# Difference between revisions of "Dictionary:Apparent resistivity"

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<b>1</b>. The resistivity of homogeneous, isotropic ground that would give the same voltage-current relationship as measured. <b>Direct current apparent resistivity</b>, ρ<sub>''a''</sub>, is an Ohm’s-law ratio of measured voltage ''V'' to applied current ''l'', multipled by a geometric constant ''k'' which depends on the electrode array: ρ<sub>''a''</sub>=''kV''/''l''. Usually has units of ohm-meters. See [[Special:MyLanguage/Dictionary:resistivity|''resistivity'']]. | <b>1</b>. The resistivity of homogeneous, isotropic ground that would give the same voltage-current relationship as measured. <b>Direct current apparent resistivity</b>, ρ<sub>''a''</sub>, is an Ohm’s-law ratio of measured voltage ''V'' to applied current ''l'', multipled by a geometric constant ''k'' which depends on the electrode array: ρ<sub>''a''</sub>=''kV''/''l''. Usually has units of ohm-meters. See [[Special:MyLanguage/Dictionary:resistivity|''resistivity'']]. | ||

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<b>2</b>. With electromagnetic methods, quantities such as the moduli of the electric and magnetic field intensities (<b>E</b> and <b>H</b>) are measured at a certain frequency or time. If the subsurface were homogeneous and isotropic, these would yield the true resistivity via a certain equation. However, use of the same equation for a heterogeneous subsurface yields the ‘‘apparent’’ resistivity ρ<sub>''a''</sub>: | <b>2</b>. With electromagnetic methods, quantities such as the moduli of the electric and magnetic field intensities (<b>E</b> and <b>H</b>) are measured at a certain frequency or time. If the subsurface were homogeneous and isotropic, these would yield the true resistivity via a certain equation. However, use of the same equation for a heterogeneous subsurface yields the ‘‘apparent’’ resistivity ρ<sub>''a''</sub>: | ||

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<center><math>\rho_\mathrm{a} = \frac{\rho_\mathrm{HS} F(V)}{F(V_\mathrm{HS})} </math></center> | <center><math>\rho_\mathrm{a} = \frac{\rho_\mathrm{HS} F(V)}{F(V_\mathrm{HS})} </math></center> | ||

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where ρ<sub>''HS''</sub>=resistivity of a homogeneous half-space, ''F'' is a function of ''V''=observed voltage, and ''V''<sub>''HS''</sub>=voltage for a half-space. Asymptotic definitions such as <b>late-time</b> and <b>early-time apparent resistivity</b> are sometimes used for apparent resistivity values over a limited range of measurement parameters. For some EM models apparent resistivity may be undefined or multivalued. | where ρ<sub>''HS''</sub>=resistivity of a homogeneous half-space, ''F'' is a function of ''V''=observed voltage, and ''V''<sub>''HS''</sub>=voltage for a half-space. Asymptotic definitions such as <b>late-time</b> and <b>early-time apparent resistivity</b> are sometimes used for apparent resistivity values over a limited range of measurement parameters. For some EM models apparent resistivity may be undefined or multivalued. | ||

See Spies and Eggers (1986)<ref name="Spies Eggers 1986 pp. 1462–1471">{{cite journal | last=Spies | first=Brian R. | last2=Eggers | first2=Dwight E. | title=The use and misuse of apparent resistivity in electromagnetic methods | journal=GEOPHYSICS | publisher=Society of Exploration Geophysicists | volume=51 | issue=7 | year=1986 | pages=1462–1471 | doi=10.1190/1.1442194}}</ref> and Strack (1992)<ref name="Strack 1992 p. ">{{cite book | author=Strack | title=Exploration with deep transient electromagnetics | publisher=Elsevier | location=Amsterdam New York | year=1992 | isbn=978-0-444-89541-7 | page=}}</ref>. | See Spies and Eggers (1986)<ref name="Spies Eggers 1986 pp. 1462–1471">{{cite journal | last=Spies | first=Brian R. | last2=Eggers | first2=Dwight E. | title=The use and misuse of apparent resistivity in electromagnetic methods | journal=GEOPHYSICS | publisher=Society of Exploration Geophysicists | volume=51 | issue=7 | year=1986 | pages=1462–1471 | doi=10.1190/1.1442194}}</ref> and Strack (1992)<ref name="Strack 1992 p. ">{{cite book | author=Strack | title=Exploration with deep transient electromagnetics | publisher=Elsevier | location=Amsterdam New York | year=1992 | isbn=978-0-444-89541-7 | page=}}</ref>. | ||

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<b>3</b>. The resistivity recorded by an electrical log that differs from the true resistivity of the formation because of the presence of mud column, invaded zone, influence of adjacent beds, etc. | <b>3</b>. The resistivity recorded by an electrical log that differs from the true resistivity of the formation because of the presence of mud column, invaded zone, influence of adjacent beds, etc. | ||

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## Latest revision as of 13:38, 11 March 2018

**1**. The resistivity of homogeneous, isotropic ground that would give the same voltage-current relationship as measured. **Direct current apparent resistivity**, ρ_{a}, is an Ohm’s-law ratio of measured voltage *V* to applied current *l*, multipled by a geometric constant *k* which depends on the electrode array: ρ_{a}=*kV*/*l*. Usually has units of ohm-meters. See *resistivity*.

**2**. With electromagnetic methods, quantities such as the moduli of the electric and magnetic field intensities (**E** and **H**) are measured at a certain frequency or time. If the subsurface were homogeneous and isotropic, these would yield the true resistivity via a certain equation. However, use of the same equation for a heterogeneous subsurface yields the ‘‘apparent’’ resistivity ρ_{a}:

where ρ_{HS}=resistivity of a homogeneous half-space, *F* is a function of *V*=observed voltage, and *V*_{HS}=voltage for a half-space. Asymptotic definitions such as **late-time** and **early-time apparent resistivity** are sometimes used for apparent resistivity values over a limited range of measurement parameters. For some EM models apparent resistivity may be undefined or multivalued.
See Spies and Eggers (1986)^{[1]} and Strack (1992)^{[2]}.

**3**. The resistivity recorded by an electrical log that differs from the true resistivity of the formation because of the presence of mud column, invaded zone, influence of adjacent beds, etc.

## References

- ↑ Spies, Brian R.; Eggers, Dwight E. (1986). "The use and misuse of apparent resistivity in electromagnetic methods".
*GEOPHYSICS*(Society of Exploration Geophysicists)**51**(7): 1462–1471. doi:10.1190/1.1442194. - ↑ Strack (1992).
*Exploration with deep transient electromagnetics*. Amsterdam New York: Elsevier. ISBN 978-0-444-89541-7.