FEM numerical modeling of 3-D DC resistivity under complicated terrain
复杂地形三维直流电阻率有限元数值模拟

The computation technique of forward modeling for three-dimensional DC resistivity under complicated terrain using the finite element method is systematically described in this paper. Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface. We test the effectiveness of the algorithm through theoretical model calculations, and give a few numerical modeling results of several common terrains and a combined model. This research effort has setup a basis for research of three-dimensional DC resistivity inversion.