Velocity and attenuation in partially molten rocks

Abstract

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 resuits 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 s of 10% and a decrease in I/•, 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, •//x, to be 0.01 at 0.05 melt fraction. Relaxation of the bulk modulus is dominated by flow between melt pockets of 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. Paper number 80B0266. 5173 5174 MAVKO: STANFORD Q CONFERENCE Thermodynamic considerations [Bulau and Waft, 1977; Bulau et al., 1979] and experimental results [Waft and Bulau, 1977, 1979] suggest that tubes, rather than films, may be the expected equilibrium melt geometry under some conditions. Frank [1968] postulated the tube geometry to model melt percolation and to explain certain aspects of heat and mass transport in a convecting upper mantle. Walker et al. [1978] refined Frank's tube model to calculate melt mobility and melt-solid segregation. The effect of solid tubular inclusions (with circular cross section) on the effective elastic properties of a composite has been treated by Wu [1966], Boucher [1974], and Walpale [1969].In the tube model suggested by Smith [1964], shown schematically in Figure 1, each tube is roughly triangular in cross section with sharp edges. In the film geometry the flat grain faces are coated. Details of the shape (e.g., tube versus film) depend on the relative solid-solid and solid-melt surface energies, as well as whether or not the system is in equilibrium. The factors affecting shape are discussed by Smith

Upper mantle seismic wave velocity: Effects of realistic partial melt geometries

“…A fluid-filled, convex circular cylinder, for example, is naturally more rigid than a cuspate, concave cylinder with the same melt fraction and aspect ratio [Mavko, 1980]. This leads to an underestimation of the amount of velocity reduction for a given partial melt fraction when using relationships based on ellipsoidal geometry.…”

Upper mantle P wave velocity structure of the eastern Snake River Plain and its relationship to geodynamic models of the region

“…The effect of partial meli on seismic velocities depends upon the geometry of the melt, which can be paramete• as where { is the malt fraction and A is a constant dependent upon the aspect ratio of the melt inclusions [Schrneling, 1985;Mavko, 1980]. Generally, i<A <3 unless the melt is distributed in very thin fikns, in which case A can be larger.…”

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.…”