Steady-state Mantle–Melt Interactions in One Dimension: II. Thermal Interactions and Irreversible Terms

Progress in development of thermodynamically based models of straint on the thermal state of the Earth’s upper mantle (e.g. Klein & Langmuir, 1987; McKenzie & Bickle, 1988; silicate equilibria with explicit entropy budgets has motivated a reexamination of the conclusion of McKenzie that isentropic upwelAsimow et al., 2001). Meaningful interpretation of these data, however, requires a thorough understanding of ling suffices as a model of mantle melting. An entropy budget equation for fractional melting with melt migration in an upwelling the temperature dependence of the extents of melting produced by mantle processes. Evaluation of the output two-phase continuum is presented. The energetically self-consistent melt production model predicted by MELTS is used to evaluate of decompression melting in these environments usually takes as a reference case the approximation that upwelling numerically the magnitudes of differences between fractional melting (with melt migration) and equilibrium melting (without relative and the resulting melting in the mantle are approximately adiabatic processes. There are many types of adiabatic movement) that can be bounded in one dimension: chemical advection by out-of-equilibrium melt; thermal disequilibrium between miprocesses, but the starting point of most treatments of mantle melting is that the process is approximately adiagrating liquid and residue; frictional dissipation of gravitational potential; dissipation as a result of solid compaction. Like the batic and reversible, i.e. isentropic (Verhoogen, 1965; Cawthorn, 1975; McKenzie, 1984; McKenzie & Bickle, familiar isobaric case in which fractional melting is significantly less productive than equilibrium melting, chemical isolation of the 1988; Asimow et al., 1995, 1997; Iwamori et al., 1995). escaping melts from the residue reduces the oceanic crustal thickness However, even for the batch melting case where liquid by >1 km. Allowing escaping melts to move on their own adiabats and solid move together, this is only an approximation: and ascend at higher temperature than the residue further suppresses for example, thermal diffusion may be negligible, but it melting but yields only >100 m less crustal thickness. Extra is never entirely absent; likewise, there are other sources crustal thickness as a result of gravitational dissipation is >100 of entropy production such as chemical diffusion and in m, much smaller than the effect of chemical isolation. Viscous the kinetics of chemical reactions, viscous deformation dissipation as a result of compaction is negligible. of solid and liquid, and radioactivity (McKenzie, 1984). Moreover, if the liquid phase moves relative to the solid residue, significantly more viscous deformation occurs, the process is no longer reversible because gravitational