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:
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) and Strack (1992). 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.