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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 464793, 12 pages
Research Article

Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

Huan Ma,1,2 Handong Tan,1,2 and Yue Guo3

1Key Laboratory of Geo-Detection, China University of Geosciences, Ministry of Education, Beijing 100083, China
2School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China
3Exploratory Drilling Corporation Well Logging Company, Daqing, Heilongjiang 163000, China

Received 19 March 2015; Accepted 27 April 2015

Academic Editor: Sergio Preidikman

Copyright © 2015 Huan Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Four kinds of array of induced polarization (IP) methods (surface, borehole-surface, surface-borehole, and borehole-borehole) are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI) and graphics processing unit (GPU) to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG) solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG) iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.