Discrimination among tectonic settings using trace element abundances of basalts

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Abstract
A wealth of chemical information may provide a false sense of security to the petrologist interested in extracting petrogenetic information from a set of major and/or trace element abundances. Such data are said to be closed, as each analysis sums to a constant (100%). Failure to sum to a constant results from a combination of errors of commission and omission. A correlation coefficient between a pair of closed components has a contribution from the linear association between the components and a contribution from the effects of closure itself. Standard statistical procedures cannot separate these two sources; therefore, the investigator cannot tell if a strong correlation (as revealed by a nearly linear trend on a binary scatter diagram, for example, is due to a strong linear association between the components or due to closure. Techniques developed by Aitchison (1984a, b) appear to be capable of providing a framework within which the user can begin to assess the relationship among closed components. These techniques are applied to a set of 35 TiO2, Zr, Y, and Sr analyses of basalts. A statistical analysis permits rejection of Aitchison's (1984a, b) hypothesis of complete subcompositional independence, indicating that there is a degree of dependency within the data set. The first two principal components extracted from the covariance matrix of the log‐centered form of these data account for more than 90% of the total variation, and three major tectonic‐related fields can be clearly recognized in the space defined by the first two principal components: ocean floor basalts, within‐plate basalts and arc‐related basalts. Analyses from six additional data sets taken from the literature were plotted on this diagram, and all reclaim the tectonic settings stated in the literature. Simple modeling reveals that the addition or subtraction of Sr from an analysis results in a linear locus of points which is parallel to the boundary between the ocean floor and the within‐plate basalts, suggesting that such a diagram may prove useful in the analysis of basalts that have been subjected to low‐ to moderate‐grade metamorphism/metasomatism.