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

碎屑矿物的激光烧蚀U-Pb测年是物源分析中最常用的方法。该方法可以快速、低成本地生成大型地质年代学数据集，还可以应用多种不同的测年方法，如U-Pb、(U-Th)/He和同一碎屑颗粒上的裂变径迹。地质年代法和热年代法的结合为认识构造过程、侵蚀、沉积搬运和再循环与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。几种不同的物源信息的组合，特别是使用单一颗粒的多方法年龄，将数据集扩展了一个或多个维度。多个来源代理的多变量分析是复杂的，大多是通过单独分析单个代理完成的。然而，这种方法并没有穷尽多方法来源分析的全部潜力，因为它忽略了每个单个谷物的不同信息的初始联系，因此，错误地假设不同信息代表独立变量。该项目的总体目标是开发一种统计程序，用于使用多方法测年分析的大量样品进行定量来源分析。通过应用贝叶斯推理、降维和聚类等现代统计方法，该过程将包括样品差异的量化、物源端元的识别、沉积混合的量化以及单一方法年龄数据集的物源预测。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。这一步将包括数据预处理、偏置和降噪。将通过测试两种方法来对多方法年代碎片样本的两两差异进行数值量化：(i)非负矩阵分解和（ii）应用分层模型进行噪声估计的跨维贝叶斯混合建模。通过探索性数据分析，特别是多维尺度和基于密度的聚类，将识别和量化物源、端元和沉积混合。统计程序将在综合生成的数据集和来自加拿大科迪勒拉斯的双重和三重日期的碎屑上进行测试。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，例如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，这需要了解内源性和外源性过程之间的复杂耦合。

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.