Statistical approaches to the discrimination of crust- and mantle-derived low-Cr garnet - Major-element-based methods and their application in diamond exploration

Multivariate statistical solutions, which incorporate a wide selection of geochemical variables, represent additional possibilities for discrimination. Using our new database, logistic regression (LR) and linear discriminant analysis (LDA) approaches are evaluated and new crust-mantle garnet discrimination schemes derived. The resulting solutions, using a wide variety of cations in garnet, provide lower misclassification rates than existing literature schemes. Both LR and LDA are successful discrimination techniques with error rates for the discrimination of crust from mantle eclogite-pyroxenite of 7.5 ± 1.9% and 8.2 ± 2.3%, respectively. LR, however, involves fewer stipulations about the distribution of training data (i.e., it is more “robust”) and can return an estimate for probability of classification certainty for single garnets. New data from diamond exploration programs can be readily classified using these new graphical and statistical methods. As the discrimination of low-Cr megacrysts from mantle eclogite-pyroxenite is not the focus of this study, we recommend the method of Schulze (2003) or Grütter et al. (2004) for low-Cr megacryst discrimination to identify megacrysts in the “mantle” suite. Runstreams for our LDA and LR approaches using the freeware “R” are provided for quick implementation.