Geochemical Discrimination Diagrams: A Simple Way of Replacing Eye-Fitted Field Boundaries With, Probability Based Classifier Surfaces

The subjective, eye-fitted, field boundaries in geochemical discrimination diagrams constitute one of the possible reasons for their often-noted inability to determine the source regime/tectonic environments of igneous rocks. A simple method is described here to replace the eye-fitted field boundaries between the groups with the probability based classifier surfaces. It involves projection of the assignment rules obtained from linear discriminant analysis onto the binary or ternary discrimination diagram of raw variables. The method is illustrated by obtaining classifier surface between I- and S-type granites in Na₂O-K₂O space and between Anorthosite/Rapakivi (AR) and Ring Complex (RC) granites in Na₂O-MgO space. The need for explicitly ensuring adequacy of samples, selection of suitable variables, evaluation of rate of misclassification and a better understanding of the unique influence of tectonic environments on magmatic process is emphasized for optimizing the performance of the classifier surface.