等距对数比变换及混合分布在区域化探数据分析中的应用

doi:10.19657/j.geoscience.1000-8527.2023.009

现代地质 ›› 2023, Vol. 37 ›› Issue (03): 662-673.DOI: 10.19657/j.geoscience.1000-8527.2023.009

• 矿床学与地球化学探矿学 • 上一篇下一篇

等距对数比变换及混合分布在区域化探数据分析中的应用

李柱¹^,²(), 张德会¹(), 杨帆³, 刘向冲⁴

1.中国地质大学(北京)地球科学与资源学院,北京 100083
2.内蒙古地质工程有限责任公司,内蒙古呼和浩特 010010
3.中国地质科学院地球物理地球化学勘查研究所,河北廊坊 065000
4.中国地质科学院地质力学研究所,北京 100081

收稿日期:2022-10-28 修回日期:2023-03-09 出版日期:2023-06-10 发布日期:2023-07-20
通讯作者: 张德会,男,教授,博士生导师,1955年出生,地球化学专业,主要从事成矿作用地球化学研究。Email:1978011191@cugb.edu.cn。
作者简介:李柱,男,博士,高级工程师,1987年出生,矿物学、岩石学、矿床学专业,主要从事矿床地球化学研究。Email:867113514@qq.com。
基金资助:
国家自然科学基金项目(41373048);国家自然科学基金项目(41773030);内蒙古自治区地质勘查基金综合研究项目(2020-KY03)

Regional Geochemical Data Analysis Using Isometric Log-ratio Transformation and Mixture Distribution

LI Zhu¹^,²(), ZHANG Dehui¹(), YANG Fan³, LIU Xiangchong⁴

1. School of Earth Sciences and Resources, China University of Geosciences (Beijing), Beijing 100083, China
2. Inner Mongolian Geological Engineering Co.,Ltd., Hohhot, Inner Mongolia 010010, China
3. Institute of Geophysics and Geochemistry,Chinese Academy of Geological Sciences, Langfang, Hebei 065000, China
4. Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China

Received:2022-10-28 Revised:2023-03-09 Online:2023-06-10 Published:2023-07-20

摘要/Abstract

摘要：

区域化探数据是典型的成分数据,等距对数比变换(ILR)可以有效构建化探数据的标准正交基,消除其闭合效应,解释数据的组成性质,但是解释ILR转换的变量仍然很困难。为使ILR转换更容易理解,本研究利用地质知识和数据驱动的方法构建可解释的ILR转换变量,并将该方法应用于从大兴安岭中南段水系沉积物地球化学数据中提取地质信息。基于地质知识和层次聚类分析,构建了Sn、W、Cr和Ni元素浓度之间的顺序二元划分(SBP),并经ILR转换后表示为变量b1、b2和b3。此外,还采用了由最小信息长度准则(MML)改进的期望最大化(EM)算法,研究上述变量的混合分布。ILR转换的变量具有镁铁质岩浆作用、Sn-W热液成矿和后期地质作用的信息,服从双正态分布或三正态分布。其中b1、b2和b3的高平均值分组对应于锡钨成矿的异常,综合圈定4个锡钨找矿潜力较高的预测区。本研究表明,ILR转换和MML-EM算法在从区域化探数据中提取地质信息和圈定异常方面是一种很有前途的方法。

关键词: 等距对数比变换, 混合分布, 成分数据, 化探, 大兴安岭

Abstract:

Regional geochemical exploration data are typical compositional data. Isometric log-ratio transformation (ILR) produces an orthonormal basis of geochemical data, which can eliminate the data closure effect and account for the data compositional nature. However, it is still difficult to interpret ILR-transformed variables. To make ILR transformations easier to understand, geological knowledge and data-driven methods are used to construct the interpretable ILR-transformed variables. This method was applied to extract geo-information from stream sediment geochemical data in the central and southern Da Hinggan Mountains, Inner Mongolia, northern China. Based on these geological information and hierarchical cluster analysis, sequential binary partition was constructed among the Sn, W, Cr, and Ni concentrations, and expressed as variables b1, b2 and b3 by ILR transformation. Furthermore, the expectation-maximization (EM) algorithm modified by a minimum message length criterion (MML) was employed to investigate the variables mixture distributions.The ILR-transformed variables follow either a bi-normal or tri-normal distribution, which were interpreted as fingerprints inherited from mafic magmatic, Sn-W hydrothermal, and later geological processes. The high-average subpopulation of b1, b2 and b3 variables of ILR transformation corresponds to the anomalies of W-Sn metallogenic system, and four areas were predicted to have high Sn-W prospecting potential. This study shows that the ILR transformation and MML-EM algorithm are promising tools to effectively extract geo-information from geochemical data and delineate anomalies.

Key words: isometric log-ratio transformation, mixture distribution, compositional data, geochemical exploration, Da Hinggan Mountains

中图分类号:

李柱, 张德会, 杨帆, 刘向冲. 等距对数比变换及混合分布在区域化探数据分析中的应用[J]. 现代地质, 2023, 37(03): 662-673.

LI Zhu, ZHANG Dehui, YANG Fan, LIU Xiangchong. Regional Geochemical Data Analysis Using Isometric Log-ratio Transformation and Mixture Distribution[J]. Geoscience, 2023, 37(03): 662-673.

图/表 15

图1 大兴安岭中南段大地构造位置(a)及区域地质简图(b)(底图据文献[17])

Fig.1 Tectonic map (a) and generalized regional geologic map (b) of the central and southern Da Hinggan Mountains (after reference [17])

图2 大兴安岭中南段代表性矿床的矿体、矿石及主要围岩岩性特征 (a)元古宙斜长片麻岩;(b)古生界林西组变质砂岩;(c)中生界白音高老组晶屑岩屑凝灰岩;(d)二叠纪辉长岩;(e)石炭纪二长花岗岩;(f)早白垩世黑云母二长花岗岩和细晶岩脉;(g)早白垩世石英斑岩;(h)拜仁达坝Zn-Pb-Cu-Ag多金属矿体;(i)维拉斯托角砾岩型锂多金属矿体;(j)维拉斯托石英脉型锡多金属矿体;(k)大井Cu-Sn矿石手标本;(l)白音查干斑岩型锡多金属矿石手标本;Apy.毒砂;Clp.黄铜矿;Cst.锡石;Fl.萤石;Gn.方铅矿;Lpd.锂云母;Po.磁黄铁矿;Py.黄铁矿;Qtz.石英;Sp.方铅矿

Fig.2 Photos showing the major wall rock and features of ore body and ore of representative deposits in the central and southern Da Hinggan Mountains

表1 变异矩阵(右上部)及ln(xi/xj)平均值(左下部)

Table 1 Variation matrix (upper right) and the mean of ln(xi/xj) (lower left)

	Ag	As	Au	Bi	Cr	Cu	F	Li	Mo	Nb	Ni	Pb	Sn	W	Zn
Ag		0.64	0.58	0.71	1.12	0.79	0.50	0.46	0.56	0.44	1.26	0.30	0.65	0.51	0.40
As	-1.62		0.90	0.80	1.09	0.72	0.63	0.52	0.67	0.72	1.10	0.65	0.85	0.65	0.54
Au	-5.05	-3.44		1.01	0.86	0.80	0.44	0.45	0.63	0.35	1.04	0.48	0.87	0.67	0.54
Bi	-5.52	-3.91	-0.47		1.57	1.13	0.87	0.80	0.88	0.84	1.74	0.67	0.71	0.67	0.82
Cr	-1.41	0.21	3.64	4.11		0.45	0.71	0.83	1.09	0.84	0.29	1.03	1.41	1.29	0.72
Cu	-1.83	-0.21	3.23	3.70	-0.42		0.57	0.66	0.83	0.72	0.41	0.77	1.10	0.99	0.42
F	1.51	3.13	6.56	7.03	2.92	3.34		0.26	0.46	0.27	0.78	0.41	0.74	0.48	0.31
Li	-1.12	0.49	3.93	4.40	0.29	0.70	-2.63		0.49	0.26	0.91	0.37	0.64	0.43	0.32
Mo	-4.50	-2.89	0.55	1.02	-3.10	-2.68	-6.02	-3.38		0.36	1.11	0.48	0.76	0.51	0.46
Nb	-1.98	-0.37	3.07	3.54	-0.57	-0.16	-3.49	-0.86	2.52		0.92	0.30	0.51	0.44	0.30
Ni	-2.09	-0.48	2.96	3.43	-0.68	-0.27	-3.60	-0.97	2.41	-0.11		1.17	1.56	1.41	0.72
Pb	-1.40	0.21	3.65	4.12	0.01	0.42	-2.92	-0.28	3.10	0.58	0.69		0.55	0.46	0.30
Sn	-3.26	-1.65	1.79	2.26	-1.85	-1.44	-4.77	-2.14	1.24	-1.28	-1.17	-1.86		0.23	0.60
W	-3.96	-2.34	1.10	1.56	-2.55	-2.13	-5.47	-2.84	0.55	-1.98	-1.87	-2.55	-0.70		0.54
Zn	-0.12	1.49	4.93	5.40	1.29	1.70	-1.63	1.00	4.38	1.86	1.97	1.28	3.14	3.84

图3 大兴安岭中南段15种元素聚类分析树图

Fig.3 Cluster dendrogram of association of 15 elements in the central and southern Da Hinggan Mountains

图4 大兴安岭中南段Cr和Ni元素地球化学图

Fig.4 Cr and Ni geochemical maps of the central and southern Da Hinggan Mountains

图5 大兴安岭中南段Sn和W元素地球化学图

Fig.5 Sn and W geochemical maps of the central and southern Da Hinggan Mountains

表2 大兴安岭中南段4种元素顺序二元划分

Table 2 Sequential binary partitions of the four elements in the central and southern Da HingganMountains

	Sn	Cr	W	Ni
b1	+	+	-	-
b2	+	-
b3			+	-

图6 大兴安岭中南段变量b1混合分布筛分结果

Fig.6 Separation results of the mixed distribution of b1 variable in the central and southern Da Hinggan Mountains

表3 大兴安岭中南段变量b1、b2和b3拟合的混合分布结果

Table 3 Results of fitting the mixture distributions of b1, b2 and b3 variables in the central and southern Da Hinggan Mountains

变量	子分布	权重	均值	方差
b1	1	0.25	0.81	0.57
b1	2	0.75	0.65	0.12
b2	1	0.47	-1.24	0.20
	2	0.25	-2.28	0.37
	3	0.28	-0.60	0.52
b3	1	0.11	-0.17	0.30
	2	0.13	-2.63	0.85
	3	0.76	-1.26	0.25

图7 大兴安岭中南段变量b1三个分组的空间分布

Fig.7 Map showing the spatial distribution of the three subpopulations of b1 variable in the central and southern Da Hinggan Mountains

图8 大兴安岭中南段变量b2混合分布筛分结果

Fig.8 Separation results of the mixed distribution of b2 variable in the central and southern Da HingganMountains

图9 大兴安岭中南段变量b2三个分组的空间分布

Fig.9 Map showing the spatial distribution of the three subpopulations of b2 variable in the central and southern Da Hinggan Mountains

图10 大兴安岭中南段变量b3混合分布筛分结果

Fig.10 Separation results of the mixed distribution of b3 variable in the central and southern Da Hinggan Mountains

图11 大兴安岭中南段变量b3三个分组的空间分布

Fig.11 Map showing the spatial distribution of the three subpopulations of b3 variable in the central and southern Da Hinggan Mountains

图12 大兴安岭中南段找矿预测图

Fig.12 Prospecting prediction map of the central and southern Da Hinggan Mountains

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等距对数比变换及混合分布在区域化探数据分析中的应用

Regional Geochemical Data Analysis Using Isometric Log-ratio Transformation and Mixture Distribution

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