Time-Domain Induced Polarization Tomography Inversion

Induced polarization (IP) tomography measurements as a near-surface geophysical method canprovide information about the degree of chargeability of subsurface materials, and are commonly usedin mineral exploration, engineering studies as well as in environmental investigations .The purpose ofthese 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 resultof such measurements can be mathematically modeled for the specific polarizability properties by thesolution of Poisson’s equation restricted by appropriate boundary conditions. In this paper, we focuson the importance of simulating induced-polarization responses and retrieving chargeabilitydistributions in geo-materials to enhance the characterization of subsurface structures. We present themethods for forward modeling and nonlinear inversion of induced-polarization measurements. To thisend, in the first step, Poisson’s equation for a two-dimensional ground with arbitrary distribution ofconductivity is solved using the finite difference numerical method and in the next step, based on theexisting relations between conductivity and chargeability (Siegel’s formulation), the apparent inducedpolarization response is calculated. Finally, we solve the nonlinear chargeability inversion problemfollowing a nonlinear apparent resistivity inversion. This is achieved by imposing physical constraintsto 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 to asimulated example and a real data set. Our numerical results show that the algorithm reliablyrepresents the main features and structure of the Earth’s subsurface in terms of the resistivity andchargeability models. All the algorithms presented in this paper have written in the MATLABprogramming language.

Keywords:

FINITE DIFFERENCE , NEWTON-BASED METHOD , NONLINEAR INVERSION , POISSON’SEQUATION , TIME DOMAIN INDUCED POLARIZATION