The Use of Multi-Component Statistical Techniques in Understanding Subduction Zone Arc Granitic Geochemical Data Sets

Abstract:

Multi-component statistical techniques and GIS visualization are emerging trends in understanding large data sets. Our research applies these techniques to a large igneous geochemical data set from southern California to better understand magmatic and plate tectonic processes. A set of 480 granitic samples collected by Baird from this area were analyzed for 39 geochemical elements. Of these samples, 287 are from the Peninsular Ranges Batholith (PRB) and 164 from part of the Transverse Ranges (TR).

Principal component analysis (PCA) summarized the 39 variables into 3 principal components (PC) by matrix multiplication and for the PRB  are interpreted as follows: PC1 with about 30% of the variation included mainly compatible elements and SiO₂ and indicates extent of differentation;  PC2 with about 20% of the variation included HFS elements and may indicate crustal contamination as usually identified by Sr_i; PC3 with about 20% of the variation included mainly HRE elements and may indicate magma source depth as often diplayed using REE spider diagrams and possibly Sr/Y. Several elements did not fit well in any of the three components: Cr, Ni, U, and Na₂O.

For the PRB, the PC1 correlation with SiO₂ was r=-0.85, the PC2 correlation with Sr_i was r=0.80, and the PC3 correlation with Gd/Yb was r=-0.76 and with Sr/Y was r=-0.66 . Extending this method to the TR, correlations were r=-0.85, -0.21, -0.06, and -0.64, respectively. A similar extent of correlation for both areas was visually evident using GIS interpolation.

PC1 seems to do well at indicating differentiation index for both the PRB and TR and  correlates very well with SiO₂, Al₂O₃,  MgO, FeO*, CaO,  K₂O, Sc, V, and Co, but poorly with Na₂O and Cr. If the crustal component is represented  by Sr_i, PC2 correlates well and less expesively with this indicator in the PRB, but not in the TR. Source depth has been related to the slope on REE spidergrams, and PC3 based on only the HREE and using the Sr/Y ratios gives a reasonable correlation for both PRB and TR, but the Gd/Yb ratio gives a reasonable correlation for only the PRB.

The PRB data provide reasonable correlation between principal components and standard geochemical indicators, perhaps because of the well-recognized monotonic variation from SW to NE. Data sets from the TR give similar results in some cases, but poor correlation in others.