3D High-Precision Forward Modeling of DC Resistivity Data Based on a High-Order Finite Element Method

The DC resistivity method is extensively employed in metal mineral exploration, hydrogeology, and engineering geology owing to its cost-effectiveness and high precision. High-precision 3D forward modeling of DC resistivity is crucial for the efficient inversion of resistivity data to delineate the true subsurface resistivity distribution. This paper presents a three-dimensional DC resistivity forward modeling algorithm based on a high-order finite element method (FEM). Initially, the model domain is discretized using an unstructured mesh composed of arbitrary tetrahedral elements. Subsequently, isoparametric element transformation techniques are utilized to construct high-order nodal basis functions. Furthermore, a novel absorption boundary condition, leveraging real number and coordinate stretching techniques, is implemented; this condition is notably straightforward to implement. The resulting finite element system of equations is then solved using the parallel direct solver MUMPS. To validate the accuracy and efficacy of the proposed algorithm, forward calculations are performed on several typical geoelectric models. The results demonstrate that increasing the element order enhances the computational accuracy of the finite element numerical solution. Moreover, the proposed absorption boundary condition outperforms conventional Dirichlet boundary conditions without incurring additional computational cost.