction between an electromagnetic field and the soil. Starting from electromagnetic data collected by a ground conductivity meter, we reconstruct the electrical conductivity of the soil with respect to depth by a regularized Gauss–Newton method. We propose an inversion method, based on the low-rank approximation of the Jacobian of the nonlinear model, which depends both on a relaxation parameter and a regularization parameter, chosen by automatic procedures. Our numerical experiments on synthetic data sets show that the algorithm gives satisfactory results when the magnetic permeability in the subsoil takes small values, even when the noise level is compatible with real applications. The inversion problem becomes much harder to solve if the value of the permeability increases substantially, that is in the presence of ferromagnetic materials.