Recovering the tectonic affinity of ancient ophiolites is a problem of
great scientific interest. In addition to field data, basalt
geochemistry is another way to address this problem. Tectonic
discrimination diagrams have been a popular technique for doing this
since the publication of landmark papers by Pearce and Cann (1971,
1973). This paper revisits some of the popular discrimination diagrams
that have been in use since then. Nearly all discrimination diagrams
that are currently in use were drawn by eye. The present paper
revisits these diagrams in a statistically more rigorous way.
First, a short introduction will be given to the discriminant analysis
method. The fundamental difference between the reduction in
dimensionality achieved by principal components and by linear
discriminant analysis will be explained. Then, the consequences of
the constant-sum constraint of geochemical data for discriminant
analysis will be discussed. In Section 4,
Aitchison's (1982, 1986) solution to this problem will be briefly
explained. Section 5 revisits some of the
historically most important and popular discrimination diagrams, based
on a new database of oceanic basalts of known tectonic affinity. The
effect of data-closure will be taken into account and a statistically
rigorous re-evaluation of these diagrams will be made in both the
linear and the quadratic case.
This paper does not restrict itself to only those geochemical features that have already been used by previous workers. Section 6 gives an exhaustive exploration of all possible bivariate and ternary discrimination diagrams using a set of 45 major, minor, and trace elements. This will result in a list of the 100 best linear and quadratic ternary discriminators, ranked according to their success in classifying the training data. Finally, Section 7 tests the most important discrimination diagrams discussed elsewhere in the paper on a second database of oceanic basalts that were not part of the training data. This provides a more objective estimator of misclassification risk on future data than the misclassification rate of the training data. Section 7 also contains a formal comparison of the new decision boundaries with the old ones of Pearce and Cann (1973), Shervais (1982), Meschede (1986) and Wood (1980). It will be shown that the new decision boundaries perform at least as well as the old ones.