碎屑锆石
  <strong>U-Pb</strong>年代学数据获取、分析与比较

doi:10.11867/j.issn.1001-8166.2020.030

地球科学进展 ›› 2020, Vol. 35 ›› Issue (4): 414 -430. doi: 10.11867/j.issn.1001-8166.2020.030

碎屑锆石 U-Pb年代学数据获取、分析与比较

张凌 ¹(

),王平 ^2, ³(

),陈玺赟 ²,殷勇 ¹

^1.南京大学地理与海洋科学学院，江苏南京 210023
^2.南京师范大学地理科学学院，江苏南京 210023
^3.江苏省地理信息资源开发与利用协同创新中心，江苏南京 210023

收稿日期:2020-01-30 修回日期:2020-03-03 出版日期:2020-04-10
通讯作者: 王平 E-mail:tigerwp@njnu.edu.cn
基金资助:
国家自然科学基金面上项目“古金沙江南流寻踪——青藏高原东南缘古近纪盆地的沉积纪录”(41572154)

Review in Detrital Zircon U-Pb Geochronology: Data Acquisition, Analysis and Comparison

Ling Zhang ¹( ),Ping Wang ^2, ³( ),Xiyun Chen ²,Yong Yin ¹

^1.School of Geographic and Oceanographic Sciences, Nanjing University, Nanjing 210023，China
^2.School of Geographical Sciences, Nanjing Normal University, Nanjing 210023，China
^3.Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023，China

Received:2020-01-30 Revised:2020-03-03 Online:2020-04-10 Published:2020-05-08
Contact: Ping Wang E-mail:tigerwp@njnu.edu.cn
About author:Zhang Ling （1993-）， male， Yancheng City, Jiangsu Province， Master student. Research areas include U-Pb dating provenance of detrital zircons. E-mail: 35515594@qq.com
Supported by:
the National Natural Science Foundation of China “Tracing the southward-flowing paleo-Jinsha River—Sedimentary records from the Paleogene basins along the southeastern margin of Tibetan Platea”(41572154)

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碎屑锆石U-Pb年代学是探寻沉积物物源的重要手段，在沉积学、大地构造学和地貌学等领域应用广泛。从数据获取、分析和比较3个方面综述了碎屑锆石U-Pb年代学研究的最新进展。在数据获取方面，从基本原理出发阐述了样品制备方法、同位素年龄数据选取和测试数量问题；在数据分析方面，对比了概率密度图、核密度估计图和累积年龄分布图的数据可视化方法；在数据比较方面，结合实例分析了定量比较的基本算法和应用优势，包括基于非参数性假设检验（K-S检验）、年龄谱对比（互相关系数）和多维定标法的相似（差异）性量化分析等。最后介绍了3款常用软件，并在数据获取、分析与比较方面分别给出了建议，供以后的研究者参考。

关键词: 碎屑锆石, U-Pb年代学, 数据获取, 可视化方法, 定量比较

The U-Pb chronology of detritus zircon is an important method to explore sediment provenance, which is widely used in sedimentology, geotectonics, geomorphology and other fields. This paper reviewed the recent progress of the U-Pb chronology of detrital zircon from three aspects: data acquisition, analysis and comparison. In terms of data acquisition, the sample preparation method, isotope age data selection and test quantity were expounded from the basic principle; In terms of data analysis, the data visualization methods of Probability Density Plot (PDP), Kernel Density Estimate (KDE) and Cumulative Age Distribution (CAD) were compared; In terms of data comparison, the basic algorithm and application advantages of quantitative comparison were analyzed with examples, including (dis)similarity measures based on non-parametric hypothesis tests (K-S test), (dis)similarity measures based on age spectrum comparison (Cross-correlation coefficients) and (dis)similarity measures based on Multi-Dimensional Scali (MDS). Finally, three commonly used software tools were introduced. Suggestions were given in terms of data acquisition, analysis and comparison for future research.

Key words: Detrital zircon, U-Pb chronology, Data acquisition, Visualized analysis, Quantitative comparison

中图分类号:

P597.3

图1 3种不同的锆石U-Pb年代获取方法示意图（据参考文献[20]修改）
(a）同位素稀释—热电离质谱法;(b) 二次离子探针法; (c) 激光剥蚀—等离子质谱

Fig.1 Schematic diagram of three U-Pb dating methods for zircon(modified after reference[20])
（a）Isotope Dilutionthermal Ionization Mass Spectrometry（ID-TIMS）；（b）Secondary Ion Mass Spectrometry（SIMS）；（c）Laser Ablation-inductively Coupled Plasma-Mass Spectrometry（LA-ICPMS）

图2 河流沉积物样品采用颗粒自然沉降（靶1）与手工随机挑选（靶2）制靶结果对比
粒径由ImageJ图像分析并计算等效粒径得到，直方图分别代表了2个靶的碎屑锆石U-Pb年龄的分布，在靶1中获得了5颗小于50 Ma的锆石年龄组分且粒径较小（54~75 μm），而在靶2中仅获得了1颗小于50 Ma的锆石年龄且粒径较大（约为90 μm）

Fig.2 River sediment samples were compared by natural particle sedimentation (target 1) and by manual random selection (target 2)
The particle size was obtained by analyzing the ImageJ image and calculating the equivalent particle size. The histogram represents the distribution of U-Pb ages of detrital zircons of the two targets. Five zircons of <50 Ma were obtained from target 1 with small size (54~75 μm), while only one zircon of <50 Ma was obtained from target 2 with large size (about 90 μm)

图3 ²⁰⁶Pb/²³⁸U，²⁰⁷Pb/²³⁵U年龄比值计算得到的U-Pb协和图
数据点的测试误差1σ（95%置信区间）或者2σ（68%置信区间）以椭圆的形式表示；平行x轴方向代表了 ²⁰⁷Pb/ ²³⁵U的年龄误差，平行y轴方向代表了 ²⁰⁶Pb/ ²³⁸U的误差，短轴方向代表了 ²⁰⁶Pb/ ²⁰⁷Pb的年龄误差

Fig.3 The U-Pb concordia diagram obtained from the age ratios of ²⁰⁶Pb/²³⁸U,²⁰⁷Pb/²³⁵U
The test error of 1 (95% confidence interval) or 2 (68% confidence interval) in the form of ellipses. The parallel x axis represents the age error of ²⁰⁷Pb/ ²³⁵U, the parallel y axis represents the error of ²⁰⁶Pb/ ²³⁸U, and the short axis represents the age error of ²⁰⁶Pb/ ²⁰⁷Pb

图4 5 200个锆石样品的U-Pb分析获得的²⁰⁶Pb/²³⁸U年龄和²⁰⁶Pb/²⁰⁷Pb年龄结果
展示了不同的年龄结果与其测试误差（1σ）的对应关系，明显看出在年龄较小（如小于1 000 Ma）的情况下， ²⁰⁶Pb/ ²³⁸U年龄的测试误差较小，而在年龄较大（大于1 200 Ma）的情况下， ²⁰⁶Pb/ ²⁰⁷Pb年龄的测试误差较小(据参考文献[27]修改)

Fig.4 U-Pb analysis of 5 200 zircon samples yielded ²⁰⁶Pb/²³⁸U and ²⁰⁶Pb/²⁰⁷Pb ages
Figure shows the corresponding relationship between the results of different ages and the test error (1σ). It is obvious that the test error of ²⁰⁶Pb/ ²³⁸U age is smaller when the age is younger (such as less than 1 000 Ma), while the test error of ²⁰⁶Pb/ ²⁰⁷Pb age is smaller when the age is older (more than 1 200 Ma)（modified after reference[27]）

图5 碎屑锆石测试数量（k）与某一年龄组分被检测失败的概率（p）之间的关系
m代表样品中包含的年龄组分数， f为某一年龄组分的占比（ f=1/ m）;交点A表示只测试60颗锆石，年龄组分检测失败的概率高达64%，交点B表示测试117颗锆石，年龄组分检测失败的概率可以降至5%（据参考文献[29]修改）

Fig.5 The relationship between the number of detrital zircons tested (k) and the probability of failure of a given age group (p)
m represents the number of age groups contained in the sample, and f represents the proportion of a certain age group ( f=1/ m). Intersection A means that only 60 zircons have been tested, and the probability of failure in age component detection is as high as 64%. Intersection B means 117 zircons have been tested, and the probability of failure in age component detection can be reduced to 5%（modified after reference[29]）

图6 碎屑锆石U-Pb 年代学数据可视化示例（以长江口崇明岛为例^[44]）
(a)概率密度图；(b)核密度估计图；(c)累积年龄分布图

Fig.6 An example of the age distribution of detrital zircons (a case study of Chongming Island in the Changjiang Estuary^[44])
(a) Probability Density Plot (PDP);(b) Kernal Density Estimate (KDE);(c) Cumulative Age Distributions (CAD)

图7 虚拟碎屑锆石样品相似（差异）性量化分析结果
(a) 用于计算的两个虚拟样品的PDP，分别具有5个年龄组分，每个不确定度为10%；(b) 基于CAD图的Kolmogorov-Smirnov Test (K-S) D值和 Kuiper Test V值， K-S和Kuiper Test中不包含与每个模拟年龄相关的不确定性或带宽；(c) 基于PDP的I和II交叉图的互相关系数(决定系数，虚线)；(d) 基于PDP计算的I和II的相似度系数；(e) 基于PDP计算的I和II的似然系数（据参考文献[52]修改）

Fig.7 Quantitative analysis of similarity (difference) of virtual detrital zircon samples
(a) Probability Density Plot (PDP) of age distributions with five modal ages, each with an associated uncertainty of 10%； (b) Kolmogorov-Smirnov (K-S) D value and Kuiper V values of based on CAD. K-S and Kuiper tests do not incorporate uncertainties or bandwidth associated with each modal age； (c) Cross-correlation coefficient of cross-plots based on PDPs I and II (coefficient of determination, dashed line)； (d) Similarity for PDPs I and II； (e) Likeness PDPs I and II (modified after reference [52])

图8 由4个年龄组分[(100±10) Ma、(200±10) Ma、(300±10) Ma和(400±10) Ma]经不同比例混合得到的多个虚拟样品的2D-MDS和3D-MDS结果
(a)2D-MDS图，其中灰色的实线和虚线连接的点表示最相似的和次相似的样品;(b)2D-MDS的谢帕德图,点位分散说明样品间差异与转换结果之间的线性关系差;(c)3D-MDS（圆圈的大小仅用于增强视觉效果）;(d)3D-MDS的谢帕德图,点位相对集中1∶1线附近，改进后的拟合结果验证了增加的维数在解决样品差异方面的价值（据参考文献[58]修改）

Fig.8 The results of 2D-MDS and 3D-MDS of multiple virtual samples obtained by mixing four component[(100±10) Ma、(200±10) Ma、(300±10) Ma and(400±10) Ma] in different proportions
(a) Two-dimensional MDS solid and dashed gray lines = nearest and next-nearest neighbors; (b) Shepard plot for two-dimensional MDS, The poor linearity between dissimilarities and distances indicates poor translation of the dissimilarity matrix; (c) Three-dimensional MDS (circle sizes are scaled to reflect distance of the circle from point of view of viewer, smaller is more distant); (d) Shepard plot for three-dimensional MDS. Points are relatively concentrated around the 1∶1 line. The improved fit demonstrates the value of the added dimension in resolving sample difference(modified after reference [58] )

图9 长江全流域样品似然系数和2D-MDS图(据参考文献[67]修改)
(a)使用似然系数量化：干流—干流、干流—支流和支流—支流的样品间比较， N表示每个直方图的比较次数,似然系数值越高表示两两比较之间的相似性越高；(b)非度量MDS图(主图)和谢帕德图(插图)；主干河流样本以填充色表示，较温暖的颜色(红橙黄)表示较下游的采样；支流边缘的颜色表示下游的位置，实线和虚线分别表示最邻近和次邻近的两个样品

Fig.9 Intersample likeness and 2D-MDS (modified after reference [67])
(a) Using the likeness comparison metric: Compare intersample of trunk-to-trunk, trunk-to-tributary, and tributary-to-tributary. N equals the number of comparisons per histogram. Higher values indicate higher similarity between pairwise comparisons. (b)The nonmetric MDS (main) and Shepard plot (inset). Trunk stream samples are given as filled colors, with warmer colors (red-orange-yellow) indicating farther downstream sampling; Tributary edge colors indicate downstream location. Solid and dashed lines indicate the closest neighbors and second closest neighbors in likeness, respectively

表1 常用碎屑锆石 U-Pb年代学分析软件

Table 1 The commonly analysis software of U-Pb chronology of detrital zircons

项目	Isoplot	IsoplotR	Dzstat/Dzmds	DetritalPy
开发时间	1988年	2013年	2016年	2018年
开发者	Kenneth R. Ludwig	Peter Vermesh	Saylor，Joel E. Sundell，Kurt E	Glenn R. Sharman
系统平台	Windows	Linux/MacOS/Windows	Windows/MacOS	Windows/MacOS
编程语言	VBA	R/Javascript/HTML	MATLAB	Python
运行平台	Excel	R	MATLAB	独立运行
是否开源	否	是	是	是
定量分析（Likeness, K-S Test等）	否	否	是	是
概率密度曲线（PDP）	是	否	是	是
核密度曲线（KDE）	否	是	是	是
累计年龄分布曲线（CAD）	否	是	是	是
多维定标图（MDS）	否	是	是	是

表1 常用碎屑锆石 U-Pb年代学分析软件

Table 1 The commonly analysis software of U-Pb chronology of detrital zircons

项目	Isoplot	IsoplotR	Dzstat/Dzmds	DetritalPy
开发时间	1988年	2013年	2016年	2018年
开发者	Kenneth R. Ludwig	Peter Vermesh	Saylor，Joel E. Sundell，Kurt E	Glenn R. Sharman
系统平台	Windows	Linux/MacOS/Windows	Windows/MacOS	Windows/MacOS
编程语言	VBA	R/Javascript/HTML	MATLAB	Python
运行平台	Excel	R	MATLAB	独立运行
是否开源	否	是	是	是
定量分析（Likeness, K-S Test等）	否	否	是	是
概率密度曲线（PDP）	是	否	是	是
核密度曲线（KDE）	否	是	是	是
累计年龄分布曲线（CAD）	否	是	是	是
多维定标图（MDS）	否	是	是	是

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