Predicting major element mineral/melt equilibria: A statistical approach

A data set has been collected from the literature, comprising 230 synthetic mineral/melt pairs for which phase composition and run temperature are known. All phase pairs were equilibrated at 1 atm under anhydrous conditions. Solid phases represented are olivine, low-Ca pyroxene, high-Ca pyroxene, and plagioclase. We have developed empirical equations for calculating the mole fractions of NaO/sub 0.5/, MgO, AlO/sub 1.5/, SiO2, KO/sub 0.5/, CaO, TiO2, and FeO in a solid phase of initially unknown identify given only the composition of the coexisting silicate melt. The approach involves a linear multivariate regression analysis in which solid composition is expressed as a Taylor series expansion of the liquid compositions. We obtain an internally consistent precision of approx. =0.94; that is, we can correctly predict the nature of the liquidus phase in our input data set for approximately 94% of the entries. The composition fo the liquidus phase may be calculated to better than 5 mol % absolute. An important feature of this 'generalized solid' model is its reversibility; that is, the dependent and independent variables in the linear multivariate regression may be inverted to permit prediction of the composition of a silicate liquid produced by equilibrium partial melting of a polymineralic source assemblage. We have added 14 points from a silica-olivine-anorthile pseudoternary phase diagram to the data set to deal with polymineralic source assemblages. The composition of the first partial melt can be calculated to better than 3 mol % absolute