JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. Bll, PAGES 19,807-19,817, NOVEMBER 10, 1993 Dilatational Anelasticity in Partial Melts' Viscosity, Attenuation, and Velocity Dispersion DOUGLAS H. GREEN Department of Geological Sciences, Ohio University, Athens REID F. COOPER Department of Materials Science and Engineering and Department of Geology and Geophysics University of Wisconsin-Madison Thermodynamic constraints on the geometry of melt/solid interfaces require that a texturally equilibrated partial melt respond to changes in mean normal stressthrough adjustment of the sizes of melt-bearing triple-grain junctions. This dilatational responseis well-modeled as that of a standard anelastic solid provided that the response rate is limited by solid-statedeformation processes attending the dilatation rather than by melt flow itself. Using this model, we have analyzed flexural creep data obtained for a fine-grained partial melt comprising a MgSiO3 polycrystalline solidphase in equilibrium with a sodium aluminosilicate melt. The anelastic dilatational (or "bulk") viscosity for this two-phase material is nearly an order of magnitude less than its shear viscosity, the latter being determined by diffusionalcreep. The corresponding modulusthat controlsthe extent of dilatation is several orders of magnitude smaller than the elastic bulk modulus of the two-phase aggregate. Applied to the case of harmonic loading, the model predicts a substantial band-limited dissipation spectrum for dilatation (Q•i) that would beabsent but forthe presence of the melt. This creates a large and strong P wave absorption (Q•7 l) band for the enstatite material, accompanied by substantial P wavevelocity dispersion. Through this enhanced P wave attenuation, the presence of the melt phase suppresses P-to-S velocity ratios and producesequivalent Q values for the two modes. INTRODUCTION The natures of anomalously weak regions of the astheno- sphere have been a puzzle to geophysicists for many years. The observed low (or at least nearly depth-independent) velocities and high attenuation of seismic waves in the low-velocity zone (LVZ) and under mid-oceanic ridges has yet to be unequivocally accounted for in terms of an upper mantle rheological model. The presence of a melt phase is often invoked to account for the increased anelasticity of these regions, although as will be discussedbelow, it is not yet clear exactly how such a second phase would weaken upper mantle rock. Basaltic melt is obviously present below mid-oceanic ridges and any model of subridge deformation has to take this fluid into account [e.g., McKenzie, 1984; Richter and McKenzie, 1984; Ribe, 1987; Phipps Morgan, 1987; Scott and Stevenson, 1989]. Determining the amount of melt, or at least its existence, in the upper mantle is in large part dependent upon seismic interpretation. Taking into account velocity anisotropy [Anderson and Dziewonski, 1982;Regan and Anderson, 1984] and lateral heterogeneity [Nataf et al., 1986] substantially reduces the inferred low-velocity and high-attenuation anomalies associated with the LVZ. Nev- ertheless, some seismic anelasticity must be present in the average upper asthenosphere in order to account for the velocity dispersion apparent from studies of body waves, surface waves, and free oscillations [Hart et al., 1976]. Several studies have suggested partial melting as the cause of low velocities and/or high attenuationsin both continental Copyright 1993 by the American Geophysical Union. Paper number 93JB01726. 0148-0227/93/93JB-01726505.00 and oceanic environments [Revenaugh and Jordan, 1989, 1991a, b; Flanagan and Wiens, 1990; Roberts et al., 1991]. Efforts have been made to connect seismic observations with melt fraction for a partially molten low-velocity zone. Estimates of melt fractions in the LVZ and mid-oceanic ridges range from zero to ---10% [Solomon, 1973; Sato et al., 1989a]. Similarly, significant melt fractions have been sug- gested as causes of seismic anelasticity beneath rift zones [Hadiouche, 1990; Halderman and Davis, 1991]. Collectively, the studies cited above show that deducing upper mantle melt fractions from seismic data relies on relations between melt fraction and seismic parameters, relations establishedtheoretically or in the laboratory. Mod- els of attenuation in partial melts either assume that the melt resides as thin sheetson two-grain boundaries or require that it be restricted to triple-grain junctions [Walsh, 1969; Mavko and Nur, 1975; O'Connell and Budiansky, 1977; Mavko, 1980; Schmeling, 1985]. For even small amounts of melt these models predict shear wave attenuation that is large relative to that for compressionalwaves. A critical factor in the estimation of the amount of attenuation to be expected for a given melt fraction is the wetting behavior of the melt with respect to the crystalline residuum, that is, whether the melt invades two-grain (pla- nar) boundaries or is instead preferentially restricted to triple-grain junction tubules. It is now generally accepted, and supported by theoretical calculations and experimental observations,that in most silicate partial melt systemsunder quasi-equilibrium conditionsthe melt is expected to reside at triple-grain junctions [Waftand Bulau, 1979, 1982; Vaughan et al., 1982; Cooper and Kohlstedt, 1982; Jurewicz and Watson, 1985; von Bargen and Waft, 1988; Daines and Richter, 1988]. Furthermore, Laporte and Watson [1993] 19,807