Eddy currents in the measurement of magnetic susceptibility of rocks

The in-phase and out-of-phase susceptibility of rocks is determined by the magnetic permeability of minerals, their viscous relaxation, and by eddy currents in electrically conductive minerals induced by the applied field. The last effect has been modelled by analytical solution of Maxwell equations for a conductive sphere immersed in a homogeneous, non-conductive medium with given permeability, in presence of an alternating field. The solution is a complex function of parameters describing the sphere (its size, conductivity and permeability), surrounding medium (permeability) and applied field (frequency). Without numerical evaluations, it is difficult to distinguish in-phase and out-of-phase (OPS) susceptibility. In this paper, approximate equations are derived for both susceptibility components, which depend only on the permeability contrast between the sphere and the surrounding medium, and the skin ratio, defined as the ratio between sphere radius and skin depth of the induced currents. These equations are used to obtain a systematic assessment of the role of electrical conductivity in determining the susceptibility of rock samples. The contribution of eddy currents to the susceptibility of diluted (<5%) magnetite particle dispersions is negligible at 1 kHz, but not at higher frequencies. Common rock-forming paramagnetic and diamagnetic minerals with weak electrical conductivity and magnetic permeability are characterized by negligible OPS at 1 kHz. Theoretically, measurable OPS and high phase angles can be produced by paramagnetic conductive minerals in certain combinations with a diamagnetic matrix. This can be excluded from practical point of view for paramagnetic minerals with susceptibilities >0.003 and conductivities not exceeding 5000 S/m.