A Weighting Inversion Method of Spectrum Induced Polarization

Wu Yu Hao

doi:doi:10.11648/j.earth.20190803.16

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A Weighting Inversion Method of Spectrum Induced Polarization

Wu Yu Hao

Received: 28 December 2018 Accepted: 23 May 2019 Published: 4 July 2019

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Abstract

The inversion results of complex resistivity method are four Cole-Cole model parameters. Among the four parameters, the frequency dependence and the time constant are more difficult to invert. It is necessary to study an algorithm that can invert the four Cole-Cole model parameters at the same time. In this paper, the least squares and OCCAM inversion algorithms are used to invert four Cole-Cole model parameters. In other words, two model constraints are added to the objective function. When inverting different Cole-Cole model parameters, the real and imaginary parts of the data are weighted to adjust the proportion of real part and imaginary part of data in inversion. Firstly, the formula of the algorithm is deduced. Then the theoretical models are designed for inversion trial calculation. In the inversion process, the inversion converges steadily by adjusting the Lagrange factor, and the inversion effect is improved by adjusting the weighting coefficients of real part and imaginary part. This method can get better inversion results by adjusting the proportion of the real and imaginary parts of the data in the inversion. The model trial results show that the weighting inversion algorithm significantly improves the results of the inversion of the four Cole-Cole parameters.

DOI	10.11648/j.earth.20190803.16
Published in	Earth Sciences (Volume 8, Issue 3, June 2019)
Page(s)	178-189
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Spectral Induced Polarization, Cole–Cole Model Parameters, Occam Inversion, The Least Squares Inversion, Weighting Inversion

References

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[2]	Brown R J. 1985. EM coupling in multi-frequency IP and a generalization of the Cole-Cole impedancemodel. Geophysical prospecting, 33 (2): 282~302.
[3]	Fan C S, Li T L, Yan J Y. 2012. Research and application experiment on 2.5D SIP inversion. Geophys. (in Chinese), 55 (12): 4044-4050.
[4]	Ingeman-Nielsen, T, Baumgartner, F. 2006. CR1Dmod: a Matlab program to model 1D complex resistivity effects in electrical and EM surveys. Computers & Geosciences 32, 1411–1419.
[5]	Liu B, Li S C, Li S C, et al. 2012. 3D electrical resistivity inversion with least-squares method based on inequality constraint and its computation efficiency optimization. Geophys. (in Chinese), 55 (1): 260-268.
[6]	Liu S, Guan S Y, Gao PF. 1994. A polarization inversion method of Cole-Cole parameters of the polarizing sphere. Geophys. (in Chinese), 37 (S2): 542~551.
[7]	Liu Y H, Yin C C. 2013. 3D inversion for frequency-domain HEM data. Chinese J. Geophys. (in Chinese), 56 (12): 4278-4287.
[8]	Liu Y L, Li T L, Hu Y C, et al. 2015. Fast quasi-linear approximation and the three-dimensional spectrum of induced polarization inversion study. Geophys. (in Chinese), 58 (12): 4709-4717.
[9]	Luo Y Z, Fang S. 1986. An approximate method to invert the spectrum of complex resistivity. Earth Science, 11 (1): 93-102.
[10]	Major J, Silic J. 1981. Restrictions on the use of Cole-Cole dispersion models in complex resistivity interpretation. Geo- physics, 46 (6): 916~931.
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[14]	Yu L B. 2010. The study of simulation and inversion of 1D spectrum induced polarization method [Master's Degree Thesis] (in Chinese). Changchun: Jilin University.
[15]	Zhou F. 2015. 1D and 2.5D Modeling and Inversion of Complex Resistivity Data [Master's Degree Thesis]. East China institute of technology.
[16]	Zhang S Z, Li Y X, Zhang S C. 1984. Characteristics and influencing factors of phase in low frequency of rocks (ore) in several metal mining areas in China. Geophys. (in Chinese), 27: 176~189.

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Wu Yu Hao. (2019). A Weighting Inversion Method of Spectrum Induced Polarization. Earth Sciences, 8(3), 178-189. https://doi.org/10.11648/j.earth.20190803.16

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ACS Style

Wu Yu Hao. A Weighting Inversion Method of Spectrum Induced Polarization. Earth Sci. 2019, 8(3), 178-189. doi: 10.11648/j.earth.20190803.16

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Wu Yu Hao. A Weighting Inversion Method of Spectrum Induced Polarization. Earth Sci. 2019;8(3):178-189. doi: 10.11648/j.earth.20190803.16

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@article{10.11648/j.earth.20190803.16,
  author = {Wu Yu Hao},
  title = {A Weighting Inversion Method of Spectrum Induced Polarization},
  journal = {Earth Sciences},
  volume = {8},
  number = {3},
  pages = {178-189},
  doi = {10.11648/j.earth.20190803.16},
  url = {https://doi.org/10.11648/j.earth.20190803.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20190803.16},
  abstract = {The inversion results of complex resistivity method are four Cole-Cole model parameters. Among the four parameters, the frequency dependence and the time constant are more difficult to invert. It is necessary to study an algorithm that can invert the four Cole-Cole model parameters at the same time. In this paper, the least squares and OCCAM inversion algorithms are used to invert four Cole-Cole model parameters. In other words, two model constraints are added to the objective function. When inverting different Cole-Cole model parameters, the real and imaginary parts of the data are weighted to adjust the proportion of real part and imaginary part of data in inversion. Firstly, the formula of the algorithm is deduced. Then the theoretical models are designed for inversion trial calculation. In the inversion process, the inversion converges steadily by adjusting the Lagrange factor, and the inversion effect is improved by adjusting the weighting coefficients of real part and imaginary part. This method can get better inversion results by adjusting the proportion of the real and imaginary parts of the data in the inversion. The model trial results show that the weighting inversion algorithm significantly improves the results of the inversion of the four Cole-Cole parameters.},
 year = {2019}
}

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TY - JOUR
T1 - A Weighting Inversion Method of Spectrum Induced Polarization
AU - Wu Yu Hao
Y1 - 2019/07/04
PY - 2019
N1 - https://doi.org/10.11648/j.earth.20190803.16
DO - 10.11648/j.earth.20190803.16
T2 - Earth Sciences
JF - Earth Sciences
JO - Earth Sciences
SP - 178
EP - 189
PB - Science Publishing Group
SN - 2328-5982
UR - https://doi.org/10.11648/j.earth.20190803.16
AB - The inversion results of complex resistivity method are four Cole-Cole model parameters. Among the four parameters, the frequency dependence and the time constant are more difficult to invert. It is necessary to study an algorithm that can invert the four Cole-Cole model parameters at the same time. In this paper, the least squares and OCCAM inversion algorithms are used to invert four Cole-Cole model parameters. In other words, two model constraints are added to the objective function. When inverting different Cole-Cole model parameters, the real and imaginary parts of the data are weighted to adjust the proportion of real part and imaginary part of data in inversion. Firstly, the formula of the algorithm is deduced. Then the theoretical models are designed for inversion trial calculation. In the inversion process, the inversion converges steadily by adjusting the Lagrange factor, and the inversion effect is improved by adjusting the weighting coefficients of real part and imaginary part. This method can get better inversion results by adjusting the proportion of the real and imaginary parts of the data in the inversion. The model trial results show that the weighting inversion algorithm significantly improves the results of the inversion of the four Cole-Cole parameters.
VL - 8
IS - 3
ER -

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Author Information

Wu Yu Hao

Tianjin Institute of Geotechnical Investigation and Surveying, Tianjin, China; College of Geo-exploration Sciences and Technology, Jilin University, Changchun, China

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APA Style

Wu Yu Hao. (2019). A Weighting Inversion Method of Spectrum Induced Polarization. Earth Sciences, 8(3), 178-189. https://doi.org/10.11648/j.earth.20190803.16

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ACS Style

Wu Yu Hao. A Weighting Inversion Method of Spectrum Induced Polarization. Earth Sci. 2019, 8(3), 178-189. doi: 10.11648/j.earth.20190803.16

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AMA Style

Wu Yu Hao. A Weighting Inversion Method of Spectrum Induced Polarization. Earth Sci. 2019;8(3):178-189. doi: 10.11648/j.earth.20190803.16

Copy | Download

@article{10.11648/j.earth.20190803.16,
  author = {Wu Yu Hao},
  title = {A Weighting Inversion Method of Spectrum Induced Polarization},
  journal = {Earth Sciences},
  volume = {8},
  number = {3},
  pages = {178-189},
  doi = {10.11648/j.earth.20190803.16},
  url = {https://doi.org/10.11648/j.earth.20190803.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20190803.16},
  abstract = {The inversion results of complex resistivity method are four Cole-Cole model parameters. Among the four parameters, the frequency dependence and the time constant are more difficult to invert. It is necessary to study an algorithm that can invert the four Cole-Cole model parameters at the same time. In this paper, the least squares and OCCAM inversion algorithms are used to invert four Cole-Cole model parameters. In other words, two model constraints are added to the objective function. When inverting different Cole-Cole model parameters, the real and imaginary parts of the data are weighted to adjust the proportion of real part and imaginary part of data in inversion. Firstly, the formula of the algorithm is deduced. Then the theoretical models are designed for inversion trial calculation. In the inversion process, the inversion converges steadily by adjusting the Lagrange factor, and the inversion effect is improved by adjusting the weighting coefficients of real part and imaginary part. This method can get better inversion results by adjusting the proportion of the real and imaginary parts of the data in the inversion. The model trial results show that the weighting inversion algorithm significantly improves the results of the inversion of the four Cole-Cole parameters.},
 year = {2019}
}

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