Time-Domain Induced Polarization Tomography Inversion

Induced polarization (IP) tomography measurements, as a near-surface geophysical method, can provide information about the degree of chargeability of subsurface materials and are commonly used in mineral exploration, engineering studies (e.g., sediment/bedrock interface identification, crushed zones and faults detection, and landslide and soil properties imaging), as well as in environmental investigations (contaminant plums identification and landfill characterization). The purpose of these measurements is to obtain the distribution of polarizability characteristics inside an object, generally below the surface, at the boundary of the object, or outside the area in question. The results of such measurements can be mathematically modeled for the specific polarizability properties by solving the Poisson’s equation restricted by appropriate boundary conditions. In this paper, we focused on the importance of simulating induced-polarization responses and retrieving chargeability distributions in geo-materials to enhance the characterization of subsurface structures. We presented the methods for forward modelling and non-linear inversion of IP measurements. To this end, in the first step, the Poisson’s equation for a two-dimensional ground with an arbitrary distribution of conductivity is solved using the finite difference numerical method. In the next step, based on the existing relations between conductivity and chargeability (the Siegel’s formulation), the apparent IP response is calculated. Finally, we solved the non-linear chargeability inversion problem following a non-linear apparent resistivity inversion. This is achieved by imposing physical constraints to prevent the estimation of unrealistic model parameters, using a Newton-based optimization method. To evaluate the efficiency of the proposed methodology, we utilized the proposed algorithm on two simulated examples and a real data set. Our numerical results show that the algorithm reliably represents the main features and structure of the Earth’s subsurface in terms of resistivity and chargeability models. All the algorithms presented in this paper have written in the MATLAB programming language.