MULTIDIMENSIONAL SCALING ANALYSIS OF DETRITAL AGE DISTRIBUTIONS AND COMPOSITIONS

The petrography and geochronology of detrital minerals form rich archives of information pertaining to the provenance of siliclastic sediments. The composition and age spectra of multi-sample datasets can be used to trace the flow of sediments through modern and ancient sediment routing systems. Such studies often involve dozens of samples comprising thousands of measurements. Objective interpretation of such large datasets can be challenging and greatly benefits from dimension-reducing exploratory data analysis tools.

Principal Components Analysis (PCA) is a proven method that has been widely used in the context of compositional data analysis and traditional heavy mineral studies. Unfortunately, PCA cannot be readily applied to geochronological data, which are rapidly overtaking petrographic techniques as the method of choice for large scale provenance studies. Multidimensional Scaling (MDS) is a standard statistical tool ideally suited to fill this void.

MDS is a robust and flexible superset of PCA which makes fewer assumptions about the data. Given a table of pairwise ‘dissimilarities’ between samples, MDS produces a ‘map’ of points on which ‘similar’ samples cluster closely together, and ‘dissimilar’ samples plot far apart. The statistical effect size of the Kolmogorov-Smirnov test is a viable dissimilarity measure. This is not the case for the p-values of this and other tests.

A number of case studies in southern Africa, China and elsewhere convincingly show that MDS can effectively unravel subtle but meaningful variations in the detrital age spectra and heavy mineral compositions of silicliclastic sediments. Thus, MDS represents a simple yet powerful new tool to distill geologically meaningful information from large, complex datasets of multivariate data.

Further information and supporting software can be found on http://mudisc.london-geochron.com.