An introduction to the statistical analysis of compositional data: applications to classification problems of clinopyroxenes from mafic and ultramafic rocks.

The analysis of compositional data cannot be performed in a correct way if the closure constraint is not taken into account. In fact, several authors have demonstrated that bias is introduced in the variability patterns of data if variables are measured as proportions of the same whole. The history of thinking about compositions is complex and only ten years ago procedures to perform an unbiased measure of the correlations in closed systems have been proposed. This important result allowed to use correctly multivariate methodologies, the application of which in the Earth Sciences is relevant to achieve discimination diagrams. An example of multivariate investigation is applied to the chemical composition of clinopyroxenes from mafic and ultramafic rocks related to different geodynamical settings. Clinopyroxenes change their composition if mantle processes such as deformation, melting or metasomatism influence their formation, thus providing useful information about the nature of the upper mantle. Discrimination diagrams obtained using large sets of clinopyroxene data may allow to formulate a general framework of their variability patterns. In this paper we analyse the classification and interpretation problems that can be encountered if the closure costraint is underestimated.