Statistical Evaluation of Bivariate, Ternary and Discriminant Function Tectonomagmatic Discrimination Diagrams


Abstract: This work applies a statistical methodology involving the calculation of success rates to evaluate a total of 28 tectonomagmatic discrimination diagrams: four bivariate (Ti/Y-Zr/Y; Zr-Zr/Y; Ti/1000-V; and Nb/Y-Ti/Y); six ternary (Zr-3Y-Ti/1000; MgO-Al2O3-FeOt, Th-Ta-Hf/3; 10MnO-15P2O5-TiO2; Zr/4-Y-2Nb; and La/10-Nb/8-Y/15); and three old (Score1-Score2; F1-F2; and F2-F3) and three sets of new discriminant function diagrams (each set consisting of five DF1-DF2 type diagrams proposed during 2004-2008). I established and used extensive geochemical databases of Miocene to Recent fresh rocks from island arcs, back arcs, continental rifts, ocean-islands, and mid-ocean ridges. Rock and magma types were inferred from a SINCLAS computer program. Although some of the existing bivariate and ternary diagrams did provide some useful information, none was found to be totally satisfactory, because success rates for pure individual tectonic settings typically varied from very low (1.1-41.6%) to only moderately high values (63.6-78.1%) and seldom exceeded them. Additionally, only "combined" tectonic settings were discriminated, or numerous samples plotted in overlap regions designated for two or more tectonic settings or even in areas outside any field. Furthermore, these old diagrams are generally characterized by erroneous statistical basis of closure problems or constant sum constraints in compositional data and by subjective boundaries drawn by eye. All such diagrams, therefore, should be abandoned and replaced by the new sets of discriminant function diagrams proposed during 2004-2010. These diagrams, especially those of 2006-2010 based on the correct statistical methodology and the boundaries drawn from probabilities, showed very high success rates (mostly between 83.4% and 99.2%) for basic and ultrabasic rocks from four tectonic settings and should consequently be adopted as the best sets of tectonomagmatic discrimination diagrams at present available for this purpose. Three case studies from Turkey (Kula, Eastern Pontides, and Lycian-Tauride) were also provided to illustrate the use of two new sets of discriminant function diagrams (2006-2008). For the Kula area, both sets of major- and trace-element based diagrams provided results consistent with a rift setting. For the Pontides area, trace-element based diagrams suggested an arc setting to be more likely, according to both basic and intermediate rocks. For the Lycian ophiolites, however, only the major-element based set of diagrams could be applied, and because of alteration effects, the tectonic inference between an arc or a MORB setting could not be decisive. A newer set of immobile element based, highly successful diagrams currently under preparation (2010) should provide a complementary set to the existing diagrams (2006-2008) for a better application of this important geochemical tool. Further work on these lines is still necessary to propose discrimination diagrams for other types of magmas such as those of intermediate silica compositions.

Keywords: volcanic rocks, basalts, geochemistry, igneous rocks, mathematical geology

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