Three-Dimensional Borehole-to-Surface Electromagnetic Resistivity Anisotropic Forward Simulation Based on the Unstructured-Mesh Edge-Based Finite Element Method

Geophysics is a discipline that studies the properties of subsurface media using physical methods, among which electromagnetic methods have long been an important technical approach in resource exploration. The anisotropy of resistivity in underground media objectively exists in electromagnetic exploration. However, most borehole-to-surface electromagnetic methods (BSEMs) currently process and interpret data based on the assumption of isotropy, which can lead to misinterpretations of observational data in regions where an isotropy is significant. To address this, we propose a 3D edge-based finite element method on unstructured meshes for simulating resistivity anisotropy in BSEMs. A principal-axis anisotropic tensor is introduced to model anisotropy, and the vertical-line transmitter is transformed into an equivalent set of point sources, enabling efficient computation. The accuracy and effectiveness of the proposed numerical algorithm are validated through comparisons with the solutions from Dipole1D and MARE2D. Furthermore, a comparative analysis of reservoir dynamic monitoring under isotropic and anisotropic conditions using the same model reveals that the relative errors in amplitude and phase exceed 40%, and anisotropy must be adequately considered in reservoir monitoring with borehole-to-surface electromagnetic methods. For reservoir models with varying extraction rates, this study further examines the influence of a transmitter’s position on the electromagnetic response characteristics in anisotropic reservoir dynamic monitoring. The results indicate that effective monitoring cannot be achieved when the transmitter is located above the reservoir; however, when the transmitter is positioned below the reservoir, the borehole-to-surface electromagnetic method can significantly enhance the monitoring of reservoir dynamics.