Abstract
A 3D DC finite element method forward program is developed in this paper for anisotropic geoelectric media. Both total and secondary field approaches have been implemented. In this paper, we focused on the structured grid scheme. The modeling shows that the symmetry of the structure grid determines the symmetry of the response potential around the point source for an anisotropic half-space. Through numerical modeling with three kinds of coarse meshes by the total field approach and secondary field approach separately, a higher accuracy can be achieved via the secondary field approach. And the relative error between the numerical solution and the analytical solution is less than 2%. Modeling results contrasting with previous scholars also verify the correctness of the algorithm. Then, the numerical results of 3D models with anisotropic properties were presented and compared to models with isotropic properties. These results clearly illustrated the strong effect of anisotropy and the problems in interpretation if anisotropy was not properly addressed. This work will establish the foundation for our future effort of building a 3D inversion program with arbitrary anisotropy.
Highlights
The direct current (DC) method is well established under the assumption of 3D isotropic geoelectric media
Pridmore et al [1] first discussed the application of the finite element method (FEM) approach to the 3D resistivity problem in isotropic media and a finite element method (FEM) based 3D inversion scheme was implemented by Sasaki [2]
Li and Uren [6] derived an analytical solution for point source potential in anisotropic half-space and solutions for a layered formation with arbitrary anisotropy were reported by Yin and Weidelt [7]
Summary
The direct current (DC) method is well established under the assumption of 3D isotropic geoelectric media. Pridmore et al [1] first discussed the application of the finite element method (FEM) approach to the 3D resistivity problem in isotropic media and a finite element method (FEM) based 3D inversion scheme was implemented by Sasaki [2]. Li and Spitzer [8] presented a study on 3D resistivity modeling with arbitrary anisotropy. Wang [11] proposed an unstructured FEM to model arbitrary anisotropic resistivity and achieved good accuracy. The unstructured grid proposed in that paper will be very difficult to implement in an inversion program. We used a tetrahedral element which can be implemented in the inversion program and investigated the effects of grids schemes and coarse meshes on the accuracy of numerical solutions. This work will establish the foundation for our effort to develop a 3D resistivity inversion program with arbitrary anisotropy
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