Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method
Chen Hui1,2,3, Deng Ju-Zhi1,3, Yin Min1,3, Yin Chang-Chun2, and Tang Wen-Wu1,3
1. Key Laboratory for Radioactive Geology and Exploration Technology, Fundamental Science for National Defense, East China University of Technology, Nanchang 330013, China.
2. Geo-Exploration Science and Technology Institute, Jilin University, Changchun 130026, China.
3. School of Geophysics and Measurement-control Technology, East China University of Technology, Nanchang 330013, China.
Abstract To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.
This study work was financially supported by the Natural Science Foundation of China (Nos. 41404057, 41674077 and 411640034), the Nuclear Energy Development Project of China, and the ‘555’ Project of GanPo Excellent People.
Cite this article:
. Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method[J]. APPLIED GEOPHYSICS, 2017, 14(1): 154-164.
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2017, Vol. 14 
