Developing a statistical approach to analyze large paired geo-thermochronological datasets with an application to the Canadian Cordilleras

碎屑矿物激光烧蚀U-Pb定年是物源分析中最常用的方法。该方法允许快速、经济地产生大量的地质年代学数据集，以及在同一碎屑颗粒上应用几种不同的测年方法，如U-Pb、(U-Th)/He和裂变径迹。地质年代学和热年代学方法的结合为理解构造作用、侵蚀、沉积搬运和再循环以及古气候之间的耦合提供了有价值的信息，年龄数据的增加使数据分析和解释变得复杂。几种不同来源信息的组合，特别是使用来自单一谷物的多方法年龄，将数据集扩展了一个或多个维度。多个种源代理的多变量分析是复杂的，主要通过单独分析单个代理来完成。然而，这种方法并没有用尽多方法来源分析的全部潜力，因为它忽略了每个单独谷物的不同信息的初始联系，从而错误地假设不同的信息代表独立变量。该项目的总体目标是开发一种统计程序，用于使用通过多种方法测年分析的大量样本进行定量来源分析。通过应用贝叶斯推理、降维和聚类等现代统计方法，该程序将包括量化样品的不同之处、识别物源端元、量化沉积混合和预测单一方法年龄数据集的物源。为了保证有地质意义的结果，首先必须对多方法数据集进行先验假设。这一步骤将包括数据预处理、偏差和降噪。通过测试两种方法：(I)非负矩阵因式分解和(Ii)应用分层模型进行噪声估计的跨维贝叶斯混合建模，将对多方法测年碎屑样品的成对差异进行数值量化。物源端元和沉积混合将通过探索性数据分析，特别是多维标度和基于密度的聚类来识别和量化。该统计程序将在人工生成的数据集和来自加拿大科迪勒拉的双重和三次测年碎屑上进行测试。新方法可以很容易地应用于其他配对的放射性同位素计时器，如U-Pb和Lu-Hf测年，这为未来的地质和热年代学研究提供了巨大的潜力。此外，它将为定量来源分析提供可靠的结果，这是理解内源和外源过程之间复杂耦合所必需的。

Laser ablation U–Pb dating of detrital minerals is the most common approach in provenance analyses. The method allows producing large geochronological datasets in a fast and cost efficient manner as wells as the application of several different dating methods such as U–Pb, (U–Th)/He, and fission track on the same detrital grain. The combination of geochronological and thermochronological methods provides valuable information for the understanding the coupling between tectonic processes, erosion, sedimentary transport and recycling, and paleo-climate.The increase of age data complicates the data analysis and thus the interpretation. The combination of several different provenance information, in particular the use of multi-method ages from single grains, expands the dataset by one or more dimensions. The multivariate analysis of more than one provenance proxy is complex and mostly done by analyzing the individual proxies separately. This approach, however, does not exhaust the entire potential of multi-method provenance analysis as it ignores the initial linkage of the different information of each individual grain and, thus, erroneously assumes that the different information represent independent variables. The overarching objective of this project is to develop a statistical procedure for quantitative provenance analysis using a large amount of samples analyzed by multi-method dating. By applying modern statistical methods such as Bayesian inference, dimensionality reduction and clustering, the procedure will include quantification of the dissimilarities of the samples, identification of the provenance endmember, quantification of sedimentary mixing, and prediction of provenance of single-method age datasets. In order to guarantee geological meaningful results, a priori assumptions on the multi-method dataset have to be made in the first place. This step will include data pre-processing, bias, and noise reduction. The numeric quantification of the pairwise dissimilarities of multi-method dated detrital sample will be pursued by testing two approaches: (i) non-negative matrix factorization and (ii) trans-dimensional Bayesian mixture modelling applying hierarchical models for noise estimation. Provenance endmember and sedimentary mixing will be identified and quantified by exploratory data analysis, in particular multidimensional scaling and density-based clustering. The statistic procedure will be tested on synthetically generated datasets and double- and triple dated detritus from the Canadian Cordilleras.The new approach can be easily applied to other paired radio-isotopic chronometers, e.g. U–Pb and Lu–Hf dating, which offers a large potential for future geo- and thermochronological studies. Moreover, it will provide robust results for quantitative provenance analysis that are required to understand the complex coupling between endogenous and exogenous processes.