Equations are presented to describe the compositional evolution of magma chambers undergoing simultaneous recharge (R), evacuation (E), and fractional crystallization (FC). Constant mass magma chambers undergoing REFC will eventually approach a steady state composition due to the "buffering" effect of recharging magma. Steady state composition is attained after similar to 3/(D alpha(x) + alpha(e)) overturns of the magma chamber, where D is the bulk solid/melt partition coefficient for the element of interest and alpha(x) and alpha(e) are the proportions of crystallization and eruption/evacuation relative to the recharge rate. Steady state composition is given by C-re/(D alpha(x) + alpha(e)). For low evacuation rates, steady state concentration and the time to reach steady state scale inversely with D. Compatible (D > 1) elements reach steady state faster than incompatible (D < 1) elements. Thus, magma chambers undergoing REFC will eventually evolve towards high incompatible element enrichments for a given depletion in a compatible element compared to magma chambers undergoing pure fractional crystallization. For example, REFC magma chambers will evolve to high incompatible element concentrations for a given MgO content compared to fractional crystallization. Not accounting for REFC will lead to over-estimation of the incompatible element content of primary magmas. Furthermore, unlike fractional crystallization alone, REFC can efficiently fractionate highly incompatible element ratios because the fractionation effect scales with the ratio of bulk D's. By contrast, in pure fractional crystallization, ratios fractionate according to the arithmetic difference between the bulk D's. The compositional impact of REFC should be most pronounced for magma chambers that are long-lived, have low rates of eruption/evacuation, and/or are characterized by high recharge rates relative to the mass of the magma chamber. The first two conditions are likely favored in deep crustal magma chambers where confining pressures are high and warm country rock decrease the cooling rates of magma chambers. By contrast, REFC should be less significant in shallow crustal magma chambers, which erupt and cool more efficiently due to lower confining pressures, colder country rock, and the cooling effects of hydrothermal systems. We thus speculate that the effects of REFC will be small in mid-ocean ridge settings and most pronounced in arc settings, particularly mature island arcs or continental arcs, where magma chambers > 10 km depth are possible. This begs the question of whether high Fe3+, H2O and CO2 (all of which can be treated as incompatible "elements") in arc basalts could be enhanced by REFC processes and thus not just reflect inheritance from the mantle source. We show that REFC can plausibly explain observed enrichments in Fe3+ and H2O in arc melts without significant depletion in MgO. Because the difference between calc-alkaline and tholeiitic differentiation series is mostly likely due to higher water and oxygen fugacity in the former, it may be worth considering the effects of REFC. Thus, if REFC is more pronounced in deep crustal magma chambers, mature island arcs and continental arcs would tend towards calc-alkaline differentiation, whereas juvenile island arcs would be more tholeiitic. To fully test the significance of REFC will require detailed analysis of other highly incompatible elements, but presently the relative differences in bulk D of such elements may not be constrained well enough. The equations presented here provide a framework for evaluating whether REFC should be considered when interpreting geochemical data in differentiated magmas. For completeness, we have also provided the more general equations for a magma chamber undergoing recharge (R), evacuation (E), crustal assimilation (A) and fractional crystallization (FC), e.g., REAFC, for constant mass, growing and dying magma chambers. (C) 2013 Elsevier Ltd. All rights reserved.
