Forward modelling of electrical resistivity and induced polarization in anisotropic media using the spectral-infinite-element method

We present a three-dimensional spectral-infinite-element method (SIEM) for simulating direct current resistivity and induced polarization (IP) in complex anisotropic media. Our method accommodates fully anisotropic and arbitrary conductivity structures. To accurately represent the unbounded domain, infinite boundary conditions are incorporated into the weak formulation of the governing Poisson equation. An anisotropic two-layer earth model is used to validate the SIEM implementation, and resistivity responses are compared to analytical solutions and the AIM4RES software package. The numerical results show reliable accuracy, with an average relative error below 9\%. Additional validation is performed by comparing chargeability responses with finite-element and finite-volume results. Tilted transverse isotropy significantly distorts potential fields and complicates data interpretation, whereas vertical transverse isotropy has a negligible effect and enables accurate anomaly localization, according to tests conducted on a flat model with a conductive target. Lastly, to investigate the combined effects of anisotropy and topography, 3D IP forward modelling is performed over uneven terrain for different dipping anisotropy angles. The results show that increasing the dipping angle increases the likelihood of misinterpretation.