Pairwise sample comparisons and multidimensional scaling of detrital zircon ages with examples from the North American platform, basin, and passive margin settings

Over the past several decades, the development of highly efficient and low-cost techniques for the acquisition of U-Pb ages has led to the rapid expansion of detrital zircon analysis and interpretation. Multidimensional scaling (MDS) is a potentially powerful approach for visualizing and interpreting such age data. This study suggests that for any study applying MDS to detrital zircons: (1) the choice of representing age distributions as either probability density plots or kernel density estimations offers no particular advantage when subjected to many inter-sample comparison measures of grain ages; (2) among the various approaches for such sample pairwise comparisons, likeness, similarity, the Kuiper test statistic, and the Sircombe-Hazelton metric are more effective than the Kolmogorov-Smirnov test statistic or the cross-correlation coefficient; (3) variable proportions of both shared and unique age components have significant effects on MDS mapping; and (4) three-dimensional MDS projections are often superior to the two-dimensional projections commonly used in detrital provenance studies. We demonstrate these findings by representing age distributions of samples from platform, basin, and passive margin settings of North America as colored surfaces defined on the basis of sample depositional age, geographic position, and importance of different detrital zircon components, and then compare these with three-dimensional MDS maps. These approaches suggest that the application of MDS techniques to detrital zircon data affords easily attainable and significant advantages in the geologic interpretation of detrital grain ages.