# Dictionary:Apparent resistivity

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1. The resistivity of homogeneous, isotropic ground that would give the same voltage-current relationship as measured. Direct current apparent resistivity, ρa, 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: ρa=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 ρa:

${\displaystyle \rho _{\mathrm {a} }={\frac {\rho _{\mathrm {HS} }F(V)}{F(V_{\mathrm {HS} })}}}$

where ρHS=resistivity of a homogeneous half-space, F is a function of V=observed voltage, and VHS=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

1. 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.
2. Strack (1992). Exploration with deep transient electromagnetics. Amsterdam New York: Elsevier. ISBN 978-0-444-89541-7.