Discriminant Function Analysis of Late Quaternary Tephras from Five Volcanoes in New Zealand Using Glass Shard Major Element Chemistry

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Abstract
The microprobe-determined glass shard major element chemistry of tephras derived from five North Island, New Zealand volcanoes (Mayor Island, Okataina, Taupo, Tongariro, and Mount Egmont) and younger than ca. 20,000 yr B.P. was subjected to discriminant function analysis. Four separate approaches were adopted to test the match of the tephras with their known sources: (1) an analysis of raw microprobe data; (2) an analysis of normalized data; (3) an analysis of the data transformed by calculating the log10 of oxide scores divided (arbitrarily) by the chlorine content; and (4) a repeat of (3) with multivariate outlier scores, as determined by principal components analysis, deleted. All yielded excellent classification functions (efficiencies of 91–100%), with the eruptives associated with each of the five volcanoes being chemically distinct from one another. In each approach, the first two canonical discriminant functions accounted for >90% of the variation between groups. The removal of multivariate outliers from the data set had only minor effects on the performance of the discriminant function procedures. Separate discriminant function analysis of the relatively alike Taupo and Okataina eruptives gave a greater degree of multivariate separation. The numerical classifications generated should enable unidentified tephras erupted since ca. 20,000 yr B.P. from the five volcanoes to be provisionally matched with their sources.