Multi-sample comparison of detrital age distributions

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. This paper proposes another standard statistical technique called multidimensional scaling (MDS) as an appropriate tool 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. It is shown that 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. To aid in the adoption of the method by the geochronological community, this paper includes some simple code using the statistical programming language R. More extensive software tools are provided on http://mudisc.london-geochron.com.