Numerical models on the influence of partial melt on elastic, anelastic and electrical properties of rocks. Part II: electrical conductivity

Abstract

Partial melting influences both the elastic and electrical properties of mantle rocks significantly, but in a different manner. A set of theoretical models of the electrical conductivity of partially molten rocks is developed for different geometries of the melt distribution. The models correspond to a similar set on elasticity and anelasticity presented in a preceding paper (part I). Both model sets allow combined interpretations of seismic and geoelectric observations from anomalous hot mantle regions by a systematic variation of the melt geometry. The following melt geometries are assumed in the conductivity models: melt films, tubes, isolated ellipsoidal inclusions, films and ellipsoidal inclusions with a variable degree of interconnection, distributed geometries, and superpositions of spheres with films and with tubes. Unexplored conduction mechanisms near the melting temperature, film thicknesses of molecular sizes, or effects of volatiles are not considered. Resistor network theory is utilized to account for a variable degree of interconnection and distributed geometries. Thereby, a new possible interpretation of Archie's law is found in terms of varying interconnection. Furthermore, it is found that a reduced degree of interconnection may have an important influence on the conductivity at melt fractions characteristic for a weak to moderate decrease in seismic velocity. The model results are compiled together with the elastic models of part I in a set of diagrams which may be applied systematically to observed electrical and seismic data to find constraints on the state of melting.