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

doi:10.19657/j.geoscience.1000-8527.2023.009

Abstract

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

CLC Number:

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.

Figures/Tables 15

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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