USE OF PRINCIPAL COMPONENTS-ANALYSIS IN PETROLOGY - AN EXAMPLE FROM THE MARTINSVILLE IGNEOUS COMPLEX, VIRGINIA, USA

The Martinsville igneous complex is located in the Smith River allocht hon, within the Piedmont of southwestern Virginia, U.S.A. This Ordovic ian complex consists of two main plutonic units: the mafic Rich Acres suite and the Leatherwood Granite. Four lithologic phases can be recog nized in the Rich Acres and two are present in the Leatherwood. Major- and trace-element analyses from these six phases have been examined by principal components analyses (PCA); the first two principal componen ts account for 86.9 percent of the total variance in the database, as opposed to about 35 percent for the first two original variables. Exam ination of variable loadings and sample scores for these two principal components has led to a number of observations about which original c hemical variables best characterize the database. Mixing lines, contro l lines, and the ''lever rule'' can be used on bivariate PC plots as t hey can on bivariate plots of original chemical variables. Results of the PCA coupled with field and petrographic relationships allow for so me hypotheses to be posed concerning petrogenetic relationships among the lithologic units. Among these hypotheses are 1) some type of mixin g process occurred between the Leatherwood and Rich Acres; 2) the Lith ologic phases within the Rich Acres form one cogenetic suite, and 3) t he Rich Acres and Leatherwood apparently are not comagmatic, in contra st to earlier suggestions. PCA can also be used to place constraints o n different crystal-fractionation models. Results for PCA are compared with those for discriminant function analysis (DFA); PCA indicates a compositional continuum between most groups, whereas DFA shows large c ompositional gaps. The results for PCA seem to be closer to the true s ituation.