Discriminant function analysis and correlation of Late Quaternary rhyolitic tephra deposits from Taupo and Okataina volcanoes, New Zealand, using glass shard major element composition

Abstract

Discriminant function analysis (DFA) is a multivariate statistical technique that provides a non-subjective means of correlating tephra deposits based on compositional or other variable characteristics. Using microprobe-determined glass shard major element composition, two DFA classification models were developed to separate (distinguish) individual tephra deposits erupted since ca. 22 ka from each of the rhyolitic Okataina and Taupo volcanoes, North Island, New Zealand. In an iterative approach, those tephras easily classified in the first DFA are removed from the dataset before applying the second DFA, hence generally improving the separation of the remaining tephras that are more closely alike. The first two canonical functions accounted for ca. 85% of variance within the Okataina dataset, and ca. 80% within the Taupo dataset. Using the first two canonical variates, we correctly classified 5 (Kaharoa, Rotoma, Waiohau, Rotorua, Te Rere) of the Okataina, and 4 (Taupo, Hatepe, Whakaipo, Karapiti) of the Taupo deposits under study, at efficiency levels of 70–100%. The incorporation of a third canonical variate, and additional sompositional data, would further improve our DFA models, which should ideally be used in conjunction with stratigraphic and other characteristic indices, where available, to facilitate accurate correlation. The Mahalanobis distance statistic (D²), a statistical measure of the multidimensional spacing of individual analyses, or groups of analyses, provides a better measure of likeness than the frequently used but subjective similarity coefficients technique.