Steady-state Mantle–Melt Interactions in One Dimension: I. Equilibrium Transport and Melt Focusing

Mantle–melt interaction during melt transport is explored in one generally moves relative to the residual solid phases. This follows from experimental and theoretical studies of the dimension and steady state. We reconsider the equivalence between one-dimensional steady equilibrium transport and batch melting. In equilibrium textures of olivine-dominated, partially molten systems, which indicate that the liquid phase is the absence of diffusion and radioactivity, conservation of mass flux requires that the major and trace element compositions of melt and interconnected at melt fractions <1% (Waff & Bulau, 1979; von Bargen & Waff, 1986; Kohlstedt, 1991), sugsolid at each point are the same as is generated by batch melting the source composition at the same pressure and temperature. Energy gesting that even at very low melt fractions, melt can begin to move by porous flow, driven by density differences or conservation requires that temperature and extent of melting are independent of melt migration except for irreversible source terms by shear of the matrix (McKenzie, 1984; Richter & McKenzie, 1984; Spiegelman & McKenzie, 1987; Sterelated to viscous compaction and gravitational energy release. The equivalence of phase compositions at each pressure between steadyvenson & Scott, 1991). For reasonable grain sizes and rates of solid-state diffusion in the residual minerals, the state equilibrium transport and batch melting simplifies melt transport calculations. We examine the effects of increasing the melt flux to expected rates of grain-scale porous flow are such that the moving melt is expected to approach closely equisimulate melt focusing by channeling or by two-dimensional flow with converging melt streamlines. Melt focusing modifies the mineralogy of librium with the matrix minerals (Navon & Stolper, 1987; both residual matrix and erupted melt. We use MELTS calculations Spiegelman & Kenyon, 1992). to model the formation of dunite by this mechanism and quantify There is, however, considerable evidence that erupted the melt flux required to exhaust orthopyroxene from the residue as mid-ocean ridge basalts (MORBs) are not in major or a function of pressure. The model dunites are found to be similar trace element equilibrium with typical lherzolite and to natural dunites observed in the mantle section of ophiolite harzburgite mantle residues at low pressure (O’Hara, sequences. 1968; Stolper, 1980; Johnson et al., 1990), suggesting that erupted magmas contain at least a component of melts that did not stay in intimate contact with residual peridotites all the way to the top of the upper mantle. Furthermore, the time scale on which basalts are isolated