DISCRIMINATION BETWEEN LATE-OROGENIC, POSTOROGENIC, AND ANOROGENIC GRANITES BY MAJOR-ELEMENT COMPOSITIONS

Multivariate discriminant analysis of four varieties of granites, classified a priori exclusively on field observations, provide assignment rules that, using major element compositions alone, successfully distinguish late-orogenic (LO) from post-orogenic (PO) granites related to orogeny as well as the anorogenic granites in the anorthosite/rapakivi complexes (AR) and the alkaline ring complexes (RC). Choice of major elements as good group predictors is based on a stepwise selection method with reduction of Wilk's Lambda as the selection criterion. In two-group (P and Q) discriminant analysis of the orogenic versus anorogenic, LO versus PO, and AR versus RC pairs of groups, the former in each pair has been considered as group (P). A sample is assigned to (P) when its discriminant rule, R, obtained from R = (D-i - C-i)\/\(M(i) - C-i), is a positive quantity; otherwise it is assigned to group (Q). Here D-i denotes the discriminant score of the sample, M(i) is the mean score of group (P), C-i is the cut-off value, and i = 1, 2, and 3 for the orogenic versus anorogenic, LO versus PO, and AR versus RC pairs of groups, respectively. For the orogenic versus anorogenic group, D-1 = (0.929241 Fe2O3 - 2.570311 MgO + 1.246346 Na2O + 1.266569 K2O - 11.75422), M(1) = -0.4898, and C-1 = 0.2915. For LO versus PO granites, D-2 = \-0.889609 Al2O3 + 0.777671 Fe2O3 + 2.03159 Na2O + 1.787924 K2O - 5.102003), M(2) = -1.2974, and C-2 = -0.2317, and for AR versus RC granites, D-3 (-2.820296 MgO + 1.980987 Na2O - 6.561133), M(3) = -1.1354 and C-3 = -0.0516. An unbiased estimate of misclassification obtained with the ''Jackknife'' technique permits objective classification of ''unknown'' samples, which preferably should be biotite granites with simple mineralogy.