Comprehensive multidimensional tectonomagmatic discrimination from log-ratio transformed major and trace elements

An initial geochemical database of a total of 26,058 Pliocene to Holocene fresh igneous rock samples, with assigned tectonic settings from combined geoscientific criteria, was established. A comprehensive discrimination scheme was proposed from linear discriminant analysis (LDA) and canonical analysis of log-ratio transformed compositional data. The multi-normality required for the LDA individually for all tectonic classes was achieved independently for isometric log-ratios (ilr) of major elements and of combined major and trace elements through an online computer program DOMuDAF. The importance of the fulfillment of the multi-normality assumption was documented because it increased the overall percent success from about 0.8% to 6%. The multivariate discordant outlier-free data were used for proposing two multidimensional discrimination models (ilrMd and ilrMTd), respectively, based on discordant outlier-free ilr of only major and of combined major and trace elements. The ilrMTd model always provided significantly higher percent success values (70.6–100%) than the ilrMd model (60.8–96.5%) and, therefore, is recommended to be used when applicable. The ilrMTd model should be preferred over the ilrMd model, in case of controversy. The discrimination of a total of 29 tectonic settings, arranged in 3 Super Groups, 9 Main Groups, 17 Groups, 9 subGroups, and 4 sub-subGroups, was successfully achieved in 19 steps through a total of 60 discriminant function equations, 98 centroids and 98 probability calculations for all classes. The usefulness of the comprehensive multidimensional scheme was demonstrated from 13 application cases. The first two cases were applied to the Pliocene to Holocene rocks from a complex tectonic setting of simultaneously ongoing subduction and rifting in the western part of Mexico. The Tepic-Zacoalco Rift was shown to be like a continental rift, whereas the Colima Rift showed Andean-type continental arc at ridge subduction. This was successfully followed by four application cases of Miocene to Neo-proterozoic ophiolites. Five cases of Neo-archean to Paleo-archean rocks were presented, in which consistent tectonic settings were generally obtained from both models. The next case presented the time-dependent tectonic settings of Tibet from the Lower Jurassic to the Pleistocene, which was possible as 7 subcases. The final case presented as 5 subcases showed time- and space-dependent tectonics for two Archean greenstone belts (Babina and Mauranipur) of the Bundelkhand craton, India. The last two time-dependent tectonic setting applications were possible because of the comprehensive nature of the new 19-step tectonic discrimination procedure. In our final application to the Bundelkhand craton, metamorphic and sedimentary (siliciclastic) rocks provided results consistent with those of the igneous rocks. In one of the earlier Archean terrane applications too (Pilbara craton, Australia), metamorphic rocks gave fully consistent results. Similarly, consistent results were obtained for moderate to highly altered Miocene rocks from the Macquarie Island. Therefore, the new comprehensive discrimination scheme can be recommended for use in all future applications for probability-based inferences on tectonic settings from all kinds of igneous, metamorphic and siliciclastic rocks.