Interpretation of resistivity sounding measurements in N-layer soil using electrostatic images

Geophysical inversion involves the estimation of soil parameters from a set of observations. Multilayer soils are modeled by N horizontal layers with distinct resistivities and depths. For known soil parameters, the apparent resistivity distribution can be computed efficiently from electrostatic images. Since the model responses are generally nonlinear functions of the model parameters, least-squared minimization techniques prove to be useful for evaluating layer resistivities and depths to agree with measurements. This paper demonstrates how electrostatic images can be combined for increasing efficiency in the computation of apparent resistivities and sensitivity factors such as the first and second gradient of the distance with respect to the model parameters. The factors are then used to solve the more demanding task of resistivity interpretation of measurements from Wenner, Schlumberger, Dipole or alternate electrode configurations. Results are presented for two-layer soil and for actual cases with three layer soil