Open-System Magma Chamber Evolution: an Energy-constrained Geochemical Model Incorporating the Effects of Concurrent Eruption, Recharge, Variable Assimilation and Fractional Crystallization (EC-E'RA{chi}FC)

Significant petrogenetic processes governing the geochemicalevolution of magma bodies include magma Recharge (includingformation of ‘quenched inclusions’ or enclaves),heating and concomitant partial melting of country rock withpossible ‘contamination’ of the evolving magma body(Assimilation), and formation and separation of cumulates byFractional Crystallization (RAFC). Although the importance ofmodeling such open-system magma chambers subject to energy conservationhas been demonstrated, the effects of concurrent removal ofmagma by eruption and/or variable assimilation (involving imperfectextraction of anatectic melt from wall rock) have not been considered.In this study, we extend the EC-RAFC model to include the effectsof Eruption and variable amounts of assimilation, A. This model,called EC-E'RAFC, tracks the compositions (trace elements andisotopes), temperatures, and masses of magma body liquid (melt),eruptive magma, cumulates and enclaves within a composite magmaticsystem undergoing simultaneous eruption, recharge, assimilationand fractional crystallization. The model is formulated as aset of 4 + t + i + s coupled nonlinear differential equations,where the number of trace elements, radiogenic and stable isotoperatios modeled are t, i and s, respectively. Solution of theEC-E'RAFC equations provides values for the average temperatureof wall rock (T_a), mass of melt within the magma body (M_m),masses of cumulates (M_ct), enclaves (M_en) and wall rock () and the masses of anatectic melt generated () and assimilated (). In addition, t trace element concentrations and i + s isotopic ratios inmelt and eruptive magma (C_m, _m, _m), cumulates (C_ct, _m, _m), enclaves(C_en, , ) and anatectic melt (C_a, , ) as a function of magma temperature (T_m) are also computed. Input parametersinclude the (user-defined) equilibration temperature (T_eq),a factor describing the efficiency of addition of anatecticmelt () from country rock to host magma, the initial temperatureand composition of pristine host melt (, , , ), recharge melt (, , , ) and wall rock (, , , ), distribution coefficients (D_m, D_r, D_a) and their temperaturedependences (H_m, H_r, H_a), latent heats of transition (meltingor crystallization) for wall rock (h_a), pristine magma (h_m)and recharge magma (h_r) as well as the isobaric specific heatcapacity of assimilant (C_p,a), pristine (C_p,m) and recharge(C_p,r) melts. The magma recharge mass and eruptive magma massfunctions, M_r(T_m) and M_e(T_m), respectively, are specified apriori. M_r(T_m) and M_e(T_m) are modeled as either continuous orepisodic (step-like) processes. Melt productivity functions,which prescribe the relationship between melt mass fractionand temperature, are defined for end-member bulk compositionscharacterizing the local geologic site. EC-E'RAFC has potentialfor addressing fundamental questions in igneous petrology suchas: What are intrusive to extrusive ratios (I/E) for particularmagmatic systems, and how does this factor relate to rates ofcrustal growth? How does I/E vary temporally at single, long-livedmagmatic centers? What system characteristics are most profoundlyinfluenced by eruption? What is the quantitative relationshipbetween recharge and assimilation? In cases where the extractionefficiency can be shown to be less than unity, what geologiccriteria are important and can these criteria be linked to fieldobservations? A critical aspect of the energy-constrained approachis 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 whileunifying observations from a number of disciplines relevantto the study of igneous rocks. KEY WORDS: assimilation; energy conservation; eruption; open system; recharge