The paradox of anisotropy in electromagnetic loop-loop responses over a uniaxial half-space

The electromagnetic loop-loop response of a uniaxial conducting half-space is derived. The solution is presented in terms of the Geonics EM34 apparent conductivity, which is based on an underlying isotropic half-space model of earth conductivity. The uniaxial medium generates an apparent conductivity that depends on the angle that the line joining the transmitter and receiver loops makes with respect to the strike of the anisotropy. Furthermore, a paradox of anisotropy occurs in which apparent conductivity is higher in the resistive across-strike direction and lower in the conductive along-strike direction. The paradox is resolved once it is recognized that the receiver loop response is controlled by the conductivity in the direction of the local induced electric current flow. Accurate geological interpretation of electromagnetic loop-loop data in fractured rock terrains depends on the ability of the geophysicist to recognize the counterintuitive effects of anisotropy.