Energy‐constrained open‐system magmatic processes 3. Energy‐Constrained Recharge, Assimilation, and Fractional Crystallization (EC‐RAFC)

Abstract

Geochemical data for igneous rock suites provide conclusive evidence for the occurrence of open‐system processes within thermally and compositionally evolving magma bodies. The most significant processes include magma Recharge (with possible enclave formation and magma mixing), Assimilation of anatectic melt derived from wallrock partial melting and formation of cumulates by Fractional Crystallization (RAFC). In this study, we extend the Energetically Constrained Assimilation and Fractional Crystallization (EC‐AFC) model [Spera and Bohrson, 2001; Bohrson and Spera, 2001] to include the addition of compositionally and thermally distinct recharge melt during simultaneous assimilation and fractional crystallization. Energy‐Constrained Recharge, Assimilation, and Fractional Crystallization (EC‐RAFC) tracks the trace element and isotopic composition of melt, cumulates and enclaves during simultaneous recharge, assimilation and fractional crystallization. EC‐RAFC is formulated as a set of 3 + t + i + s coupled nonlinear differential equations, where the number of trace elements and radiogenic and stable isotope ratios modeled are t, i, and s, respectively. Solution of the EC‐RAFC equations provides values for the average wallrock temperature (Ta), mass of melt within the magma body (Mm), mass of cumulates (Mct) and enclaves (Men), mass of wallrock involved in the thermal interaction (Mao), mass of anatectic melt assimilated (M*a), concentration of t trace elements and i + s isotopic ratios in melt (Cm), cumulates (Cct), enclaves (Cen), and anatectic melt (Ca) as a function of magma temperature (Tm). Input parameters include the equilibration temperature (Teq), the initial temperature and composition of pristine melt (Tmo, Cmo, εmo), recharge melt (Tro, Cro, εro), and wallrock (Tao, Cao, εao), temperature‐dependent trace element distribution coefficients (Dm, Dr, Da), heats of transition for wallrock (Δha), pristine melt (Δhm), and recharge melt (Δhr), and the isobaric specific heat capacity of assimilant (Cp,a), pristine melt (Cp,m), and recharge melt (Cp,r). The magma recharge mass function, Mr(Tm), is specified a priori and defines how recharge magma is added to standing magma. The present EC‐RAFC simulator incorporates a weak coupling to major element mass balance and phase relations based on laboratory experiments or Gibbs Energy minimization [e.g., Ghiorso, 1997]. EC‐RAFC can be applied to a variety of magmatic systems including volcanic suites that show evidence of magma mixing, layered mafic intrusions, and granitoid plutons. Predictions for masses, as well as compositions of magmatic products, are part of the EC‐RAFC solution. The “systems” approach provides an opportunity to quantitatively assess the roles of assimilation, fractional crystallization, and magma recharge in magma evolution using trace element and isotopic constraints together with energy conservation.