Modeling the compositional evolution of recharging, evacuating, and fractionating (REFC) magma chambers: Implications for differentiation of arc magmas

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 ∼3/(Dαx+αe) overturns of the magma chamber, where D is the bulk solid/melt partition coefficient for the element of interest and αx and αe are the proportions of crystallization and eruption/evacuation relative to the recharge rate. Steady state composition is given by Cre/(Dαx+αe). 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 (D10km depth are possible.