Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

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-differen...

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Bibliographic Details
Published in:Applied geophysics Vol. 14; no. 1; pp. 154 - 164
Main Authors: Chen, Hui, Deng, Ju-Zhi, Yin, Min, Yin, Chang-Chun, Tang, Wen-Wu
Format: Journal Article
Language:English
Published: Beijing Chinese Geophysical Society 01.03.2017
Springer Nature B.V
Geo-Exploration Science and Technology Institute, Jilin University, Changchun 130026, China
Subjects:
Algebra
Algorithms
Boundary conditions
Earth and Environmental Science
Earth Sciences
Electrical resistivity
Geophysics
Geophysics/Geodesy
Geotechnical Engineering & Applied Earth Sciences
Mathematical analysis
Mathematical models
Modelling
Multigrid methods
Numerical analysis
Three dimensional models
3D modeling
finite difference method
DC resistivity method
AGMG
ISSN:1672-7975, 1993-0658
Online Access:Get full text
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Summary: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.
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ISSN:1672-7975
1993-0658
DOI:10.1007/s11770-017-0605-1