Two-dimensional resistivity inversion

Abstract

Resistivity data on a profile often must be interpreted in terms of a complex two-dimensional (2-D) model. However, trial-and-error modeling for such a case can be very difficult and frustrating. To make interpretation easier and more objective, we have developed a nonlinear inversion technique that estimates the resistivities of cells in a 2-D model of predetermined geometry, based on dipole?dipole resistivity data. Our numerical solution for the forward problem is based on the transmission-surface analogy. The partial derivatives of apparent resistivity with respect to model resistivities are equal to a simple function of the currents excited in the transmission surface by transmitters placed at receiver and transmitter sites. Thus, for the dipole?dipole array the inversion requires only one forward problem per iteration. We use the Box?Kanemasu method to stabilize the parameter step at each iteration. We have tested our inversion technique on synthetic and field data. In both cases, convergence is rapid and the method is practical if the number of parameters is not too large. The main limitations of the method are that the geometry of the model must be specified in advance, and that it is difficult to determine whether model misfit is due to 3-D effects or to underparameterization in the 2-D model. The technique should be used interactively, with models constrained by geologic information.