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.
. 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 
