Application of cluster analysis to geochemical compositional data for identifying ore-related geochemical anomalies

Abstract

Cluster analysis is a well-known technique that is used to analyze various types of data. In this study, cluster analysis is applied to geochemical data that describe 1444 stream sediment samples collected in northwestern Xinjiang with a sample spacing of approximately 2 km. Three algorithms (the hierarchical, k-means, and fuzzy c-means algorithms) and six data transformation methods (the z-score standardization, ZST; the logarithmic transformation, LT; the additive log-ratio transformation, ALT; the centered log-ratio transformation, CLT; the isometric log-ratio transformation, ILT; and no transformation, NT) are compared in terms of their effects on the cluster analysis of the geochemical compositional data. The study shows that, on the one hand, the ZST does not affect the results of column- or variable-based (R-type) cluster analysis, whereas the other methods, including the LT, the ALT, and the CLT, have substantial effects on the results. On the other hand, the results of the row- or observation-based (Q-type) cluster analysis obtained from the geochemical data after applying NT and the ZST are relatively poor. However, we derive some improved results from the geochemical data after applying the CLT, the ILT, the LT, and the ALT. Moreover, the k-means and fuzzy c-means clustering algorithms are more reliable than the hierarchical algorithm when they are used to cluster the geochemical data. We apply cluster analysis to the geochemical data to explore for Au deposits within the study area, and we obtain a good correlation between the results retrieved by combining the CLT or the ILT with the k-means or fuzzy c-means algorithms and the potential zones of Au mineralization. Therefore, we suggest that the combination of the CLT or the ILT with the k-means or fuzzy c-means algorithms is an effective tool to identify potential zones of mineralization from geochemical data.

Keywords

cluster analysis / compositional data / geochemical anomaly / mineral exploration

References

[1] Abdel-Halim R E, Abdel-Aal R E (1998). Classification of urinary stones by cluster analysis of ionic composition data. Comput Methods Programs Biomed, 58(1): 69–81

[2] Afzal P, Khakzad A, Moarefvand P, Omran N R, Esfandiari B, Alghalandis Y F (2010). Geochemical anomaly separation by multifractal modeling in Kahang (Gor Gor) porphyry system, Central Iran. J Geochem Explor, 104(1–2): 34–46

[3] Agharezaei M, Hezarkhani A (2016). Delineation of geochemical anomalies based on Cu by the boxplot as an exploratory data analysis (EDA) method and concentration-volume (C-V) fractal modeling in Mesgaran mining area, Eastern Iran. Open Journal of Geology, 6(10): 1269–1278

[4] Agterberg F P (2012). Multifractals and geostatistics. J Geochem Explor, 122: 113–122

[5] Aitchison J (1982). The statistical analysis of compositional data. J R Stat Soc B, 44(2): 139–177

[6] Aitchison J (1999). Logratios and natural laws in compositional data analysis. Math Geol, 31(5): 563–580

[7] Aitchison J, Barcelo-Vidal C, Martin-Fernandez J A, Pawlowsky-Glahn V (2000). Logratio analysis and compositional distance. Math Geol, 32(3): 271–275

[8] Aitchison J, Egozcue J J (2005). Compositional data analysis: where are we and where should we be heading? Math Geol, 37(7): 829–850

[9] Bölviken B, Stokke P R, Feder J, Jossang T (1992). The fractal nature of geochemical landscapes. J Geochem Explor, 43(2): 91–109

[10] Bounessah M, Atkin B P (2003). An application of exploratory data analysis (EDA) as a robust non-parametric technique for geochernical mapping in a semi-arid climate. Appl Geochem, 18(8): 1185–1195

[11] Buccianti A (2013). Is compositional data analysis a way to see beyond the illusion? Comput Geosci, 50: 165–173

[12] Carranza E J M (2009). Geochemical anomaly and mineral prospectivity mapping in GIS. Handbook of exploration and environmental geochemistry, 11. Elsevier Science

[13] Carranza E J M (2010). Catchment basin modelling of stream sediment anomalies revisited: incorporation of EDA and fractal analysis. Geochem Explor Environ Anal, 10(4): 365–381

[14] Carranza E J M (2011). Analysis and mapping of geochemical anomalies using logratio-transformed stream sediment data with censored values. J Geochem Explor, 110(2): 167–185

[15] Carranza E J M, Hale M (1997). A catchment basin approach to the analysis of reconnaissance geochemical-geological data from Albay Province, Philippines. J Geochem Explor, 60(2): 157–171

[16] Cheng Q, Agterberg F P (2009). Singularity analysis of ore-mineral and toxic trace elements in stream sediments. Comput Geosci, 35(2): 234–244

[17] Cheng Q, Agterberg F P, Bonham-Carter G F (1996). A spatial analysis method for geochemical anomaly separation. J Geochem Explor, 56(3): 183–195

[18] Davis J C (2002). Statistics and Data Analysis in Geology (3rd ed). New York, Chichester, Brisbane, Toronto, Singapore: John Wiley and Sons

[19] Egozcue J J, Pawlowsky-Glahn V, Mateu-Figueras G, Barcelo-Vidal C (2003). Isometric logratio transformations for compositional data analysis. Math Geol, 35(3): 279–300

[20] Eilermann M, Post C, Schwarz D, Leufke S, Schembecker G, Bramsiepe C (2017). Generation of an equipment module database for heat exchangers by cluster analysis of industrial applications. Chem Eng Sci, 167: 278–287

[21] Fatehi M, Asadi H H (2017). Application of semi-supervised fuzzy c-means method in clustering multivariate geochemical data, a case study from the Dalli Cu-Au porphyry deposit in central Iran. Ore Geol Rev, 81: 245–255

[22] Fattahi H (2016). Indirect estimation of deformation modulus of an in situ rock mass: an ANFIS model based on grid partitioning, fuzzy c-means clustering and subtractive clustering. Geosci J, 20(5): 681–690

[23] Filzmoser P, Hron K, Reimann C (2009). Univariate statistical analysis of environmental (compositional) data: problems and possibilities. Sci Total Environ, 407(23): 6100–6108

[24] Filzmoser P, Hron K, Reimann C (2010). The bivariate statistical analysis of environmental (compositional) data. Sci Total Environ, 408(19): 4230–4238

[25] Ghosh T, Kanchan R (2014). Geoenvironmental appraisal of groundwater quality in Bengal alluvial tract, India: a geochemical and statistical approach. Environ Earth Sci, 72(7): 2475–2488

[26] Han J, Kamber M (2006). Data Minning: Concepts and Techniques (2nd ed). Beijing: China Machine Press

[27] Hassanpour S, Afzal P (2013). Application of concentration–number (C–N) multifractal modeling for geochemical anomaly separation in Haftcheshmeh porphyry system, NW Iran. Arab J Geosci, 6(3): 957–970

[28] Hawkes H E, Webb J S (1962). Geochemistry in Mineral Exploration.New York: Harper

[29] He G Q, Chen S D, Xu X, Li J Y, Hao J (2004). An Introduction to the Explanatory Text of the Map of Tectonics of Xinjiang and Its Neighbouring Area (1:250000). Beijing: Geological Publishing House (in Chinese)

[30] Howarth R J (1983). Statistics and Data Analysis in Geochemical Prospecting. Handbook of Exploration Geochemistry, 2. Amsterdam-Oxford-New York Elsevier

[31] Kim T, Moon D C, Park W B, Park K H, Ko G W (2007). Classification of springs of Jeju Island using cluster analysis of annual fluctuations in discharge variables: investigation of the regional groundwater system. Geosci J, 11(4): 397–413

[32] Kitzig M C, Kepic A, Kieu D T (2017). Testing cluster analysis on combined petrophysical and geochemical data for rock mass classification. Explor Geophys, 48(3): 344–352

[33] Lee J Y, Song S H (2007). Groundwater chemistry and ionic ratios in a western coastal aquifer of Buan, Korea: implication for seawater intrusion. Geosci J, 11(3): 259–270

[34] Leite M L C (2016). Applying compositional data methodology to nutritional epidemiology. Stat Methods Med Res, 25(6): 3057–3065

[35] Meng H, Song Y, Song F, Shen H (2011). Research and application of cluster and association analysis in geochemical data processing. Computat Geosci, 15(1): 87–98

[36] Sahraei Parizi H, Samani N (2013). Geochemical evolution and quality assessment of water resources in the Sarcheshmeh copper mine area (Iran) using multivariate statistical techniques. Environ Earth Sci, 69(5): 1699–1718

[37] Parsa M, Maghsoudi A, Yousefi M, Carranza E J M (2017). Multifractal interpolation and spectrum–area fractal modeling of stream sediment geochemical data: implications for mapping exploration targets. J Afr Earth Sci, 128: 5–15

[38] Pazand K, Hezarkhani A, Ataei M, Ghanbari Y (2011). Application of multifractal modeling technique in systematic geochemical stream sediment survey to identify copper anomalies: a case study from Ahar, Azarbaijan, Northwest Iran. Chemie der Erde- Geochemistry, 71(4): 397–402

[39] Reimann C, Filzmoser P (2000). Normal and lognormal data distribution in geochemistry: death of a myth. Consequences for the statistical treatment of geochemical and environmental data. Environmental Geology, 39(9): 1001–1014

[40] Reimann C, Filzmoser P, Garrett R G (2002). Factor analysis applied to regional geochemical data: problems and possibilities. Appl Geochem, 17(3): 185–206

[41] Reimann C, Filzmoser P, Garrett R G (2005). Background and threshold: critical comparison of methods of determination. Sci Total Environ, 346(1–3): 1–16

[42] Reimann C, Garrett R G (2005). Geochemical background- concept and reality. Sci Total Environ, 350(1–3): 12–27

[43] Rock N M S (1988). Numerical Geology. Lecture Notes in Earth Sciences, 18. New York, Berlin, Heidelberg: Springer-Verlag

[44] Stück H, Koch R, Siegesmund S (2013). Petrographical and petrophysical properties of sandstones: statistical analysis as an approach to predict material behaviour and construction suitability. Environ Earth Sci, 69(4): 1299–1332

[45] Su Y, Tang H, Hou G, Liu C (2006). Geochemistry of aluminous A-type granites along Darabut teconic belt in west Junggar, Xinjiang. Geochimica, 35(1): 55–67 (in Chinese)

[46] Templ M, Filzmoser P, Reimann C (2008). Cluster analysis applied to regional geochemical data: problems and possibilities. Appl Geochem, 23(8): 2198–2213

[47] Templ M, Hron K, Filzmoser P (2017). Exploratory tools for outlier detection in compositional data with structural zeros. J Appl Stat, 44(4): 734–752

[48] Tolosana-Delgado R, McKinley J (2016). Exploring the joint compositional variability of major components and trace elements in the Tellus soil geochemistry survey (Northern Ireland). Appl Geochem, 75: 263–276

[49] Tukey J W (1977). Exploratory Data Analysis. Reading: Addison-Wesley

[50] Wang L, Wang Y, Zhang W, Xu C, An Z (2014). Multivariate statistical techniques for evaluating and identifying the environmental significance of heavy metal contamination in sediments of the Yangtze River, China. Environ Earth Sci, 71(3): 1183–1193

[51] Wang X Q, Xie X J, Zhang B R, Hou Q Y (2011). Geochemical probe into China’s continental crust. Acta Geoscientica Sinica, 32: 65–83 (in Chinese)

[52] Xie X, Mu X, Ren T (1997). Geochemical mapping in China. J Geochem Explor, 60(1): 99–113

[53] Xie X, Wang X, Zhang Q, Zhou G, Cheng H, Liu D, Cheng Z, Xu S (2008). Multi-scale geochemical mapping in China. Geochem Explor Environ Anal, 8(3–4): 333–341

[54] Yusta I, Velasco F, Herrero J M (1998). Anomaly threshold estimation and data normalization using EDA statistics: application to lithogeochemical exploration in lower Cretaceous Zn-Pb carbonate-hosted deposits, northern Spain. Appl Geochem, 13(4): 421–439

[55] Zhang C, Huang X (1992). The ages and tectonic settings of ophiolites in West Junggar, Xinjiang. Geological Review, 38(6): 509–524 (in Chinese)

[56] Zhang F (2003). The study of geological characteristics of the gold associated minerals and gold vine of Hatu gold deposit. Journal of Xinjiang Nonferrous Metals, 26(3): 5–6 (in Chinese)

[57] Zhu Y, An F, Xu C, Guo H, Xia F, Xiao F, Zhang F, Lin C, Qiu T, Wei S (2013a). Geology and Au-Cu Deposits in the Hatu and its Adjacent Region (Xinjiang): Evolution and Prospecting Model. Beijing: Geological Publishing House

[58] Zhu Y, Chen B, Xu X, Qiu T, An F (2013b). A new geological map of the western Junggar, north Xinjiang (NW China): implications for Paleoenvironmental reconstruction. Episodes, 36(3): 205–220

[59] Zumlot T, Goodell P, Howari F (2009). Geochemical mapping of New Mexico, USA, using stream sediment data. Environmental Geology, 58(7): 1479–1497

[60] Zuo R (2012). Exploring the effects of cell size in geochemical mapping. J Geochem Explor, 112: 357–367

[61] Zuo R, Cheng Q (2008). Mapping singularities- a technique to identify potential Cu mineral deposits using sediment geochemical data, an example for Tibet, west China. Mineral Mag, 72(1): 531–534

[62] Zuo R, Wang J, Chen G, Yang M (2015). Identification of weak anomalies: a multifractal perspective. J Geochem Explor, 148: 12–24

[63] Zuo R, Xia Q, Wang H (2013a). Compositional data analysis in the study of integrated geochemical anomalies associated with mineralization. Appl Geochem, 28: 202–211

[64] Zuo R, Xia Q, Zhang D (2013b). A comparison study of the C-A and S-A models with singularity analysis to identify geochemical anomalies in covered areas. Appl Geochem, 33: 165–172

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