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

Abstract

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.