1-D INVERSION OF RESISTIVITY AND INDUCED POLARIZATION DATA FOR THE LEAST NUMBER OF LAYERS

An automatic inverse method has been developed for generating layered earth models from electrical sounding data. The models have the minimu m number of layers required to fit a resistivity sounding curve or a c ombined resistivity and induced polarization sounding. The ground is m odeled using a very large number of thin layers to accommodate arbitra ry variations. The properties of the layers are optimized using as a c onstraint the L-1 norm of the vertical derivative of the resistivity d istribution. The use of linear programming leads to piecewise smooth d istributions that simulate traditional models made up of a few uniform layers. The process considers from the simplest model of a uniform ha lfspace to models of many layers, without fixing a priori the number o f discontinuities. The solution is sought by iterating a new linear ap proximation, similar to the classical process of linearization, except that a reference model is not present in either the data vector or th e unknown function. For induced polarization soundings, the problem is linear and the solution is obtained in a single iteration, provided a n adequate resistivity model is available. The performance of the meth od is illustrated using numerical experiments and published deep resis tivity data from Australia. The method also is applied to combined res istivity and induced polarization soundings from a local groundwater p rospect in Mexico.