Two‐Dimensional Quantitative Comparison of Density Distributions in Detrital Geochronology and Geochemistry

Abstract

Detrital geochronology provides insight into a broad range of Earth Science questions. However, detrital zircon U‐Pb age distributions are inherently univariate, and thus quantitative comparison methods are limited to one‐dimension (1D) and subject to nonunique results due to overlapping age groups. We developed two‐dimensional (2D) quantitative comparison measures for bivariate kernel density estimates (KDEs) and cumulative distribution functions (CDFs). These methods are extensions of 1D quantitative comparison measures commonly used in detrital geochronology: Similarity, Likeness, and Cross‐correlation of KDEs and Kolmogorov‐Smirnov (K‐S) and Kuiper tests of CDFs. We demonstrate the efficacy of these methods by applying them to a global compilation of detrital and igneous zircon univariate U‐Pb data (n = 767,660) and bivariate U‐Pb and Hf (i.e., εHfT) data (n = 114,311) parsed geographically into eight continental landmasses demarcated by Paleozoic sutures. The 2D quantitative comparison measures behave in a similar fashion to their 1D counterparts in terms of sensitivity and consistency regardless of parameterization (e.g., kernel bandwidth and discretization interval). Results show that the detrital record reliably reflects the igneous record for both univariate U‐Pb and bivariate εHfT distributions between 4,400 and 0 Ma. In contrast, 1D and 2D quantitative comparison results differ over the narrower Ediacaran‐Cambrian time interval due to nonunique univariate zircon U‐Pb age groups; the 2D quantitative results consistently identify continental landmasses involved in the formation of Gondwana. We implemented the 2D methods in a new MATLAB‐based graphical user interface, DZstats2D, which is available as open‐source code and as standalone applications for macOS and Windows.

Short Communication: The Wasserstein distance as a dissimilarity metric for comparing detrital age spectra, and other geological distributions

“…As a result, some form of the Wasserstein distance could prove useful for analysing a number of other geological datasets such as the geochemical compositions of detrital minerals, or joint U-Pb and Lu-Hf isotope analysis. Statistics for comparing distributional data in multiple dimensions are increasingly needed (Sundell and Saylor 2021).…”

Continental shelves as detrital mixers: U–Pb and Lu–Hf detrital zircon provenance of the Pleistocene–Holocene Bering Sea and its margins

“…Bivariate mixing calculations, which implement both U–Pb ages and Lu–Hf compositions of individual detrital zircon grains, can specify mixtures in two dimensions making it a useful application toward refining provenance interpretations in settings where U–Pb ages may be non‐unique (Saylor & Sundell, 2021; Sundell & Saylor, 2021). In aggregate, the Bering Sea basin samples are juvenile to moderately evolved except for a substantial proportion of ca 100 Ma grains which are more highly evolved (Figure 4B).…”

Reorganization of continent‐scale sediment routing based on detrital zircon and rutile multi‐proxy analysis

“…However, MDS using univariate data, i.e., using U-Pb ages alone, where several potential sources are broadly coeval, is unlikely to provide a sophisticated sediment routing model. Bivariate statistical comparison integrating U-Pb and Lu-Hf data of detrital zircon may be a more robust tool (Sundell & Saylor, 2021) to understand the sediment routing system on a basin-wide scale. MDS using bivariate data of potential intermediate sources (Figure 10b) suggest, analogous to univariate MDS results, high similarity to the glaciogenic sediments of the lower Permian Grant Group located in the northern part of the basin.…”