Inverse Modeling of Time-Domain Induced Polarization Data with the Aim of Imaging Mineralization Zones

Time-domain induced polarization (TDIP) measurements provide valuable information about the degree of polarization of subsurface geological layers. This geophysical technique plays a crucial role in a wide range of applications, including mineral exploration (for determining bedrock depth, identifying cavities, fracture zones, and faults), geotechnical investigations (such as assessing the stability of dams, airport runways, and other infrastructures), as well as in environmental studies (as detecting and monitoring contaminated areas). The primary objective of TDIP measurements is to determine the spatial distribution of the subsurface’s electrical properties, whether within a buried object along its boundaries, or in the surrounding medium. These electrical characteristics are typically influenced by factors such as mineral composition, porosity, fluid saturation, and grain surface chemistry. Mathematically, the behavior of the electric potential in the earth is governed by Poisson’s equation, which must be solved under appropriate boundary conditions. By solving this equation, a model of the subsurface can be generated, offering deeper insight into its geological structure. In the forward modeling process, for a two-dimensional environment with an arbitrary distribution of electrical conductivity, the governing partial differential equation is solved numerically—commonly using the finite difference method (FDM). Based on the conductivity distribution, apparent induced polarization (IP) responses are calculated by incorporating the relationship between conductivity and IP parameters such as chargeability. These apparent IP responses include the calculation of Frechét derivatives, which form the elements of the sensitivity matrix (Jacobian matrix). This matrix plays a key role in defining the objective function for the inversion process. Inversion of TDIP data is inherently nonlinear and typically involves a two-step procedure. In the first step, the direct current (DC) resistivity data is used to estimate the distribution of electric potential within the medium, which leads to the estimation of the background conductivity. In the second step, using this conductivity model as a fixed or initial condition, the main goal is to recover the chargeability distribution that best explains the observed IP data. This is achieved by solving the inverse problem using suitable numerical optimization methods. The final chargeability model is considered acceptable when it produces simulated data that adequately match the measured field data within a defined error tolerance.
To evaluate the effectiveness and robustness of the proposed inversion algorithm, both synthetic datasets and field measurements from the Borzamin area were utilized. Numerical results demonstrate that the algorithm can provide reasonable reconstructions of synthetic models. However, as the complexity of the IP model increases (e.g., due to heterogeneity or anisotropy), the uncertainty in precisely determining the chargeability distribution also increases. Field data inversion results indicate the presence of chargeable anomalies across multiple profiles in the study area. When interpreted alongside lithological information, these anomalies suggest the potential existence of mineralized zones within the Borzamin region. Such integrated geophysical and geological interpretations can significantly enhance exploration strategies and reduce the uncertainty in locating economically viable ore deposits.