A thermodynamic model of adiabatic melting of the mantle

Mid-ocean ridge basalts (MORB) are mixtures of melts produced over a range of pressure and temperature in a nearly adiabatic open system undergoing changes in composition as melting proceeds. Interpretation of the compositional variations observed in MORB and their correlation with geophysical aspects of the ridge therefore requires complex forward models to connect experimental observations of isothermal, isobaric batch melting of peridotite to natural compositions. Previous attempts to construct such models have relied on parameterizations of melt composition or partition coefficients and extent of melting in pressure-temperature space from experimental batch melting data. This thesis undertakes the examination of an alternative approach using thermodynamic models of silicate minerals and melts to predict equilibria under quite arbitrary constraints, including variable bulk composition and constant entropy. The liquids predicted from the thermodynamic models along polybaric paths can then be integrated to produce comprehensive forward models of MORB genesis.;Chapter 1 introduces the nature of the MORB modeling problem and the motivation of the thermodynamic approach in greater detail. Chapter 2 illustrates the thermodynamic approach by demonstrating that the effect of the garnet-spinel and spinel-plagioclase peridotite transitions, which retard or reverse isentropic melting, can be easily understood. Chapter 3 looks at the variables affecting isentropic melt productivity (i.e., the increment of additional melting per decrement of pressure at constant entropy). I find that this quantity is likely to increase during progressive melting, punctuated by drops where phases are exhausted from the residuum. Chapter 4 extends this approach to issues of melt transport in one dimension and steady state; I evaluate the magnitude of entropy production due to gravitational dissipation and thermal interactions with migrating fractional melts and examine the effect of focused melt flow. Finally, chapter 5 deals with the compositions and mean properties of MORB obtained by integrating the compositions and melt fractions predicted by our models. We compare our results to published models of MORB compositions and consider the implications. The algorithms and source code, including subsolidus capability, added to the MELTS package of Ghiorso and Sack for these calculations are included as appendices.