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8 - Electric Resistivity

Published online by Cambridge University Press:  19 November 2021

Nikolai Bagdassarov
Nikolai Bagdassarov
Affiliation:
Goethe-Universität Frankfurt Am Main
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Summary

Electrical conductivity and resistance obey Ohm’s law. Specific resistance may be measured in two- or four-electrode schemes. Mechanisms of electrical conductivity in rocks are ionic, electronic, anionic and protonic. Some mantle minerals, i.e. olivine, possess polaron conductivity. Conduction bands and density of states are considered for some minerals. Effective conductivity in heterogeneous rocks can be estimated from Wiener or Hashin–Shtrikman bounds, effective medium approximation (EMA) and resistor network models. The electrical conductivity of mineral aggregates can be effectively described by brick and percolation models. Diluted electrolytes and Kohlrausch’s law of independent movement of ions are considered in fluid-bearing rocks, whose electric conductivity obeys Archie’s law. Formation factor and cementation exponent are analyzed for sedimentary rocks. The relationship between rock conductivity and pore saturation is described by the Waxman–Smith model. Focus Box 8.1: Calculations of density of states (Fermi gas model). Focus Box 8.2: Reciprocal lattice and band gaps. Focus Box 8.3: Olivine structure.

Keywords

Ohm’s lawcomplex electrical conductivitymechanisms of electrical conductivity in rocks and minerals: ionicelectronicanionic and protoniceffective conductivity in heterogeneous rocksmodels of electrical conductivity: brick modelpercolation modelWiener and Hashin-Shtrickman boundsformation factorArchie’s lawcementation exponentrelationship between conductivityporosity and permeability.

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Fundamentals of Rock Physics , pp. 292 - 360
Publisher: Cambridge University Press
Print publication year: 2021

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  • Electric Resistivity
  • Nikolai Bagdassarov, Goethe-Universität Frankfurt Am Main
  • Book: Fundamentals of Rock Physics
  • Online publication: 19 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108380713.009
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  • Electric Resistivity
  • Nikolai Bagdassarov, Goethe-Universität Frankfurt Am Main
  • Book: Fundamentals of Rock Physics
  • Online publication: 19 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108380713.009
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  • Electric Resistivity
  • Nikolai Bagdassarov, Goethe-Universität Frankfurt Am Main
  • Book: Fundamentals of Rock Physics
  • Online publication: 19 November 2021
  • Chapter DOI: https://doi.org/10.1017/9781108380713.009
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