Theoretical considerations of electrical conductivity in a partially molten mantle and implications for geothermometry

Abstract

Relationships between bulk effective electrical conductivity, melt fraction, and liquid path connectivity are derived for a partially melted material. Hashin‐Shtrikman bounds are determined for the conductivity on the basis of entropy production and compared with results obtained for exact geometrical models for the limiting cases of isolated melt pockets and complete grain boundary wetting. Models used are (1) a spherical particle assemblage of an infinite number of different‐sized composite spheres, each containing an inner core of one phase, surrounded by an outer shell of a second phase, and (2) a three‐dimensional periodic array of identical‐sized cubes of one phase, surrounded by a second phase that extends continuously throughout the body. Both models yield the same expressions as those of the upper Hashin‐Shtrikman bound for the bulk conductivity dependence on melt fraction for small melt fractions with complete liquid bridging. A small dependence on grain size and shape is inferred. Partial melting in the form of isolated melt pockets is found to be ineffective in raising bulk conductivity significantly over that of the solid phase material. Quasi‐continuous grain boundary wetting is considered in terms of analog modeling. Melt fraction and liquid path connectivity are found to be main determining factors for electrical conductivity. It is concluded that grain boundary and/or edge wetting is necessary for partial melting to raise bulk conduction in the mantle appreciably over that of its solid phase material. Such wetting is therefore inferred to be a highly probable mechanism responsible for high conductivity anomalies observed in deep geomagnetic soundings. Implications for geothermometry are considered.

A three‐dimensional electromagnetic model of the southern Kenya Rift: Departure from two dimensionality as a possible consequence of a rotating stress field

“…[1997] interpret this low-velocity zone as the axial continuation of a lowvelocity zone imaged to the north, which has been attributed to the presence of 3-5% partial melt [Mechie et al, 1994]. Melt resistivities are highly temperature-and composition-dependent, but the maximum bulk resistivity for a 3%, dry (volatiles can be expected to substantially lower the resistivity), basaltic melt fraction is expected to be <15 • m [e.g., Waff, 1974], assuming that such a high melt fraction forms an interconnected network. The model fit is substantially degraded by the introduction of a 20 • m axial conductor directly below the rift which could be said to relate to a zone of partial melt confined within the subrift mantle at the latitude (1.8øS) of the survey (Figure 11).…”

Olivine crystallographic control and anisotropic melt distribution in ultramafic partial melts

“…Many authors have proposed that the seismic properties of low-velocity zones can be explained in terms of a small melted fraction [Anderson and Sammis, 1970;Solomon, 1972;Stocker and Gordon, 1975; Shankland et al, 1981; Mavko, 1980;Schmeling, 1985]. Electrical conductivity anomalies [Waff, 1974;Shankland and Waff, 1977;Tyburczy and Waft, 1983] also contribute strong evidence that partial melting phenomena exist in the upper mantle. Melt distribution in partially molten zones is important in determining their bulk physical properties.…”

Electrical conductivity images of Quaternary faults and Tertiary detachments in the California Basin and Range

“…This mode responds primarily to conductive bodies with the same strike as the geologic structure, but truncations of these bodies off the profile can have a profound effect on the data. The TE mode is thus more affected by 3-D structure than is the TM mode [Wannamaker, 1999].…”

“…For our model, the N-S mode is the TE mode discussed above. The N-S impedances from the remaining sites were included, but given lesser weights in the inversion because the TE mode is often affected by truncation of structure along strike (in this case, to the north or south of the profile) [Wannamaker et al, 1984;Wannamaker, 1999]. Specific to our profile, Mackie et al [1996] show that the N-S mode, but not the E-W mode, at a site in Panamint Valley is affected by regional 3-D structure including the Transverse Ranges adjacent to the Pacific Ocean.…”