Numerical treatment for inverse problems in applied Geophysics

This thesis is concerned with numerical methods for inverse problems in applied Geophysics. Its main purpose is to reconstruct the electrical conductivity and the magnetic permeability of the soil by Electromagnetic induction (EMI). By taking measurements at several heights by a Ground Conductivity Meter (GCM), we can gain information about the depth profile of electrical conductivity. Nevertheless, the noninvasive determination of it, using only above-ground electromagnetic induction measurements, remains difficult since it involves inverse problems which typically lead to mathematical models that are not well–posed. This means especially that their solution is unstable under data perturbations. Numerical methods that can cope with this problem are the so–called regularization methods. This thesis reports distinct algorithms and techniques to overpass these difficulties since mathematical problems having these undesirable properties pose severe numerical adversities. Along the thesis we deal with linear and nonlinear models, that involve the solution of ill–conditioned problems for reconstructing the electrical conductivity and the magnetic permeability of the soil, and we propose for each of these problems an inversion procedure to get a good approximation of the solution.