3-D resistivity modeling of undulating terrain using space-wavenumber mixed domain approach

Abstract This study presents an innovative 3D numerical simulation approach tailored for the direct current resistivity method under undulating terrain conditions. The method utilizes 2D Fourier transform technology to convert complex 3D problems into 1D problems in the space-wavenumber mixed domain, thereby simplifying the computational process. We assume a layered background medium and utilize the weighted residual method to solve this simplified 1D problem. Additionally, to precisely handle terrain boundary nodes, we introduce an isogeometric gradient method applied in the logarithmic domain of conductivity. By constructing 3D trapezoidal ridge and valley models, we have validated the effectiveness and accuracy of the proposed algorithm. Further experiments involving a spherical low-resistivity body and a prismatic high-resistivity body beneath ridge terrain demonstrate the significant impact of undulating terrain on the observed results. This highlights the importance of considering terrain undulations in field observations and emphasizes the necessity of making appropriate corrections when interpreting data to prevent erroneous interpretations or significant deviations in results.