2D DC resistivity forward modeling based on the integral equation method and a comparison with the RES2DMOD results

A 2D forward modeling code for DC resistivity is developed based on the integral equation (IE) method. Here, a linear relation between model parameters and apparent resistivity values is proposed, although the resistivity modeling is generally a nonlinear problem. Two synthetic cases are considered for the numerical calculations and the results derived from IE code are compared with the RES2DMOD that is a standard software for 2D resistivity forward modeling. For the first synthetic case, a model of resistive block surrounded by a homogenous medium is considered in different depths from 0.5 m to 4 m. For the nearest case to the surface, the IE pseudo-section is similar to its counterpart derived by RES2DMOD but its RMS error is a large value of 13.9 %. Increasing the depth of the anomaly results in decreasing of RMS values to 5.4 % for the deepest case and it is in correspondence with diminishing of the nonlinearity effects of electric fields for larger distances from the sources. The second model is composed of four conductive anomalies embedded in different depths. Visual comparison of IE response with software is indicative of high similarity of them, and RMS error for this relatively complex model is 7.5%, which can be an acceptable misfit for a linear forward operation. A very simple inversion algorithm using linear forward operator is applied on a real data set of a landfill survey in Germany collected by Wenner alfa array to demonstrate its productivity for practical applications. Reconstructed model using IE method is comparable with the inverted model derived by RES2DINV software, and it represents a good similarity with the original model.