Multivariate statistical analysis of geochemical data exemplified by Proterozoic dyke swarms in Sweden

Abstract

The multivariate statistical analysis of chemical data in petrology and geochemistry entails principles that are little known among geological practitioners. Such data are compositional, and hence, lie in a sub-space of full space, the simplex. The concept of product-moment correlation of full space cannot be validly applied to them, because of the subcompositional incoherency of that statistic in the simplex. A second type of problem concerns the stability of multivariate estimates. Appropriate techniques, such as principal component cross-validation, are discussed exemplified and contrasted with inappropriate procedures using geochemical data on Swedish Proterozoic dyke swarms. Essential features of compositional covariance structure are exemplified in an Appendix.