3D DC resistivity forward modeling by finite-infinite element coupling method

Abstract

To solve the problems caused by artificial boundary conditions in conventional finite element modeling, a new 3D DC resistivity finite -infinite element coupling method was proposed. Firstly, the 3D mapping functions of infinite elements were derived. Then, a new type of shape functions was proposed and proved to be the optimal one in both accuracy and time consumption by comparing with several other shape functions. After that, we integrated infinite element method into conventional finite element method to replace the mixed boundary conditions, which made the electrical potential distribute continuously in half space and decay to zero at infinity. Meanwhile, the global system matrix was independent with the locations of source points but still sparse and symmetric. Finally, analyses of numerical tests showed that the finite -infinite coupling method presented in this paper could obtain reasonable numerical solutions in a relatively small meshing area, the accuracy of which was equivalent with that obtained by mixed boundary conditions and higher than that of Neumann boundary conditions. Due to the reduction of the discretization domain and the invariability of the global system matrix with variant source positions, this new method is able to alleviate the computational burden and speed up inversions.