An Introduction to SGTPPR: Sparse Geochemical Tectono-Magmatic Setting Probabilistic MembershiP DiscriminatoR

We present a new and easy-to-use geochemical tectono-magmatic setting discriminator to calculate the probability of membership (the Sparse Geochemical Tectono-magmatic setting Probabilistic membershiP discriminatoR, SGTPPR) that runs in Excel. It outputs the probability of membership for eight different tectono-magmatic settings (mid-ocean ridge, oceanic island, oceanic plateau, continental flood basalt province, intra-oceanic arc, continental arc, island arc, and back-arc basin) for a given volcanic rock sample based on major and selected trace element contents (SiO2, TiO2, Al2O3, Fe2O3, MgO, CaO, K2O, Na2O, Rb, Sr, Y, Zr, Nb, and Ba). We consider all possible ratios and multiplications of these contents, in addition to the contents themselves, which improves the discrimination accuracy. We use a statistical method called sparse multinomial logistic regression to construct a robust and predictive discrimination model. By imposing the sparsity, only a small number of essential variables are included in the model. The variables are objectively extracted from 287 possible geochemical variables, including all possible ratios and multiplications of the major and trace element contents. The constructed model exhibits a high classification ability, indicating that tectonic discrimination using major and selected trace elements yields a high classification ability when ratios and multiplications are considered. The system outputs the relative weights of the variables (i.e., contents, and ratios and multiplications of contents) of the input geochemical data to the calculated membership probabilities. This information can be used to evaluate and interpret the results. We apply the model to multiple samples of a geological unit, to determine the tectonic setting. Plain Language Summary Identifying the source geochemical characteristics of a volcanic rock is essential for understanding magma generation processes and evaluating the tectonic setting of magmatism. We constructed a geochemical discriminator that runs in Excel to characterize volcanic rocks based on their chemical composition. It outputs the probability of membership to eight tectono-magmatic settings based on the input chemical composition of a volcanic rock sample. The analysis can be conducted with major elements and commonly analyzed six trace elements, making it applicable to a wide range of samples from mafic to silicic compositions. We used a statistical method called sparse multinomial logistic regression to construct the discriminator, in which all possible ratios and multiplications of eight major and six trace element contents were considered. This system provides the relative weights of the input variables (major and trace element contents, and their ratios and multiplications) on the final results, making it easy to interpret and discuss the output. The discriminator can also be used to characterize a geological unit and volcanic body based on multiple samples, and determine its tectonic setting of formation.