A Layer Stripping Fast Algorithm for the Two-Dimensional Direct Current Inverse Resistivity Problem

The inverse problem of reconstructing the resistivity of the earth, varying both laterally and with depth, from direct current measurements is considered. The problem is formulated as a multidimensional inverse scattering problem and solved using a layer stripping algorithm. This algorithm recursively reconstructs the resistivity and electrical potential on horizontal planes of increasing depth by downward continuation. This is the first exact solution to the inverse resistivity problem for resistivity varying laterally as well as with depth. The algorithm is an extension of an algorithm proposed by Levy for resistivity varying in one dimension.