Evaluation of magma mixing and fractional crystallization using whole‐rock chemical analyses: Polytopic vector analyses

Magma mixing and crystal fractionation are fundamental processes that lead to the diversity of magma compositions, but rarely are all of the major and trace element data on whole rocks used simultaneously in evaluating proposed models. Polytopic vector analysis (PVA) is an oblique factor analysis procedure designed specifically to evaluate mixing or unmixing (fractional crystallization) in geologic systems using all of the analytes (major and trace elements) simultaneously. It differs from other techniques in that it not only determines the number of end‐members and their compositions, but also partitions the relative proportions of the end‐members into each sample in the data array. These samples, expressed as proportions of end‐members, can be used as input in other multivariate analyses. The purpose of this paper is to use PVA to evaluate some examples of magma mixing and fractional crystallization and use these examples as templates for more complicated systems in order to show both the strengths and the weaknesses of the approach. Five well‐constrained examples illustrate how PVA can discriminate between these two processes and provide additional petrogenetic information. Using PVA, mixing between magma types can be easily distinguished from crystal fractionation. With fractional crystallization the end‐members, generated by PVA, are the initial and final liquids and the compositions where new phases join the crystallizing assemblage.