Open-system magma chamber evolution:: an energy-constrained geochemical model incorporating the effects of concurrent eruption, recharge, variable assimilation and fractional crystallization (EC-E′RAχFC)

Significant petrogenetic processes governing the geochemical evolution of magma bodies include magma (R) under bar echarge (including formation of 'quenched inclusions' or enclaves), heating and concomitant partial melting of country rock with possible 'contamination' of the evolving magma body ((A) under bar ssimilation), and formation and separation of cumulates by (D) under bar ractional (X) under bar rystallization (RAFC). Although the importance of modeling such open-system magma chambers subject to energy conservation has been demonstrated, the effects of concurrent removal of magma by eruption and/or variable assimilation (involving imperfect extraction of anatectic melt from wall rock) have not been considered. In this study, we extend the EC-RAFC model to include the effects of (E) under bar ruption and variable amounts of assimilation, (A) under bar chi. This model, called EC-E'RAchiFC, tracks the compositions (trace elements and isotopes), temperatures, and masses of magma body liquid (melt), eruptive magma, cumulates and enclaves within a composite magmatic system undergoing simultaneous eruption, recharge, assimilation and fractional crystallization. The model is formulated as a set of 4 + t + i + s coupled nonlinear differential equations, where the number of trace elements, radiogenic and stable isotope ratios modeled are t, i and s, respectively. Solution of the EC-E'RAchiFC equations provides values for the average temperature of wall rock (T-a), mass of melt within the magma body (M-m), masses of cumulates (M-ct), enclaves (M-en) and wall rock (M-a(o)) and the masses of anatectic melt generated (M-a(*)) and assimilated (chiM(a)(*)). In addition, t trace element concentrations and i + s isotopic ratios in melt and eruptive magma (C-m, epsilon(m), delta(m)), cumulates (C-ct, epsilon(m), delta(m)), enclaves (C-en, epsilon(r)(o), delta(r)(o)) and anatectic melt (C-a, epsilon(a)(o), delta(a)(o)) as a function of magma temperature (T-m) are also computed. Input parameters include the (user-defined) equilibration temperature (T-eq), a factor describing the efficiency of addition of anatectic melt (chi) from country rock to host magma, the initial temperature and composition of pristine host melt (T-m(o), C-m(o), epsilon(m)(o), delta(m)(o)), recharge melt (T-r(o), C-r(o), epsilon(r)(o), delta(r)(o)) and wall rock (T-a(o), C-a(o), epsilon(a)(o), delta(a)(o)), distribution coefficients (D-m, D-r, D-a) and their temperature dependences (DeltaH(m), DeltaH(r), DeltaH(a)), latent heats of transition (melting or crystallization) for wall rock (Deltah(a)), pristine magma (Deltah(m)) and recharge magma (Deltah(r)) as well as the isobaric specific heat capacity of assimilant (C-p,C-a), pristine (C-p,C-m) and recharge (C-p,C-r) melts. The magma recharge mass and eruptive magma mass functions, M-r(T-m) and M-e(T-m), respectively, are specified a priori. M-r(T-m) and M-e(T-m) are modeled as either continuous or episodic (step-like) processes. Melt productivity functions, which prescribe the relationship between melt mass fraction and temperature, are defined for end-member bulk compositions characterizing the local geologic site. EC-E'RAchiFC has potential for addressing fundamental questions in igneous petrology such as: What are intrusive to extrusive ratios (I/E) for particular magmatic systems, and how does this factor relate to rates of crustal growth? How does I/E vary temporally at single, long-lived magmatic centers? What system characteristics are most profoundly influenced by eruption? What is the quantitative relationship between recharge and assimilation? In cases where the extraction efficiency can be shown to be less than unity, what geologic criteria are important and can these criteria be linked to field observations? A critical aspect of the energy-constrained approach is that it requires integration of field, geochronological, petrologic, and geochemical data, and, thus, the EC-ERAFC 'systems' approach provides a means for answering broad questions while unifying observations from a number of disciplines relevant to the study of igneous rocks.