A MASS PROPORTION METHOD FOR CALCULATING MELTING REACTIONS AND APPLICATION TO MELTING OF MODEL UPPER-MANTLE LHERZOLITE

We present a method for calculating quantitative melting reactions in systems with multiple solid solutions that accounts for changes in the mass proportions of phases between two points at different temperatur es along a melting curve. This method can be applied to any data set t hat defines the phase proportions along a melting curve. The method yi elds the net change in mass proportion of all phases for the chosen me lting interval, and gives an average reaction for the melting path. In stantaneous melting reactions can be approximated closely by choosing sufficiently small melting intervals. As an application of the method, reactions for melting of model upper mantle peridotite are calculated using data from the system CaO-MgO-Al2O3-SiO2-Na2O (CMASN) over the p ressure interval 0.7-3.5 GPa. Throughout almost this entire pressure r ange, melting of model Iherzolite involves the crystallization of one or more solid phases, and is analogous to melting at a peritectic inva riant point, In addition, we show that melting reactions for small mel ting intervals(< 5%) along the solidus of mantle peridotite are signif icantly different from those calculated for large melting intervals. F or large melting intervals (> 10%), reaction stoichiometries calculate d in CMASN are usually in good agreement with those available for melt ing of natural peridotite, The coefficients of melting reactions calcu lated from this method can be used in equations that describe the beha vior of trace elements during melting. We compare results from near-fr actional melting models using (1) melting reactions and rock modes fro m CMASN, and (2) constant reactions representative of those used in th e literature. In modeling trace element abundances in melt, significan t differences arise for some elements at low degrees of melting(< 10%) . In modeling element abundances in the residue, differences increase with increase in degree of melting. Reactions calculated along the mod el Iherzolite solidus in CMASN are the only ones available at present for small degrees of melting so we recommend them for accurate trace e lement modeling of natural lherzolite.