| Summary: | The statistically correct handling of compositional data requires log-ratio transformation whereas the multivariate technique of linear discriminant analysis (LDA) assumes a normal distribution of the transformed variables. In addition to other requirements, both these aspects were considered for proposing five new discriminant function diagrams based on log-ratios of five high-field strength elements � (TiO2)adj, Nb, V, Y, and Zr. A representative world database of 1877 analyses of basic and ultrabasic magmas from four tectonic settings of island arc, continental rift, ocean-island, and mid-ocean ridge, was used. After identifying discordant outliers in log-transformed ratios using single outlier tests, 1793 analyses proved to be normally distributed in terms of the following four variables: ln(Nb/(TiO2)adj), ln(V/(TiO2)adj), ln(Y/(TiO2)adj), and ln(Zr/(TiO2)adj). Use of LDA of the complete dataset of 1877 analyses divided into 1477 analyses for training set and 400 for testing set provided high success rates of 78.5�92.2% and 81.7�93.0% for the discrimination of the four tectonic settings based on the training and testing sets, respectively. However, using LDA of the normally distributed 1793 analyses divided into 1393 for training set and 400 for testing set, we obtained new diagrams that showed still higher success rates of 80.2�93.5% and 84.0�94.0%, respectively. The advantage of fulfilling the requirement of normal distributions of log-ratio variables resides in the observation that an overall net gain in success rates of 0.5�3.3% was achieved when the LDA was correctly applied to discordant-outlier-free log-transformed ratios (1793 analyses) than to the complete data set (1877 analyses). The application of these discrimination diagrams to ophiolites from Taitao Peninsula (southern Chile), Gabal Gerf complex (northeastern Africa), Jormua (northeastern Finland) and Macquarie Island (southwest Pacific) indicated tectonic setting of mid-ocean ridge, transitional between island arc and mid-ocean ridge, ...
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