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.

中文翻译：

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碎屑年代学和地球化学中密度分布的二维定量比较

碎屑年代学提供了对广泛的地球科学问题的见识。但是，碎屑锆石的U-Pb年龄分布固有地是单变量的，因此，定量比较方法仅限于一维（1D），并且由于年龄组重叠而受到非唯一结果的影响。我们针对双变量核密度估计（KDE）和累积分布函数（CDF）开发了二维（2D）定量比较方法。这些方法是碎屑年代学中常用的一维定量比较方法的扩展：KDE的相似性，相似性和互相关性以及CDF的Kolmogorov-Smirnov（KS）和Kuiper检验。我们通过将这些方法应用于碎屑和火成锆石单变量U-Pb数据的整体汇编（n = 767,660）以及双变量U‐Pb和Hf（即εHfT）数据（n = 114,311）在地理上解析为由古生代缝合线划定的八个大陆陆块。无论参数化（例如内核带宽和离散化间隔）如何，在灵敏度和一致性方面，二维定量比较度量的行为均与其一维相似。结果表明，碎屑记录可靠地反映了4,400和0 Ma之间的单变量U-Pb和双变量εHfT分布的火成记录。相比之下，由于非唯一单变量锆石U-Pb年龄组，一维和二维定量比较结果在更窄的Ediacaran-Cambrian时间间隔内有所不同。2D定量结果一致地确定了与冈瓦纳形成有关的大陆陆块。我们在基于MATLAB的新图形用户界面中实现了2D方法，DZstats2D，可以作为开源代码使用，也可以作为macOS和Windows的独立应用程序使用。