3D forward modeling of DC resistivity method based on finite element with mixed grid

The DC resistivity method is widely used in the mineral resources exploration and geological survey industries because of its high efficiency and low cost, such as non-ferrous metals and coal fields. However, in the process of borehole–to–surface and surface–to–borehole resistivity method exploration, the influence of borehole factors (borehole fluid resistivity and borehole diameter) on the apparent resistivity response in different exploration modes is unclear, and whether it will affect the interpretation of apparent resistivity data is an issue worth exploring. Therefore, we proposed a mixed grid finite element method to realize the 3D forward modeling of DC resistivity. Then we gave the boundary value problem and the finite element variational problem satisfied by the abnormal electric potential method, applied the trigonal and tetrahedral grid to achieve a fast discretization of the computational region, and established the linear interpolation basis function and the element matrix of the two kinds of the grids. Finally, we used the SSOR–PCG iterative algorithm to solve the large-scale linear equations satisfied by the secondary potential and obtained the response of every observation point. On the premise of ensuring the calculation accuracy, we applied the mixed grid to discrete the borehole geoelectric model and explored the characteristics of the influence of borehole factors on the apparent resistivity data of the borehole-to-surface and surface-to-borehole observation methods. For the borehole-to-surface observation method: the apparent resistivity near the borehole is most influenced by the borehole factor, which seriously affects the reasonable interpretation of the apparent resistivity data. However, with the increase of the transmit-receive distance of the observation point, the apparent resistivity response gradually inclines to the resistivity of the surrounding rock. And with the depth of the emission source increases, the influence of borehole on the apparent resistivity response of the surface is also gradually reduced. For surface-to-borehole observation method: the borehole factor has a greater influence on shallow data and less influence on deep data, and the apparent resistivity response is more susceptible to the influence of borehole diameter than borehole fluid resistivity. The 3D forward modeling of mixed grid finite element method of DC resistivity method will provide theoretical guidance for practical borehole-to-surface and surface-to-borehole resistivity exploration, geophysical workers can combine the borehole information with the 3D forward modeling and select the appropriate transmit-receive distance to effectively suppress the influence of borehole on the observed data.