New tectonic discrimination diagrams for basic and ultrabasic volcanic rocks through log-transformed ratios of high field strength elements and implications for petrogenetic processes

  • Surendra P. Verma Departamento de Sistemas Energéticos, Centro de Investigación en Energía, Universidad Nacional Autónoma de México, 62580, Temixco, Mor., México.
  • Salil Agrawal Department of Geology, University of Rajasthan, Jaipur 3002 004, India.
Keywords: discordant outliers, normal sample, tectonic setting, log-transformation, adjusted major- elements, ophiolites, Archean, Turkey, Sweden.


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, mid-ocean ridge and continental rift, respectively. Although only a few rock samples from a study of south-central Sweden could be identified as mafic, the present diagrams indicated an arc setting for this area. The application to three case studies from Turkey, being a country with highly complex geological history, suggested continental rift setting for Kula Quaternary basic volcanic rocks, inconclusive evidence for Jurassic volcanic rocks from eastern Pontides, arc setting for Tauride belt ophiolite, and continental rift setting for East Anatolian and Dead Sea fault zones, the latter application being based on probability calculations for each sample without any need to plot the samples in the discrimination diagrams. The use of normal discordant outlier-free samples of log-transformed ratios from each area in our new discrimination diagrams reinforced these conclusions for all areas, providing somewhat better discrimination in those cases in which such discordant observations were observed. We suggest that the new diagrams be used for tectonic discrimination of basic and ultrabasic rock samples that are confirmed to have discordant outlier-free normally distributed log-transformed variables. Basic and ultrabasic character of the rock samples could be determined from computer program SINCLAS and the discordant outliers of log- transformed variables identified from DODESSYS, whereas the use of new diagrams proposed during 2004-2011 would be facilitated from program TecD.