Electrical resistivity and induced polarization modelling using the spectral-infinite-element method

Abstract

Accurate and efficient modelling of the subsurface electrical properties is crucial for several applications, such as geophysical exploration, environmental studies, and resource identification. This study presents a versatile and efficient forward modelling tool for calculating the electric potential of 3D complex models, incorporating heterogeneities, topography, and anisotropy based on the Spectral-Infinite-Element Method (SIEM). SIEM combines spectral and infinite elements to simulate complex resistivity or conductivity models accurately and efficiently, incorporating the infinite boundary conditions associated with the Poisson/Laplace equation that governs the electrical potential. Two different numerical quadrature methods, namely, the Gauss–Legendre–Lobatto (GLL) and the Gauss–Radau quadrature, are used for solving the discretized form of the governing equations within and outside the domain of interest, respectively. To validate the method, comprehensive simulations were performed, and results were compared with analytical and existing methods for various examples. With an appropriate mesh element size, SIEM achieved remarkable accuracy, with maximum relative errors of about 1%. Furthermore, the substantial reduction in simulation times demonstrates the computational efficiency of the methodology, particularly when using local mesh refinement. Additionally, the effects of anisotropy and topography were investigated on resistivity and induced polarization (IP) data interpretation. Results show that anisotropic and topographic models exhibited distinct patterns from isotropic and flat models, respectively. These findings emphasize the importance of incorporating both directional resistivity and terrain variation effects in geoelectrical modelling. This research establishes a foundation for a future 3D adjoint inversion program that incorporates topography, heterogeneities, and anisotropy, enhancing the accuracy of subsurface modelling and interpretation.