Interpretation of seismic velocity and attenuation in partially molten rocks has been limited, with few exceptions, to models that assume the melt to be distributed either as spheres or as thin films. However, other melt phase geometries, such as interconnected tubes along grain edges, might equally well account for seismic observations if there is a much larger fraction of melt. Seismic velocity and attenuation are estimated in rocks in which the melt phase has the tube geometry, and the results are compared with results expected for the more familiar film model under similar conditions. For a given melt fraction, tubes are found to give moduli intermediate between moduli for rigid spherical inclusions and compliant films. For example, in polycrystalline olivine at 20 kbar the model predicts a decrease in V/sub s/ of 10% and a decrease in V/sub p/ of 5% at 0.05 melt fraction, without considering inelastic relaxation. Shear attenuation appears to be dominated by viscous flow of melt between the tubes and/or films. For olivine the tube model predicts the increment of relaxation due to melt, ..delta mu../..mu.., to be 0.01 at 0.05 melt fraction. Relaxation of the bulk modulus is dominated by flow between melt pockets ofmore » different shape, heat flow, and solid-melt phase change. If melt is present, considerable bulk attenuation is expected, although the relaxation may be observable only at long periods, outside the seismic body wave band.« less

Velocity and attenuation in partially molten rocks

In the system CaO-MgO-Al2O3-SiO2, the tetrahedron CaMgSi2O6(di)-Mg2SiO4(fo)-SiO2-CaAl2 SiO6(CaTs) forms a simplified basalt tetrahedron, and within this tetrahedron, the plane di-fo-CaAl2Si2O8(an) separates simplified tholeiitic from alkalic basalts. Liquidus phase relations on this join have been studied at 1 atm and at 7, 10, 15, and 20 kbar. The temperature maximum on the 1 atm isobaric quaternary univariant line along which forsterite, diopside, anorthite, and liquid are in equilibrium lies to the SiO2-rich side of the join di-fo-an. The isobaric quaternary invariant point at which forsterite, diopside, anorthite, spinel, and liquid are in equilibrium passes, with increasing pressure, from the silica-poor to the silica-rich side of the join di-fo-an, which causes the piercing points on this join to change from forsterite+diopside+anorthite+liquid and forsterite +spinel+anorthite+liquid below 5 kbar to forsterite +diopside+spinel+liquid and diopside +spinel+anorthite+liquid above 5 kbar. As pressure increases, the forsterite and anorthite fields contract and the diopside and corundum fields expand. The anorthite primary phase field disappears entirely from the join di-fo-an between 15 and 20 kbar. Below about 4 kbar, the join di-fo-an represents, in simplified form, a thermal divide between alkalic and tholeiitic basalts. From about 4 to at least 12 kbar, alkalic basalts can produce tholeiitic basalts by fractional crystallization, and at pressures above about 12 kbar, it is possible for alkalic basalt to be produced from oceanite by crystallization of both olivine and orthopyroxene. If alkalic basalts are primary melts from a lherzolite mantle, they must be produced at high pressures, probably greater than about 12 kbar.

Liquidus phase relations on the join diopside-forsterite-anorthite from 1 atm to 20 kbar: Their bearing on the generation and crystallization of basaltic magma

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.

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

For mantle regions of anomalously high electrical conductivity (greater than 0.1 S/m) the bulk conductivity is modeled by effective medium theory as a basalt melt fraction within a mainly olivine matrix. In order for the highly conducting melt to affect the bulk conductivity it must form interconnections, so that the very existence of mantle conductivity anomalies constitutes evidence for such interconnections. The inclusion of petrological data on the partial melting of peridotite strongly constrains the range of temperatures and melt fractions that can be used to yield an observed electrical conductivity. Thus from anomalous conductivities which are observed under rift zones, volcanic belts, geothermal areas, and beneath the oceans, it is possible to estimate both the temperature and the degree of partial melting. While other mechanisms for mantle conductivity enhancement may exist, e.g., contributions from contaminated grain boundaries or high volatile contents, these explanations associate a chemical differentiation in the mantle with thermal manifestations and in most cases create conditions that favor melting.

Partial melting and electrical conductivity anomalies in the upper mantle

A computer simulation study of natural silicate melts. Part I: Low pressure properties

The electrical conductivity of a synthetic basalt has been determined at atmospheric pressure in air at temperatures between 700 ø and 1600øC. The conductivity increases by about 2 orders of magnitude in the melting interval between 1130 ø and 1263øC. It is suggested that partial fusion in the seismic low-velocity zone of the upper mantle may account for the correlation of increased electrical conductivity with development of this zone.

C. L. Simmons

Papers

Changes in electrical conductivity of a synthetic basalt during melting