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

In diamond exploration, the accurate distinction between garnets from the crust or mantle, or from those having a cognate origin with kimberlite (low-Cr megacrysts), is important for the assessment of indicator mineral samples; misclassifications potentially result in costly misdirection of exploration efforts. Existing literature databases and graphical classification schemes for garnets suffer from a paucity of craton-derived, lower-crustal garnets that - as shown here - are among the most difficult to distinguish from garnets of mantle origin. To improve this situation, a large database of new and literature garnet major element analyses has been compiled. Using this dataset, it is shown that the conventionally used Mg# (Mg/(Mg + Fe)) vs. Ca# (Ca/(Mg + Ca)) plot (Schulze, 2003) for discrimination of crust and mantle garnets results in significant overlap (39.2% crustal failure rate using our dataset). We propose a new graphical classification scheme that uses the parameters In(Ti/Si) and In(Mg/Fe) to discriminate low-Cr garnets of crust origin from those of a mantle eclogite-pyroxenite origin with an error rate of 10.1 +/- 2.1% at the 95% confidence level (assessed via K-fold cross-validation with ten random test datasets), significantly lower than existing methods. 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 Grutter 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.