Topography incorporated inversion of DC resistivity data using integral equation vs. Res2dinv software

In this paper, the direct-current (DC) resistivity inversion problem, based on the integral equation (IE), is expanded to data sets, including uneven topography, which has never been done before. For the inversion procedure, a weighted damped minimum length solution is implemented and depth weighting is used as the model weighting matrix. The regularisation parameter is estimated utilising an initial guess equal to the maximum value of the kernel matrix (forward operator). Then, the optimal value is adopted by a few trials and errors. To investigate the productivity of the presented method, the inversion results are compared with the inversion models derived from Res2dinv software, which works based on nonlinear equations. At first, a model of a conductive dyke under a valley is considered for which the retrieved model by the extended IE technique is even superior to the Res2dinv result. Because of the promising consequence derived from the synthetic case, the efficiency of the presented method is tested on the data set of the Robat Sang mine in Iran. The inversion model obtained from the extended IE method shows a high consistency with Res2dinv.