Tectonic discrimination of basalts with classification trees

manuscript accepted for publication in Geochimica et Cosmochimica Acta

Pieter Vermeesch

Department of Geological and Environmental Sciences, Stanford University

Currently at Institute of Isotope Geology and Mineral Resources, ETH Zürich, Switzerland

Abstract:

Traditionally, geochemical classification of basaltic rocks of unknown tectonic affinity has been performed by discrimination diagrams. Although easy to use, this method is fairly inaccurate because it only uses bi- or trivariate data. Furthermore, many popular discrimination diagrams are statistically not very rigorous because the decision boundaries are drawn by eye, and they ignore closure, thus violating the rules of compositional data analysis. Classification trees approximate the data space by a stepwise constant function, and are a more rigorous and potentially more effective way to determine tectonic affinity. Trees allow the simultaneous use of an unlimited number of geochemical features, while still permitting visualization by an easy-to-use, two-dimensional graph. Two classification trees are presented for the discrimination of basalts of mid-ocean ridge (MORB), ocean island (OIB) and island arc (IAB) affinities. The first tree uses 51 major, minor and trace elements and isotopic ratios and should be used for the classification of fresh basalt samples. A second tree only uses high field strength (HFS) element analyses and isotopic ratios, and can also be used for basalts that have undergone alteration. The probability of successful classification is 89% for the first and 84% for the second tree, as determined by ten-fold cross-validation. Even though the trees presented in this paper use many geochemical features, it is not a problem if some of these are missing in the unknown sample. Classification trees solve this problem with surrogate variables, which give more or less the same decision as the primary variables. The advantages of the classification tree approach over discrimination diagrams are illustrated by a comparative test on a sample dataset of known tectonic affinities. Although arguably better than discrimination diagrams, classification trees are not perfect, and the limitations of the method are illustrated on a published dataset of basalts from the Pindos Basin (Greece).