Computer Science
Scientific paper
May 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985e%26psl..73..361r&link_type=abstract
Earth and Planetary Science Letters, Volume 73, Issue 2-4, p. 361-376.
Computer Science
61
Scientific paper
A set of equations is presented which combines the constraints of fluid dynamics and multicomponent phase equilibrium to provide a unified description of partial melting in the earth's mantle. The equations are applied to a one-dimensional model for pressure-release melting of a simplified mantle material, which contains only two chemical components exhibiting either (a) complete solid solution or (b) a binary eutectic. In both cases, melting occurs over a range of depths. The unmelted crystalline residue (``matrix'') is modeled as a saturated porous medium, through which the melt can migrate because of its differential buoyancy. Since melt interacts continuously with the matrix during ascent, melting occurs by equilibrium rather than fractional fusion. This equilibrium fusion is not the same as batch fusion, however, since material elements are quickly dispersed by migration of melt relative to the matrix. To a first approximation, the temperature profiles (adiabats) in the partially molten zone are independent of melt migration. The slope of the adiabats varies in inverse proportion to the number of degrees of freedom which characterizes the melting. Melting of a complete solid solution occurs along a ``wet'' adiabat whose slope is controlled by absorption of latent heat. Melting of a eutectic system occurs along a steeper ``univariant'' adiabat until one solid phase is exhausted, and subsequently along a wet adiabat. The velocity of melt migration can exceed the mantle upwelling velocity by an order of magnitude or more. The volume fraction of melt present is always less than the fraction of the material which has melted, and is unlikely to exceed a few percent. For a wide range of initial conditions, melting of a eutectic system produces erupted melts having constant major element composition and widely varying trace element composition. This result may provide a partial explanation for the characteristic major- and LIL-element patterns observed in MORB. Liquid compositional paths during pressure-release melting cannot be determined from isobaric sections of phase diagrams, and can only be calculated by solving the energy equation subject to the appropriate depth-dependent phase equilibrium constraints.
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