Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy

Branislav Sretenovic; Filip Arnaut

doi:doi:10.11648/j.earth.20190802.14

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Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy

Branislav Sretenovic, Filip Arnaut

Published in Earth Sciences (Volume 8, Issue 2)

Received: 11 February 2019 Accepted: 9 April 2019 Published: 29 April 2019

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Abstract

Universal property of matter is the variation of a certain physical characteristic in different direction. The Substances that do not display this property are an exception. Anisotropy, as this property is named, is also notable in electrical conductivity of minerals, ores, rocks and geological formations. In order to properly define a geological model of an investigated area, it is necessary to account for electrical anisotropy and lateral effects of different origin that are almost always present phenomena. The degree of knowledge of these phenomena determines the quality of interpretation. The effects of electrical anisotropy on 1D, 2D and 3D inversion of apparent resistivity data were examined and the way to detect, quantify and analyse electrical anisotropy in 3D case is proposed. The results of this analysis showed that electrically anisotropic models have led to the totally erroneous results of 3D inversion while the effects of electrical anisotropy on 1D and 2D inversion were less pronounced. Among several existing ways of collecting 3D apparent resistivity data the complete Pole-pole array data set is the only one suitable for detection of electrical anisotropy. Pole-pole resistivity data enable calculating of corresponding resistance or apparent resistivity values for all other collinear or square arrays. This fact makes possible to use standard grid of electrodes in performing 3D Pole-pole apparent resistivity measurements for calculating square array apparent resistivity data. In the special case of vertical stratification (fracturing, schistosity..) this calculated square array data were used for electrical anisotropy analysis thus determining values of coefficient of anisotropy () and mean geometric resistivity (_m). The simple two and three layer 1D synthetic anisotropic models, were used to determine parameters of electrical anisotropy by using 3D forward modelling to calculate Pole-pole and then square array apparent resistivity values. The mean geometric resistivity data obtained by using square array, which are orientation-independent, were used for 1D inversion leading to more realistic results. In the case of oblique stratification (lamination, fracturing, schistosity or karstification) crossed square resistivity data can be reconstructed from 3D Pole-pole data set and then can be used to get parameters of electrical anisotropy, namely apparent coefficient of anisotropy (n), mean geometric resistivity (_m) and apparent electrical strike (). These parameters provide an indication that investigations of electrical anisotropy should be conducted (by using square and crossed square array) in order to avoid erroneous results of 3D inversion.

Published in	Earth Sciences (Volume 8, Issue 2)
DOI	10.11648/j.earth.20190802.14
Page(s)	102-116
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), 2019. Published by Science Publishing Group

Keywords

Electrical Anisotropy, Oblique Lamination, Rock Fracturing, Schistosity, Coefficient of Anisotropy, Forward Resistivity Modelling, Inverse Resistivity Modelling

References

[1]	N. Inyang Udosen. N. Jimmy George, 2018, Characterization of electrical anisotropy in North Yorkshire, England using square arrays and electrical resistivity tomography Geomech. Geophys. Geo-energ. Geo-resour. July 2018 DOI: 10.1007/s40948-018-0087-5.
[2]	Habberjam, G. M., Apparent resistivity, anisotropy and strike measurements. Geophysical Prospecting, 23, p. 211-247, 1975.
[3]	Bhattacharya B. B., Patra H. P. Direct methods in geoelectric sounding: Principle and interpretation. Elsevier Science Publ. Co. Inc., 1968, 131 p.
[4]	Loke, M. H., Tutorial: 2-D and 3-D electrical imaging surveys 1996-2018, 2018.
[5]	Loke, M. H., Rapid 2-D Resistivity & IP inversion using the least-squares method, 2008.
[6]	Loke, M. H., Rapid 3D Resistivity & IP inversion using the least-squares method, 2008.
[7]	Bart Vander Velpen, RESIST. A computer program to process resistivity sounding data on PC Compatibles, Computers & Geosciences, 19(5):691-703 • May 1993, DOI: 10.1016/0098- 3004(93)90102-B.
[8]	Koefoed. O., Geosounding Principles: Resistivity Sounding Measurements (METHODS IN GEOCHEMISTRY AND GEOPHYSICS), Elsevier Scientific Publishing Company, 1979.
[9]	Habberjam G. M., Apparent resistivity observations and the use of square array techniques. (Geoexploration Monographs, Number 9), 1979. ISBN 978-3-443-13013-8.
[10]	Habberjam, G. M., The effects of anisotropy on square array resistivity measurements. Geophysical Prospecting, 20, p. 249-266, 1972.
[11]	Habberjam, G. M., and Watkins, G. E. The use of a square configuration in resistivity prospecting. Geophysical Prospecting, 15, p. 445-467, 1967.
[12]	Lane, J. W., Jr., Haeni, F. P., and Watson, W. M., 1995, Use of square-array direct-current resistivity methods to detect fractures in crystalline bedrock in New Hampshire: Groundwater, v. 33, no. 3, p. 476-485.
[13]	Geological Survey (USGS), Nye County Nuclear Waste Repository Project, 2005, Square-Array Direct-Current Resistivity Measurements Conducted at Nye County near Borehole NC-EWDP-29P.

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Branislav Sretenovic, Filip Arnaut. (2019). Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy. Earth Sciences, 8(2), 102-116. https://doi.org/10.11648/j.earth.20190802.14

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Branislav Sretenovic; Filip Arnaut. Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy. Earth Sci. 2019, 8(2), 102-116. doi: 10.11648/j.earth.20190802.14

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AMA Style

Branislav Sretenovic, Filip Arnaut. Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy. Earth Sci. 2019;8(2):102-116. doi: 10.11648/j.earth.20190802.14

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@article{10.11648/j.earth.20190802.14,
  author = {Branislav Sretenovic and Filip Arnaut},
  title = {Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy},
  journal = {Earth Sciences},
  volume = {8},
  number = {2},
  pages = {102-116},
  doi = {10.11648/j.earth.20190802.14},
  url = {https://doi.org/10.11648/j.earth.20190802.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20190802.14},
  abstract = {Universal property of matter is the variation of a certain physical characteristic in different direction. The Substances that do not display this property are an exception. Anisotropy, as this property is named, is also notable in electrical conductivity of minerals, ores, rocks and geological formations. In order to properly define a geological model of an investigated area, it is necessary to account for electrical anisotropy and lateral effects of different origin that are almost always present phenomena. The degree of knowledge of these phenomena determines the quality of interpretation. The effects of electrical anisotropy on 1D, 2D and 3D inversion of apparent resistivity data were examined and the way to detect, quantify and analyse electrical anisotropy in 3D case is proposed. The results of this analysis showed that electrically anisotropic models have led to the totally erroneous results of 3D inversion while the effects of electrical anisotropy on 1D and 2D inversion were less pronounced. Among several existing ways of collecting 3D apparent resistivity data the complete Pole-pole array data set is the only one suitable for detection of electrical anisotropy. Pole-pole resistivity data enable calculating of corresponding resistance or apparent resistivity values for all other collinear or square arrays. This fact makes possible to use standard grid of electrodes in performing 3D Pole-pole apparent resistivity measurements for calculating square array apparent resistivity data. In the special case of vertical stratification (fracturing, schistosity..) this calculated square array data were used for electrical anisotropy analysis thus determining values of coefficient of anisotropy () and mean geometric resistivity (m). The simple two and three layer 1D synthetic anisotropic models, were used to determine parameters of electrical anisotropy by using 3D forward modelling to calculate Pole-pole and then square array apparent resistivity values. The mean geometric resistivity data obtained by using square array, which are orientation-independent, were used for 1D inversion leading to more realistic results. In the case of oblique stratification (lamination, fracturing, schistosity or karstification) crossed square resistivity data can be reconstructed from 3D Pole-pole data set and then can be used to get parameters of electrical anisotropy, namely apparent coefficient of anisotropy (n), mean geometric resistivity (m) and apparent electrical strike (). These parameters provide an indication that investigations of electrical anisotropy should be conducted (by using square and crossed square array) in order to avoid erroneous results of 3D inversion.},
 year = {2019}
}

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TY  - JOUR
T1  - Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy
AU  - Branislav Sretenovic
AU  - Filip Arnaut
Y1  - 2019/04/29
PY  - 2019
N1  - https://doi.org/10.11648/j.earth.20190802.14
DO  - 10.11648/j.earth.20190802.14
T2  - Earth Sciences
JF  - Earth Sciences
JO  - Earth Sciences
SP  - 102
EP  - 116
PB  - Science Publishing Group
SN  - 2328-5982
UR  - https://doi.org/10.11648/j.earth.20190802.14
AB  - Universal property of matter is the variation of a certain physical characteristic in different direction. The Substances that do not display this property are an exception. Anisotropy, as this property is named, is also notable in electrical conductivity of minerals, ores, rocks and geological formations. In order to properly define a geological model of an investigated area, it is necessary to account for electrical anisotropy and lateral effects of different origin that are almost always present phenomena. The degree of knowledge of these phenomena determines the quality of interpretation. The effects of electrical anisotropy on 1D, 2D and 3D inversion of apparent resistivity data were examined and the way to detect, quantify and analyse electrical anisotropy in 3D case is proposed. The results of this analysis showed that electrically anisotropic models have led to the totally erroneous results of 3D inversion while the effects of electrical anisotropy on 1D and 2D inversion were less pronounced. Among several existing ways of collecting 3D apparent resistivity data the complete Pole-pole array data set is the only one suitable for detection of electrical anisotropy. Pole-pole resistivity data enable calculating of corresponding resistance or apparent resistivity values for all other collinear or square arrays. This fact makes possible to use standard grid of electrodes in performing 3D Pole-pole apparent resistivity measurements for calculating square array apparent resistivity data. In the special case of vertical stratification (fracturing, schistosity..) this calculated square array data were used for electrical anisotropy analysis thus determining values of coefficient of anisotropy () and mean geometric resistivity (m). The simple two and three layer 1D synthetic anisotropic models, were used to determine parameters of electrical anisotropy by using 3D forward modelling to calculate Pole-pole and then square array apparent resistivity values. The mean geometric resistivity data obtained by using square array, which are orientation-independent, were used for 1D inversion leading to more realistic results. In the case of oblique stratification (lamination, fracturing, schistosity or karstification) crossed square resistivity data can be reconstructed from 3D Pole-pole data set and then can be used to get parameters of electrical anisotropy, namely apparent coefficient of anisotropy (n), mean geometric resistivity (m) and apparent electrical strike (). These parameters provide an indication that investigations of electrical anisotropy should be conducted (by using square and crossed square array) in order to avoid erroneous results of 3D inversion.
VL  - 8
IS  - 2
ER  -

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Author Information

Branislav Sretenovic

University of Belgrade, Faculty of Mining and Geology, Department of Geophysics, Belgrade, Serbia
Filip Arnaut

University of Belgrade, Faculty of Mining and Geology, Department of Geophysics, Belgrade, Serbia

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APA Style

Branislav Sretenovic, Filip Arnaut. (2019). Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy. Earth Sciences, 8(2), 102-116. https://doi.org/10.11648/j.earth.20190802.14

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ACS Style

Branislav Sretenovic; Filip Arnaut. Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy. Earth Sci. 2019, 8(2), 102-116. doi: 10.11648/j.earth.20190802.14

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AMA Style

Branislav Sretenovic, Filip Arnaut. Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy. Earth Sci. 2019;8(2):102-116. doi: 10.11648/j.earth.20190802.14

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@article{10.11648/j.earth.20190802.14,
  author = {Branislav Sretenovic and Filip Arnaut},
  title = {Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy},
  journal = {Earth Sciences},
  volume = {8},
  number = {2},
  pages = {102-116},
  doi = {10.11648/j.earth.20190802.14},
  url = {https://doi.org/10.11648/j.earth.20190802.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20190802.14},
  abstract = {Universal property of matter is the variation of a certain physical characteristic in different direction. The Substances that do not display this property are an exception. Anisotropy, as this property is named, is also notable in electrical conductivity of minerals, ores, rocks and geological formations. In order to properly define a geological model of an investigated area, it is necessary to account for electrical anisotropy and lateral effects of different origin that are almost always present phenomena. The degree of knowledge of these phenomena determines the quality of interpretation. The effects of electrical anisotropy on 1D, 2D and 3D inversion of apparent resistivity data were examined and the way to detect, quantify and analyse electrical anisotropy in 3D case is proposed. The results of this analysis showed that electrically anisotropic models have led to the totally erroneous results of 3D inversion while the effects of electrical anisotropy on 1D and 2D inversion were less pronounced. Among several existing ways of collecting 3D apparent resistivity data the complete Pole-pole array data set is the only one suitable for detection of electrical anisotropy. Pole-pole resistivity data enable calculating of corresponding resistance or apparent resistivity values for all other collinear or square arrays. This fact makes possible to use standard grid of electrodes in performing 3D Pole-pole apparent resistivity measurements for calculating square array apparent resistivity data. In the special case of vertical stratification (fracturing, schistosity..) this calculated square array data were used for electrical anisotropy analysis thus determining values of coefficient of anisotropy () and mean geometric resistivity (m). The simple two and three layer 1D synthetic anisotropic models, were used to determine parameters of electrical anisotropy by using 3D forward modelling to calculate Pole-pole and then square array apparent resistivity values. The mean geometric resistivity data obtained by using square array, which are orientation-independent, were used for 1D inversion leading to more realistic results. In the case of oblique stratification (lamination, fracturing, schistosity or karstification) crossed square resistivity data can be reconstructed from 3D Pole-pole data set and then can be used to get parameters of electrical anisotropy, namely apparent coefficient of anisotropy (n), mean geometric resistivity (m) and apparent electrical strike (). These parameters provide an indication that investigations of electrical anisotropy should be conducted (by using square and crossed square array) in order to avoid erroneous results of 3D inversion.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Inadequacy of 1D, 2D and 3D Resistivity Inverse Modelling in the Presence of Electrical Anisotropy
AU  - Branislav Sretenovic
AU  - Filip Arnaut
Y1  - 2019/04/29
PY  - 2019
N1  - https://doi.org/10.11648/j.earth.20190802.14
DO  - 10.11648/j.earth.20190802.14
T2  - Earth Sciences
JF  - Earth Sciences
JO  - Earth Sciences
SP  - 102
EP  - 116
PB  - Science Publishing Group
SN  - 2328-5982
UR  - https://doi.org/10.11648/j.earth.20190802.14
AB  - Universal property of matter is the variation of a certain physical characteristic in different direction. The Substances that do not display this property are an exception. Anisotropy, as this property is named, is also notable in electrical conductivity of minerals, ores, rocks and geological formations. In order to properly define a geological model of an investigated area, it is necessary to account for electrical anisotropy and lateral effects of different origin that are almost always present phenomena. The degree of knowledge of these phenomena determines the quality of interpretation. The effects of electrical anisotropy on 1D, 2D and 3D inversion of apparent resistivity data were examined and the way to detect, quantify and analyse electrical anisotropy in 3D case is proposed. The results of this analysis showed that electrically anisotropic models have led to the totally erroneous results of 3D inversion while the effects of electrical anisotropy on 1D and 2D inversion were less pronounced. Among several existing ways of collecting 3D apparent resistivity data the complete Pole-pole array data set is the only one suitable for detection of electrical anisotropy. Pole-pole resistivity data enable calculating of corresponding resistance or apparent resistivity values for all other collinear or square arrays. This fact makes possible to use standard grid of electrodes in performing 3D Pole-pole apparent resistivity measurements for calculating square array apparent resistivity data. In the special case of vertical stratification (fracturing, schistosity..) this calculated square array data were used for electrical anisotropy analysis thus determining values of coefficient of anisotropy () and mean geometric resistivity (m). The simple two and three layer 1D synthetic anisotropic models, were used to determine parameters of electrical anisotropy by using 3D forward modelling to calculate Pole-pole and then square array apparent resistivity values. The mean geometric resistivity data obtained by using square array, which are orientation-independent, were used for 1D inversion leading to more realistic results. In the case of oblique stratification (lamination, fracturing, schistosity or karstification) crossed square resistivity data can be reconstructed from 3D Pole-pole data set and then can be used to get parameters of electrical anisotropy, namely apparent coefficient of anisotropy (n), mean geometric resistivity (m) and apparent electrical strike (). These parameters provide an indication that investigations of electrical anisotropy should be conducted (by using square and crossed square array) in order to avoid erroneous results of 3D inversion.
VL  - 8
IS  - 2
ER  -

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