INTRODUCTION

Igneous rocks form in a wide variety of tectonic settings, including mid-ocean ridges, ocean islands, and volcanic arcs. It is a problem of great interest to igneous petrologists to recover the original tectonic setting of mafic rocks of the past. When the geological setting alone cannot unambiguously resolve this question, the chemical composition of these rocks might contain the answer. The major, minor and trace elemental composition of basalts shows large variations, for example as a function of formation depth (e.g., Kushiro and Kuno, 1963). Traditionally, statistical classification of geochemical data has been done with discrimination diagrams (e.g., Chayes and Velde, 1965; Pearce and Cann, 1971, 1973; Pearce, 1976; Wood, 1980; Shervais, 1982). The decision boundaries of most tectonic discrimination diagrams are drawn by eye (e.g., Pearce and Cann, 1973; Wood, 1980; Shervais, 1982). Although still widely used, these diagrams have some serious problems, including:

• Although (linear) discriminant analysis works in any number of dimensions, visual interpretation is only possible for bi- or trivariate data. By only using two or three geochemical features, a lot of information is not used, resulting in poor performance (large misclassification error).
• The geochemical discrimination diagrams of Pearce and Cann (1971, 1973) and others are often based on collections of the means of many analyses of a certain sample area. This means that, strictly speaking, such diagrams should only be used for the classification of similar data, i.e., not individual samples but means of composites of multiple samples. Moreover, taking the mean of compositional data is a dangerous thing to do, considering the fact that elemental concentrations are subject to a constant-sum constraint, which is generally not taken into account (e.g., Chayes, 1971; Aitchison, 1986; Woronow and Love, 1990).
• Discrimination diagrams do not easily handle samples with missing data, for example if only Ti and not V were measured in the diagram of Shervais (1982).

As an alternative to discriminant analysis which resolves all these issues, this paper suggests classification trees, which are one of the most powerful and popular ``data mining'' techniques (Hastie et al., 2001). One application in which classification trees have been quite successful is email spam filtering (e.g., Hastie et al., 2001; Carreras and Màrquez, 2001). Based on a large training database of predetermined genuine and spam messages, spam filters automatically generate a series of nested yes/no questions that decide which of the two categories (genuine or spam) a new message belongs to. The attributes used in a tree-based spam filter can be the frequencies of certain words or characters as a percentage of the total length of the message, the average length of uninterrupted sequences of capital letters, the total number of capital letters, etc. Spam filtering has many similarities with the problem of tectonic discrimination. In the latter case, the training data will not contain two but three classes (mid-ocean ridge, ocean island and island arc). The attributes used for the classification will be chemical concentrations and isotopic ratios.

Section 2 will give an introduction to the construction of classification trees. As for discrimination diagrams, it is not really necessary for the end-user to know all the details of the building process, because this has to be done only once (hence this paper) after which they are very easy to use; trees in fact easier to use than discrimination diagrams. Therefore, only a brief introduction to the technique will be given, along with the necessary references for the interested reader.

In Section 3, two classification trees will be presented for the discrimination between basalts from mid-ocean ridge (MORB), ocean island (OIB) and island arc (IAB) settings, based on 756 major and trace element measurements and isotopic ratio analyses, compiled from two publicly available petrologic databases. The first tree uses all major, minor and trace elements, and should be used for the classification of unaltered samples of basalt. The second tree only uses immobile elements and can also be used for samples that underwent some degree of weathering and/or metamorphism. Beyond this initial selection of suitable features, the construction of the trees is entirely statistical, and involves no further petrological considerations or arbitrary decision boundaries.

In Section 4, both classification trees will be tested. First, a suite of modern basalts of known tectonic affinity will be classified by trees as well as discrimination diagrams. Then, a published dataset of twenty basalts from the Pindos Basin (Greece) will be classified. This will illustrate the limitations of the tree method and serve as a cautionary note, which is valid for all statistical classification methods.