Linear and quadratic programs for the conductivity reconstruction of subsurface

An approach for constructing vertical sections of the electrical conductivity of the Earth on the basis of surface measurements is presented. Electromagnetic measurements are effected every few meters across strike using pairs of horizontal and vertical coils, with the separation between source and receiver varying in order to sample different depths. The data provide information about the vertical and horizontal distribution of electrical conductivity of a section of the Earth. The recovering of the true conductivity distribution from the measurements is a nonlinear inverse problem that allows some useful linear approximations, which we exploit here using linear programming techniques. A regularization approach is considered using epsiv-insensitive functions for both the fitness to the data and the penalizing function. This representation enforces a model structure of blocks immersed in a homogeneous basement, an useful model in many practical instances