Constraint inversion of three-dimensional borehole-to-surface resistivity based on unstructured finite element

WANG Zhi; WANG Cheng; FANG Si-Nan

doi:10.11720/wtyht.2022.0181

2022 Vol. 46, No. 6

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Article navigation > Geophysical and Geochemical Exploration > 2022 > 46(6): 1431-1443

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WANG Zhi, WANG Cheng, FANG Si-Nan. 2022. Constraint inversion of three-dimensional borehole-to-surface resistivity based on unstructured finite element. Geophysical and Geochemical Exploration, 46(6): 1431-1443. doi: 10.11720/wtyht.2022.0181

Citation:

WANG Zhi, WANG Cheng, FANG Si-Nan. 2022. Constraint inversion of three-dimensional borehole-to-surface resistivity based on unstructured finite element. Geophysical and Geochemical Exploration, 46(6): 1431-1443. doi: 10.11720/wtyht.2022.0181

Constraint inversion of three-dimensional borehole-to-surface resistivity based on unstructured finite element

1. Electronics and Information School, Yangtze University, Jingzhou 434023,China；
2. Xi’an Research Institute Co. Ltd., China Coal Technology and Engineering Group Corp., Xi’an 710077, China；
3. College of Geophysics and Petroleum Resources,Yangtze University,Wuhan 430100,China

Received Date: 13 April 2022

Revised Date: 20 December 2022

Publish Date: 03 January 2023

Abstract

Abstract

The inversion of electromagnetic detection data is a typical ill-posed problem and is prone to cause a multiplicity of solutions of the inversion results. The ill-posedness is an inherent characteristic of inversion and is difficult to overcome without additional information. An effective way to solve this problem is constrained inversion. In this study, the Gauss-Newton - conjugate gradient (GN-CG) method was used to directly impose constraints on the inversion objective function. Specifically, the dielectric resistivity range was introduced into the inversion objective function as the prior information and constraints using the exterior penalty function method. Compared with the conventional three-dimensional resistivity inversion objective function, the objective function with inequality constraints can suppress the multiplicity of solutions in theory. As revealed by the testing results of various theoretical models, the three-dimensional borehole-to-surface resistivity inversion algorithm based on inequality constraints effectively improves the precision of inversion results, and the way of imposing inequality constraints using the penalty function method is feasible and effective.
- borehole-to-surface resistivity method /
- inversion /
- GN-CG /
- inequality constraint /
- penalty function method

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References

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