Three-dimensional DC Resistivity Modeling using Galerkin Finite Element Method Composed by Tetrahedral Elements

Successful interpretation of DC resistivity data depends on the availability of a proper forward modeling scheme. In this study, a three-dimensional DC resistivity forward modeling scheme was developed using the finite element method. The finite element equations were obtained using a weakened form of the weighted-residual method called the Galerkin method. Discretization of the modeling domain was carried out by dividing it into smaller three-dimensional blocks and subdividing each block into five tetrahedral elements. A linear interpolation function was employed and elemental linear equations were set up, followed by formation of global matrix systems of equation and incorporation of proper boundary conditions. The conjugate gradient method was applied to solve the global system of equations, which in this study was proven to be more efficient than a direct solver, contributing to a 67% time reduction. Using a Wenner array configuration, comparison with theoretical calculation of the electric potential for a homogeneous model yielded a relative error of 3.66%. To confirm the applicability of this forward modeling scheme, apparent resistivity profiles for several basic three-dimensional subsurface resistivity models were compared with the analytical profiles, yielding an acceptable level of fitting.