Deciphering magma mixing: The application of cluster analysis to the mineral chemistry of crystal populations

Cluster analysis, a classification technique used to group data in many fields, is developed here as a tool to study magma mixing and mixed crystal populations in volcanic rocks. The method is based on the quantification of the chemical degree of similarity among populations of mineral chemistry data, which allows identification of discrete clusters. In order to apply the technique for the particular problem of mixed crystal populations, the mineral chemistry of a given crystalline phase is represented by a vector with “n” coordinates, in which each coordinate is a real number that represents the amount of a given component in cations per formula unit present in the phase. These vectors are in a set, which is a subset of Rn, the real vector space of n dimensions. Because mineral chemistry data are a particular case of compositional data (i.e. the components sum to a constant value, usually 100% or the numbers of cations per formula unit), the conventional Euclidean distance cannot be used to quantify how similar the data are, in order to apply cluster analysis. To avoid this predicament, Aitchison's metric is proposed to measure similarities instead. Here, average linkage, a hierarchical clustering technique, combined with the Aitchison metric and stoichiometrical constraints, is applied to mineral chemistry data. This approach is evaluated using well-characterized lava samples from the Vancori period of activity (26–13.8 ky) of Stromboli volcano, Italy, in which magma mixing has been identified between a basaltic andesite–latite, hosted in the magma chamber and a less evolved basaltic recharge magma. The results are in agreement with previous interpretations of magma mixing, which validates the use of the cluster analysis technique in the context of magma mixing relationships, and opens the possibility to expand this methodology to other aspects of igneous petrology.