Inversion of the assimilation and fractional crystallization (AFC) equations; characterization of contaminants from isotope and trace element relationships in volcanic suites

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Abstract
The assimilation and fractional crystallization (AFC) equations of DePaolo (1981) are inverted, with the aim of characterizing the chemistry of contaminants involved in magma evolution from observed isotope and trace element relationships. Equations are derived for contours of the ratio of the rate of assimilation to the rate of fractional crystallization in the isotope or trace element region where the contaminant might be located. Even for volcanic suites in which AFC is thought to have been the dominant process, the characterization of the contaminant is poorly constrained. Although AFC is likely to be a normal process, it leaves a recognizable isotopic signature in volcanics only when magmas assimilate material derived from continental crust. In subduction-related volcanics, this can be the case where the volcanic arc lies on or near continental crust.