Forward Modelling of Electrical Resistivity and Induced Polarization Using the Spectral-Infinite-Element Method

Accurate and efficient modelling of subsurface electrical properties is critical for a wide range of applications, including mineral exploration, environmental studies and hydrogeological investigations. Traditional numerical approaches often use low-order discretization and impose artificial boundary conditions to approximate the unbounded spatial domain. These approximations can lead to inaccuracies and computational inefficiency, particularly in geologically complex environments. In this study, we present a spectral-infinite-element method (SIEM) for forward modelling of electrical resistivity and induced polarization. The approach couples high-order spectral elements within the finite domain with a single outer layer of mapped infinite elements, enabling precise representation of far-field boundary conditions. To achieve optimal numerical performance, we employ two distinct quadrature schemes: Gauss–Legendre–Lobatto quadrature for the spectral elements and Gauss–Radau quadrature for the infinite elements. We first verify the accuracy of our method by comparing the computed electric potential from a buried charged block with direct numerical integration. We conducted a convergence study by refining the mesh and increasing the order of the interpolation polynomials. To further evaluate the robustness of SIEM, we benchmark its results for a layered earth model against an analytical solution and an open-source Python-based geophysical modelling library, SimPEG. The comparisons demonstrate the accuracy, convergence and efficiency of SIEM. Finally, we apply SIEM to a complex heterogeneous conductivity model incorporating topography, generating apparent resistivity and chargeability pseudo-sections to illustrate its practical applicability under realistic survey conditions.