Modeling the electrical conductivity of multi-phase mineral aggregates from the electrical conductivity of single-phases

Magnetotellurics can be used to produce electrical conductivity maps of the crust and mantle of the Earth. The interpretation of these maps to infer rock type requires the knowledge of how the conductivities of constituent minerals are combined to give the whole rock conductivity. However, the relationship between the electrical conductivity of rocks and constituent minerals is still not well understood. I have reviewed literature mixing models and estimated the electrical conductivity-depth profile of the upper mantle and transition zone using laboratory measured conductivities of various minerals and these mixing models. The results show that the difference between conductivities calculated using the various mixing models is less significant than the uncertainties in the conductivity of the constituent minerals. The effective medium theory appears to provide the best estimate of bulk electrical conductivity of multiphase rocks derived from the conductivity of the single-phase minerals.

To experimentally test the validity of these mixing models for estimating the bulk electrical conductivity of rocks I prepared three single-phase minerals, quartz, orthoclase and albite, in grain and powder forms. These powders and grains were mixed to generate two multi-phase powder aggregates and two multi-phase grain aggregates. The electrical conductivities of the six single-phase aggregates and the four multi-phase aggregates were measured with the varying temperatures at both 1 GPa and ambient pressure. For both powder and grain forms, the two multi-phase aggregates show higher electrical conductivities and lower activation energies than the three single-phase aggregates at both 1 GPa and ambient pressure, which may be explained by the interdiffusion of Na-K observed between albite and orthoclase in the multiphase aggregates.

Two granites, Hartly granite from Hartly Village, Sydney, Australia, and Quarry granite from Quarry Park, Rockline, California, USA, were used to investigate the conductivity relationship between constituent minerals and natural rocks. The electrical conductivities of the cored and powdered granites were measured over a range of temperatures at both 1 GPa and ambient pressure. To model the electrical conductivities of the powdered granites, I combined conductivities of three single-phase powder aggregates (quartz, albite and orthoclase) based on the modal compositions of the two natural granites using the effective medium theory. The measured conductivities of the powdered granites are significantly higher than those calculated conductivities. This difference correlates with the high-water content in the feldspars in the natural granites implying that water in feldspars enhances the conductivity of feldspars and hence the overall conductivity of granites. Compared to the multi-phase aggregates with similar modal composition to the two natural granites, the granites show lower electrical conductivities, which may be due to enhancement of the Na-K interdiffusion between feldspars in the multiphase aggregates. Therefore, water in constituent minerals and Na-K interdiffusion enhancement between feldspars should be taken into consideration when modeling the electrical conductivity of natural granites using the conductivities of quartz and feldspar. These findings have implications for the interpretation of geophysical observations under some chemically non-equilibrium regions such as North New Zealand and Tibet.