recharge mass and Teq, the mass of wallrock heated to Teq is Geochemical data for igneous rocks provide definitive evidence for computed and the geochemical trajectory of melt is determined as the occurrence of open-system processes in magma bodies, including magma temperature approaches Teq from its starting value, Tm°. Replenishment by intrusion of primitive magma, Assimilation of The effects of imperfect extraction of anatectic wallrock melt may anatectic wallrock melt and cumulate formation by Fractional be accounted for by introduction of an extraction efficiency factor. Crystallization. A general class of models (Energy ConservedMathematical details of a simpler model, EC-AFC (no reRAFC or EC-RAFC) can be constructed, which allow simulation plenishment) are provided. Energy-constrained models have the of geochemical paths for trace elements and isotopic ratios for magma advantage of linking thermal and chemical properties of magma undergoing simultaneous replenishment, assimilation and fractional chambers. Compared with ‘classical’ models that conserve mass crystallization during the approach to thermal equilibration. The and species only, they represent more complete assessments of general problem of EC-RAFC is formulated as a set of 3 + t the complex physicochemical dynamics governing the geochemical + i + s coupled nonlinear ordinary differential equations, where evolution of open-system magma bodies. Results of EC-AFC the number of trace elements, radiogenic and stable isotope ratios simulations demonstrate that geochemical trends can differ sigsimultaneously modeled are t, i and s, respectively. Partial melting nificantly from predictions based on ‘classical’ AFC even when of wallrock, modeled as fractional melting, is incorporated, as are recharge plays no role. Incorporation of energy conservation and sensible and latent heat effects. Temperature-dependent partition partial melting into geochemical models allows important coupled coefficients are used to describe trace element distributions. Solution effects to play their natural role. of the set of differential equations, with magma temperature (Tm ) as the independent variable, provides values for the average temperature of wallrock (Ta ), fraction of melt within the magma body (Mm ),
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