Iterative geostatistical electrical resistivity tomography inversion

Electrical resistivity tomography (ERT) is a geophysical method used to create an image of the subsurface due to its sensitivity to porosity, water saturation, and pore fluid salinity. This geophysical method has been widely applied in the investigation of mineral and groundwater resources, as well as in archaeological, environmental, and engineering studies. The prediction of subsurface properties, such as electrical conductivity, from measured ERT data requires solving a challenging geophysical inversion problem. This work proposes an iterative geostatistical resistivity inversion method using stochastic sequential simulation and co-simulation as stochastic model perturbation and update techniques. Electrical resistivity models are generated conditioned to a target histogram, often retrieved from available resistivity borehole data, and assuming a spatial continuity pattern described by a variogram model. From the electrical resistivity models, a finite-volume approximation of Poisson’s equation is used to compute synthetic ERT data. The misfit between predicted and observed data drives the convergence of an iterative procedure and conditions the co-simulation of new models in the subsequent iterations. This methodology is applied to a two-dimensional synthetic case, and a set of two-dimensional profiles obtained from an ERT survey carried out in southern Portugal. In both application examples, the final models predict ERT data that match the observed ones while reproducing borehole data and imposed variogram models. The results obtained in both data sets are compared against a commercial deterministic ERT inversion methodology, showing the ability of the proposed method to model small-scale variability and assess spatial uncertainty.