Mapping of Fe Mineral Potential by Spatially Weighted Principal Component Analysis in the Eastern Tianshan Mineral District, China

Journal of Geochemical Exploration 164 (2016) 107–121

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Journal of Geochemical Exploration

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Mapping of Fe mineral potential by spatially weighted principal component analysis in the eastern Tianshan mineral district, China

Jie Zhao a,b,c,WenleiWangd,⁎, Qiuming Cheng a,c,e, Frits Agterberg f a State Key Lab of Geological Processes and Mineral Resources, China University of Geosciences (Beijing), Beijing 100083, China b The Key Laboratory of Development and Research for Land Resource Information, China University of Geosciences (Beijing), Beijing 100083, China c School of Earth Sciences and Resources, China University of Geosciences (Beijing), Beijing 100083, China d Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China e Department of Earth and Space Science and Engineering, Department of Geography, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada f Geological Survey of Canada, 601 Booth Street, Ottawa K1A 0E8, Canada article info abstract

Article history: Principal component analysis (PCA) is one of the commonly used methods to integrate multi-source geological Received 4 July 2015 data to enhance understanding of geo-information. Each principal component (PC) obtained by PCA reflects a dif- Revised 23 October 2015 ferent aspect of the geo-information contained in a dataset. Confined by statistical significance, some PCs are not Accepted 8 November 2015 acceptable for interpretation. In this paper, the same problem in PCA occurs in mapping potential areas of Fe min- Available online 10 November 2015 eralization in eastern Tianshan mineral district, China. By spatially weighting correlation coefficient matrixes between variables, a spatially weighted principal component analysis (SWPCA) can deal with the shortcoming of Keywords: Fe-polymetallic mineralization PCA, thus improving the statistical acceptability of eigenvectors and eigenvalues derived by ordinary PCA. PCA extension Based on the geological model in the study area, a current weighting factor is defined to enhance the geo- Singularity mapping technique information possessed by the ordinary PC1. Compared with the loading of input layers on ordinary PCA, Gobi desert coverage SWPC1 shows more significant physical meaning than PC1. Meanwhile, remarkable increases on the eigenvalues SWPCA modeling of SWPC2 and SWPC3 are demonstrated to exist making these spatially weighted principal components more acceptable in a statistical sense. In comparison with both loadings and scores on ordinary PCs, the improved geo- information carried by SWPCs can help with better interpretations of the geological phenomena. © 2015 Elsevier B.V. All rights reserved.

1. Introduction scattered in latticed fault systems nearby (BGEDXP, 2009). Influenced by subsequent emplacement of intermediate-felsic magma, previously The Eastern Tianshan mineral district located in the juncture zone of formed Fe ore bodies were enriched by hydrothermal and metasomatic the Junggar and Tarim crusts is one of the most important prospective activities (Li et al., 2012, 2014; Zhang and Ding, 1984). Therefore, con- areas of Fe mineral resources in China (Muhetaer et al., 2010). A tact zones of the Yamansu Formation and intermediate-felsic intrusions prolonged history of tectonic evolution and frequent magmatic activi- are often considered as exploration targets. ties (e.g., volcanic eruption and igneous intrusion) resulted in an envi- As the study area is located in the Gobi Desert area, recognition of ronment suitable for Fe mineralization in this district (Cui et al., 2008). anomalous geochemical features in the eastern Tianshan mineral dis- Among known mineralization types, marine volcanic–sedimentary Fe trict is limited by surficial cover mainly consisting of aeolian sand, cali- deposits (e.g., Fe, Fe–V–Ti, Fe–Mn and Fe–Cu–Zn deposits) of great eco- che, and regolith (BGEDXP, 2009). Stream sediment geochemical data, nomic value have been the foci of various studies for decades (BGEDXP, record geochemical signatures inherited from bedrocks and are there- 2009). Most of these Fe deposits are located within the extent of the fore commonly employed to identify geochemical anomalies associated Jueluotag rift and are strongly associated with volcanic eruptions in with geological bodies (Cheng, 2007a; Wang et al., 2011a,b; Wang et al., the Early Carboniferous (i.e., the Yamansu volcanic strata) (Han and 2012; Zhao et al., 2012) and provide useful geological information in Zhao, 2003; Hou et al., 2006; Zhou et al., 2001). Spatially and temporally covered environments (Bogoch et al., 1993; Brantley and White, 2009; controlled by tectonic activities, magmatism (e.g., volcanic eruption, ig- Hao et al., 2007). Therefore, within the study area, provided that impact neous emplacement and hydrothermal activities) occurred along faults of overburden can be eliminated during data analysis, stream sedimen- or at intersections of faults trending in different directions (Xu et al., tary geochemical data can be an important source of geo-information 2011). Iron deposits confined within volcanic edifices are, therefore, for identifying geological features and mapping of mineral potential (Jiang et al., 2006). ⁎ Corresponding author. The developments in statistical and spatial data analyses E-mail address: [email protected] (W. Wang). (e.g., regression analysis, characteristic analysis, principal component

http://dx.doi.org/10.1016/j.gexplo.2015.11.004 0375-6742/© 2015 Elsevier B.V. All rights reserved. 108 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 analysis, and weights of evidence) and spatial database in past de- Aqikekuduke–Shaquanzi fault, the Yamansu fault, etc.), as well as volca- cades have stimulated a great improvement in techniques for nic belts (e.g., the late Carboniferous Yamansu strata) and metal extracting geological information from multi-source and multi- metallogenic belts (e.g., Kanggurtag gold, the Yamansu Fe and the scale geo-datasets (e.g., Wang and Cheng, 2008; Zagayevskiy and Huangshang Cu–Ni belts) (Wang, 2005; Li and Sun, 1984). Deutsch, 2015). These developments promote the characterization In the eastern Tianshan mineral district, China, most of Fe deposits of geo-anomalies (Bonham-Carter, 1994; Geranian et al., 2015; (e.g., the Yamansu, the Hongyuntan, the Bailingshan Fe deposits) are ge- Ranjbar and Honarmand, 2004). Principal component analysis (PCA) netically associated with marine volcanic activity and developed within is frequently employed in the Earth sciences (e.g., Cheng et al., 2011; the convergent field of paleovolcanic edifices (i.e., volcano-sedimentary El-Makky, 2011). One of the primary objectives of using PCA is to basin) (Wang, 2005). Known Fe deposits in this district were mainly achieve overall variability from multi-source datasets. It supports iden- discovered in the early Carboniferous Yamansu Formation, while a tification of different associations of major and trace element variations few of them are contained in the Late Carboniferous Tugutubulak to select target areas. In order to enhance the efficiency of PCA, several Formation (Wang et al., 2006). Associated with volcanic edifices, the re- extensions of PCA have been proposed by former researchers gional distribution of these Fe deposits demonstrates a well-developed (e.g., robust PCA, weighted PCA, kernel PCA) (Jolliffe, 2002; Zhao et al., zoning characteristic: (1) the Yamansu type Fe deposits (relatively high 2007). Cheng (2006) extended three PCA algorithms consisting of spa- temperature), whose metallogeny will be introduced in the following tially weighted PCA (SWPCA) and high-order PCA based on correlation section, formed close to volcanic centers; (2) the volcanic–sedimentary matrix, and spatial autocorrelation and cross-correlation matrix-based and hydrothermal metasomatic Fe mineralization occurred near the PCA to enhance objective interpretation of geo-information. Several ap- volcanic edifices (middle temperatures). For example, the Chilongfeng plications of SWPCA have been published in past decade. Wang and (35% Fe, 1% Cu, 1 g/t Au), the Caihongshan and the Hongtieshan Fe de- Cheng (2008) used buffer zones around outcropping intrusive rocks posits were discovered in volcanic breccias and basalts around volcanic as spatially weighting factors to enhance the spatial distribution of in- domes. With increasing distance from the center, structures of ore bod- trusions. Cheng et al. (2011) applied SWPCA to integrate stream sedi- ies vary from stratiform, vein-type, brecciated to massive form. Ore ment geochemical data related to felsic intrusions, and the results rocks mainly consisting of hematite and little specularite and magnetite were compared by using various weighting factors. Xiao et al. (2012) are intensively chloritized, epidotized and silicified; and (3) the volcanic applied spatially weighted factors associated with fault information to hydrothermal–sedimentary siderite deposits formed at positions away detect and map geochemical anomalies associated with Ag and Pb–Zn from volcanic edifices (relatively low temperature). Taking the polymetallic mineralization. The three existing applications of SWPCA Shaquanzi Fe deposit as an example, ore bodies located in the interlayer are based on the criteria that selected weighting factors should be de- of ferrous dolomite are stratiform. Ore rocks mainly consist of siderite. fined with physical meanings, results of which demonstrate the effi- Other minerals including limonite, magnetite, hematite, specularite, ciency of SWPCA on enhancing objective geo-anomalies. The current and psilomelane can also be observed (Ma et al., 1997; Yan, 1985). study, based on formerly recognized ore controlling factors in the The horizontal zoning of Fe mineralization types frequently guided the eastern Tianshan mineral district (China) further utilized the SWPCA iron ore exploration. to delineate spatial distributions of Fe-polymetallic mineralization- Previous researches (BGEDXP, 2009; Ma et al., 1997; Zhang et al., associated geochemical signatures, the results of which are compared 2013; Zhao et al., 2012) revealed that the formation of marine volca- with results of ordinary PCA. Therefore, an improved capability to delin- nic–sedimentary Fe deposits in this district (i.e., Yamansu-type) are ge- eate geochemical signatures associated with various geological features netically and spatially governed by the Yamansu Formation, well- is developed and demonstrated to exist in this paper by using the ex- developed fault systems and multi-stage magmatic activity. First of all, tended PCA algorithm SWPCA. most of the large-scale Fe deposits in the study area (e.g., the Yamansu, Baishanquan, Aqishan and Tieling Fe deposits) are hosted in the Yamansu 2. Geological background Formation which consists of marine bimodal volcanic rocks, marine car- bonaceous shale–siliceous rocks, with clastic carbonates (Xu et al., 2.1. Geological background and regional Fe mineralization 2011; Zhang et al., 2013; Wang et al., 2006; Yang et al., 1996). The ore- bearing strata are generally alkali-rich (i.e., high in potassium), and with-

The study area, the eastern Tianshan mineral district is located in the in local area the K2O content reaches 9.5% (Qi et al., 1985). Secondly, the Jueluotag Carboniferous aulacogen (i.e., the northern margin of the spatial distribution of regional volcanic–sedimentaryFedepositsisinflu- Tarim block). It is regionally confined by the Dacaotan–Dananhu fault enced by their tectonic environment (Zhang et al., 2013). Paleovolcanic zone in the north, the Aqikekuduk–Shaquanzi fault in the south, the edifices including eruption centers, volcanic domes and volcano- Xiaorequanzi area in the west, and the border of Gansu Province and sedimentary basins provide regional tectonic settings for the Fe mineral- Xinjiang Uyghur Autonomous Region in the east (BGEDXP, 2009; Feng ization (Jiang et al., 2002; Yan, 1985; Zhang and Ding, 1984). On the other et al., 2009; Wang et al., 2015b; Yang et al., 1996). Complex tectonic hand, positions within latticed faults or at intersections of faults trending evolution of the passive continental margin between the early Carbon- along diverse directions provide favorable spaces for variable Fe mineral- iferous and the Cenozoic had led to intensive magmatic activities, ization associated with magmatism in this district (BGEDXP, 2009; Xu which are believed to benefit the Fe mineralization (Wang et al., 2012; et al., 2011). Thirdly, the controlling effects of magmatism for the Fe Xu et al., 2011; Feng et al., 2002). Transition from the terrigenous mineralization are two-fold: (1) most of the Fe deposits are confined to clastic-calc-alkaline igneous rock suite to bimodal volcanic formation the extents of the Early Carboniferous volcanic edifices and eruption- can be viewed in sediments, and noticeable Fe mineralization in the sedimentary basins (Zhao, 2003); and (2) the formation, alteration and study area occurred in this period (Feng et al., 2002). During the early enrichment of Fe ore bodies were influenced by regional emplacement Late Carboniferous, compression of the aulacogen took the place of of intermediate-felsic magma and subsequent hydrothermal activities plate spreading, during which formations of flysch, intermediate-felsic (Xu et al., 2011; Ding, 1990; Jiang et al., 2002). volcanic formations and calc-alkaline granitic formations were prominent. Solidification of these sediments and local molasse sedimentation 2.2. The Yamansu-type marine volcanic sedimentary Fe deposit occurred from the middle to late Carboniferous onward. In the Permian, the study area entered a tectonically calm period (Feng et al., 2009; Comprehensive study and summary descriptions of typical mineral Wang et al., 2006; Xu et al., 2011; Chen et al., 2003; Han et al., 2002). deposits play a fundamental role in mineral prediction and exploration The N–Stension–compression processes (Xu et al., 2011)hadproduced in an area (Feng et al., 2009). The metallogeny and geological setting of E–W trending tectonic framework (e.g., the Kanggur fault, the the Yamansu deposit is used as typical marine volcanic sedimentary Fe J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 109 deposit in the study area and the characteristics are brieflyreviewedto 2.2.3. Magmatic activity derive the GIS-based mineral prospectivity modeling criteria to be used. Magmatic activity in the Yamansu mineral district included the Early Carboniferous bimodal eruption that caused the formation of a K spilite/ 2.2.1. Strata quartz keratophyre suite (rich in K and Na, poor in Ca). In addition, In the Yamansu mineral district, the Early Carboniferous Yamansu multi-stage subvolcanism during the middle Hercynian produced por-

Formation (C1y) consists of sub-marine intermediate-basic volcanic phyritic basalt, augite-porphyritic andesite, augite-porphyritic diorite, clastic rocks including the ore-bearing strata (Wang, 2005). The and synchronous vein-type porphyritic spilite, diabase, and spessartite Yamansu Formation can be divided into two subformations. The lower (amphibole-plagioclase-lamprophyre) (BGEDXP, 2009; Ma et al., 1997). subformation located in the northwestern part of the Yamansu mineral district consists of andesitic tuff, basalt, and andesitic volcanic breccias, 2.2.4. Wall-rock alteration while the upper subformation located in the south-central part of the Wall rocks in the Yamansu mineral district are commonly altered in- district consists of limestone, andesite, spilite, and andesitic tuff fluenced by multi-stage tectonic and magmatic activities. Lateral alter- (Wang et al., 2006; Yang et al., 1996; BGEDXP, 2009). ation–mineralization zoning patterns can be observed. Alteration type varies with distance from ore bodies in the following sequence 2.2.2. Tectonic settings (Wang, 2005; Zhang and Xie, 2001): (1) garnet skarn (Fe polymetallic The tectonic framework of the Yamansu deposit consists of the belt) with altered minerals such as garnet, chlorite and actinolite; Yamansu anticline (or volcanic dome) and a group of faults trending (2) complex skarn (pyrite belt) with alteration minerals such as epi- along nearly EW direction (Wang, 2005; Zhang and Ding, 1984). The de- dote, chlorite and a few of garnet and actinolite; (3) epidote- posit was formed within the upper subformation at the south limb of carbonatization belt (pyrite belt) with alteration minerals such as cal- the anticline close to the axis (Zhang and Ding, 1984). Faults, which cite, chlorite, epidote, actinolite, and a little chalcopyrite; and (4) silicifi- are well developed in the district, can be divided into syn- and post- cation belt (ore-free belt). mineralization faults based on their temporal relationships with Fe mineralization. The syn-mineralization faults acted as migration channels 2.2.5. Mineralization period for ore-bearing fluids and provided spaces for ore precipitation. There- Whole-rock Rb–Sr ages of porphyritic augite–andesite sampled in fore, these faults control the spatial distribution of ore bodies. On the this district vary around 374 ± 44 Ma, representing the time of other hand, post-mineralization faults are mostly thrust faults that cut subvolcanic eruption; Sm–Nd ages of garnet and epidote in skarns or reshaped the previously formed Fe ore bodies (Wang, 2005). vary around 352 ± 47 Ma, representing the time of mineralization (Li

Fig. 1. The geologic maps of eastern Tianshan mineralization district. a: The study area and its tectonic settings. F1 = Kanggurtag–Huangshan fault. F2 = the Yamansu fault. F3 = the Aqikekuduke–Shaquanzi fault. F4 = the Toksun–Gangou fault. F5 = the Xingxingxia fault. Grey lines conﬁne the study area. Red lines indicate fault traces in the study area (modiﬁed from Wang et al., 2006). b: Geologic map of the study area. 110 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121

Table 1 can be significantly blurred or masked by addition of unrelated mate- PCA results of singularity indices of selected elements associated with faults. rials (Ren et al., 1989). The influence of the aeolian sand on elemental PC1 PC2 PC3 PC4 concentration in sediments was eliminated by collecting samples in sizes of −4 to +20 meshes, which are much coarser than sand grains, Fault Component variance 1.92 0.91 0.83 0.33 – 2 Cumulative importance 0.48 0.71 0.92 1 and with sampling areas of 1 4km (BGEDXP, 2009). Similarly, caliche as another cover type in the study area can obscure elemental concen- α (As) α (Au) α (Hg) α (Sb) trations in sediments as well. In order to remove the impact of caliche, Loadings on PC1 0.62 0.38 0.33 0.60 samples were collected from the eluvium under the layers of caliche in an interval of 1–2km(Xie et al., 2009). By means of X-ray fluores- cence, the samples were analyzed for 39 major, minor, trace and et al., 2004; XIGS, 2013). These data indicate that the Fe mineralization subtrace elements/oxides (Xie et al., 1997; Zhuang et al., 2003), whose might have occurred during Late Devonian to Early Carboniferous. concentrations were smoothed by averaging all samples collected within each 2 km × 2 km cell. Detailed information about the RGNR can be 2.2.6. Metallogenic model found in Xie et al. (1997). In this study, geochemical data are interpolat- Nowadays, the discussions on metallogeny of the Yamansu Fe de- ed by the inverse distance weighting (IDW) to delineate geochemical posit mainly focus on four opinions (Ma et al., 1997): (1) it resulted signatures of 39 elements/oxides across the space. from volcanic eruption and metasomatism of volcanic exhalations (Zhang and Ding, 1984); (2) it was volcanic-type associated with hydrothermal and pneumatolytic activities; (3) it was volcanic-type associat- 3. Methodology ed with volcano-hydrothermal and volcanic sedimentary processes; and (4) it resulted from volcanic eruption-sedimentary processes and 3.1. Ordinary PCA with superimposed hydrothermal alteration (Xu et al., 2011; Jiang et al., 2002). These opinions, although different, emphasize that the Fe PCA is a well-known multivariate statistical technique and has been mineralization was strongly associated with volcanic activity and was broadly used to examine relationships between variables. By orthogonal controlled by basement faults and volcanic edifices. transformation, a series of interrelated variables can be converted into The ore-forming process can be divided into two stages: the volcanic uncorrelated principal components (PCs) based on their covariance or eruption-sedimentation stage and the hydrothermal alteration stage correlation matrix (Horel, 1984; Loughlin, 1991). Eigenvalues of PCs (XIGS, 2013; Ma et al., 1997; Qi et al., 1985; Ding, 1990). In the volcanic are descendingly ordered. In general, the first few PCs account for eruption-sedimentation stage, oxygen isotope data from XIGS (2013) most variance in the original dataset (Panahi et al., 2004). Therefore, suggest that the iron was separated from a magma chamber in the PCA performs well in reducing dimensionality of datasets and is fre- form of FeCl3 and/or FeCl2 gases, which ascended to the surface, became quently utilized to increase information interpretability (Cheng et al., oxidized due to reaction with underground water and vapor flows from 2011; Christophersen and Hooper, 1992; Horel, 1984; Jolliffe, 2002; depth, and then ore-bearing fluids were progressively formed. Iron min- Singh and Harrison, 1985). According to the algorithm of PCA, PCs are eralization occurred after the ore-bearing fluids erupted and precipitat- linear combinations of the original variables. Each PC integrates input ed in sea basins (XIGS, 2013; Xu et al., 2011). In addition, sulfur isotope variables in a unique way and represents only partial information data suggest that ore-forming materials may have originated from the contained by the whole dataset (Abdi and Williams, 2010; Nomikos mantle (Wang, 2005; Zhang and Xie, 2001). and MacGregor, 1994). In other words, PCA can perform both as integra- tor of parts and decomposer of the whole. Since its introduction to the 2.3. Datasets geological field, PCA has been extensively applied to geochemical data for identification of geological bodies (e.g., ores, igneous rocks, strata, The geo-datasets employed for the current paper include a digitized etc.) (Cheng, 2007b; Grunsky, 1986; Grunsky et al., 2009; Grunsky geological map and stream sediment geochemical data, which were et al., 2014; Deutsch et al., 2015; Wang et al., 2010; Wang et al., collected and analyzed under the Chinese National Geochemical Map- 2011a,b; Zhao et al., 2012). From a geochemical perspective, different ping Project as part of the “Regional Geochemistry National Reconnais- geochemical distributions (i.e., elemental concentrations) are caused sance (RGNR) Project” (Xie et al., 1997; Zhao et al., 2012). In the arid by effects of diverse geo-processes (Jiang et al., 2006). Elemental assem- environment, aeolian sand and caliche are two main interference factors blages associated with geological bodies can be characterized by differ- for acquiring realistic elemental concentration values in sediments. Sed- ent PCs (i.e., linear combinations of corresponding geochemical iments at/near surface are strongly diluted by aeolian sand under effects distributions), which may represent geochemical signatures of the end of strong winds. Therefore, the elemental concentrations in sediments products of the geo-processes.

Table 2 PCA results of singularity indices of selected elements associated with the Yamansu Formation.

PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10

The Yamansu Formation Component variance 6.86 2.77 1.46 0.93 0.76 0.59 0.53 0.44 0.35 0.29 Cumulative importance 0.43 0.60 0.69 0.75 0.80 0.84 0.87 0.90 0.92 0.94

PC11 PC12 PC13 PC14 PC15 PC16

Component variance 0.24 0.22 0.20 0.16 0.13 0.08 Cumulative importance 0.95 0.96 0.98 0.99 0.99 1

α (Al2O3) α (Fe2O3) α (CaO) α (K2O) α (MgO) α (Na2O) α (SiO2) α (Ag) α (As) α (Cd) Loadings on PC1 0.04 0.33 0.24 −0.22 0.33 −0.03 −0.20 0.12 0.21 0.20

α (Co) α (Cu) α (Mn) α (Sb) α (V) α (Zn)

Loadings on PC1 0.32 0.31 0.31 0.15 0.34 0.30 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 111

Table 3 PCA results of singularity indices of selected elements associated with the felsic intrusions.

PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10

Intermediate-felsic intrusions Component variance 3.46 2.01 1.29 0.98 0.67 0.53 0.36 0.33 0.20 0.16 Cumulative importance 0.35 0.55 0.68 0.77 0.84 0.89 0.93 0.96 0.98 1

α (Al2O3) α (Ba) α (Be) α (CaO) α (Fe2O3) α (K2O) α (Li) α (MgO) α (Na2O) α (SiO2) Loadings on PC1 −0.77 −0.20 −0.14 0.44 0.35 −0.39 0.27 0.46 −0.15 −0.39

PCA can be done by eigenvalue decomposition of a data correlation spatially weighted correlation coefficients between any two variables matrix (Cheng, 2002; Cheng et al., 2011). According to the orthogonal as: transformation, eigenvectors of the matrix form an orthogonal Euclidian 1 X space with the PCs as axes, while the eigenvalues correspond to the var- W A −A B −B ij ij ij iances of the PCs. The PC with maximum eigenvalue (i.e., the greatest R ðÞ¼A; B rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimn r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ X X variance) is termed the first PC (PC1). The second PC (PC2) has the sec- 1 2 1 2 Wij Aij−A Wij Bij−B ond largest eigenvalue, and so forth (Christophersen and Hooper, mn mn 1992). Suppose a geochemical dataset consisting of p elemental concentrations (measured from a 2-dimensional map) is subjected to PCA. where Wij is the spatially weighting factor. In practice, Wij ranging from Then the correlation coefficient between any two elemental concentra- 0 to 1 (i.e., 0 ≤ Wij ≤ 1) is used. Wij = 0 implies that the location at (i, j)is tions is defined by the following equation (Cheng, 2006; Cheng et al., not important or irrelevant with respect to the target of interest, and its 2011; Wang and Cheng, 2008): effect will be removed from the calculation of the correlation coefficient. Wij = 1 implies that the location at (i, j) is very important or highly as- X 1 − − sociated with the target of interest, and its effect will be highlighted dur- Aij A Bij B fi RAðÞ¼; B rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimn r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1Þ ing the calculation of the correlation coef cient. Values of the spatially X X 1 2 1 2 weighting factors assigned to locations ranging from 0 b W b 1are A −A B −B ij mn ij mn ij based on their significance with respect to the target of interest. In

other words, the greater the Wij is, the more important is the location where Aij and Bij are the concentration values of the geochemical distri- (i, j). In addition, if Wij is constant across the entire sampling space, butions of elements A and B at location (i, j), respectively, and m and n then Eq. (5) will be same as the ordinary formula Eq. (1).IfWij is a bina- represent the number of rows and columns of these two variables. ry pattern with two values 1 and 0, then Wij is similar to using an ordi- The correlation coefficients of the p elemental concentrations will nary mask (i.e., on or off). Depended on spatial and/or intrinsic form a p × p symmetrical correlation coefficient matrix R (Cheng et al., characteristics of geological features, defining weighting factors is 2011). sometimes, subjective and need to be cautious. Based on this matrix, the eigenvalues and eigenvectors can be calcu- As described before, reasonable loadings of original variables of PCs latedbyEqs.(2) and (3), respectively: can be used to describe the geological features. If a spatially weighing factor is applied to enhance the geo-information supported by the ith ðÞ¼−λ ð Þ det R I 0 2 PC (PCi), then SWPCA will produce a new PCi (i.e., SWPCi)(Fig. 2). The eigenvector of SWPCi will be stretched along similar but not exactly ðÞ−λ ¼ ð Þ R I U 0 3 the same direction as PCi:

¼ þ þ ::: þ ð Þ where R is the correlation coefficient matrix of multivariate datasets, I is SWPCi b1iX1 b2iX2 bpiXp 6 the p × p identity matrix, and “det” is the determinant of the matrix − λ λ … T formed by R I. Each i (i =1,2, , p) calculated from the character- where [b1i, b2i, …, bpi, i =1,2,…, p] forms a new eigenvector matrix. … … istic equation of R is an eigenvalue, and U =[ai1, ai2, , aip, i =1,2, , p] Since the observations of original variables Xp are not changed by is the eigenvector matrix consisting of the PCs with m rows and n col- using the Wij, while the eigenvector matrix is derived from spatially umns. Mathematically, each PC can be expressed as a linear combina- weighted correlation coefficient matrix R⁎, the eigenvalues … tion of the p variables (i.e., X1, X2, , Xp)with: (i.e., variances) of PCi and SWPCi should be different (Fig. 2). As a result, SWPC1 does not necessarily retain the greatest variance as the ordinary ¼ þ þ … þ : ð Þ PCi a1iX1 a2iX2 apiXp 4 PC1 does and the eigenvectors and eigenvalues of other newly produced SWPCs by Eq. (6) are different (Fig. 2) accordingly. SWPC1 possessing smaller eigenvalue than PC1 can be considered as a rotation of PC1 in 3.2. SWPCA a new direction with interesting new information enhanced. Moreover, the eigenvectors of other SWPCs perpendicular to SWPC1 can have The geological significance of variables must be taken into consider- greater eigenvalues than of the ordinary PCs (Fig. 2). ation by using a spatially weighting factor (Cheng, 2006; Cheng et al., A geographically weighted PCA (GWPCA) is another commonly used 2011; Wang and Cheng, 2008; Xiao et al., 2012). Proposed by Cheng PCA extension. Both GWPCA and SWPCA can be applied to raster data (2000), SWPCA applies a spatially weighting factor by calculation of (i.e., geochemical distributions or remote sensing bands). However,

Table 4 Comparison of numbers of retainable PCs by using different thresholds of cumulative variance.

Threshold of cumulative variance (x%)

70% 75% 80% 85%

Number of PCA to retain (PCs) 1 (PC1) 1 (PC1) 2 (PC1, PC2) 3 (PC1, PC2, PC3) Number of SWPCA to retain (SWPCs) 1 (SWPC1) 2 (SWPC1, SWPC2) 3 (SWPC1, SWPC2, SWPC3) 3 (SWPC1, SWPC2, SWPC3) 112 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121

Velicer, 1986; Jolliffe, 2002). Jolliffe (1972) revised the criterion and

suggested 0.7 as the cut-off (i.e., λi ≥ 0.7) which is specifically designed for correlation matrices-based PCA. Selecting a cumulative percentage of total variation is another attempt to determine number of PCs in prac- tical. An x%isusedasathresholdtodefine the cumulative percentage of total variation of retainable PCs. The x% generally varies between 70% and 90% but it sometimes goes down to 50% when information contained by more PCs is of interest. Once the x% is set, the smallest number of PCs contributing to the total variation or information higher than the threshold (≥x%) are consequently determined. By this method, both statistical sense and information of interest are considered (Jolliffe, 2002); however, the decision made to choose a threshold is somehow arbitrary, since the number may vary significantly by changing of x% (i.e., the higher of x%, the more of retainable PCs) (Himes et al., 1994). The scree test (Cattell, 1966)defines the number of retainable PCs

from the scree plot (i.e., a plot of eigenvalues λi against number of PCs i, shown as a decreasing curve). When the slope of the plot demon-

strates a sharp transition, the number of corresponding PC (PCm) will be defined as the number of retainable PCs. In other words, the number Fig. 2. Schematic diagram of eigenvectors of principle components (PCs) and spatially of retainable PCs, m, is determined when the curves it joins are ‘steep’ to weighted principle components (SWPCs) in 2-dimensional scenario. Blue area denotes the left but ‘not steep’ to the right. Although it is easy to apply and al- the plot of observations on two variables X and Y. In this demonstration, the information contained by the first principal component is supposed to be enhanced. The comparison ready in common use, the selection to the cut-off point is even more between these two methods can be extended to n-dimensional scenario. subjective than the ‘x%’ method, especially when the slopes of the two curves on both sides are similar. Therefore, this method is often queried for its reliability (Jolliffe, 2002; Himes et al., 1994; Zwick and Velicer, 1986). Due to the length of paper, only a few methods are listed here. differences between SWPCA and geographically weighted PCA More criteria to decide the number of components can be found in (GWPCA) are necessary to be clarified. The GWPCA uses a moving win- Jolliffe (2002). dow weighting method. Observations (i.e., values) within the moving window are multiplied by their respective weights and then PCA is ap- 3.4. Singularity theory plied. Conducting the process for all locations, the loadings of input variables are continuously varied across the space; whereas, loadings of Geo-anomaly, termed as significant geological differences from sur- input variables by both ordinary PCA and SWPCA are constants roundings (Zhao, 1992) is often aroused by and indicative to minerali- throughout the whole area. Therefore, the GWPCA is a localized statis- zation. These differences may be present in broad respects, such as tics, while PCA and SWPCA are global ones. More detailed reviews re- fault system, lithological composition, elemental concentration, gravity garding PCA on spatial data can be found in Demšar et al. (2013). field, etc. and always spatially follow fractal/multifractal distributions. In recent years, many studies have been implemented to interpret these anomalies and further improve understandings of related geolog- 3.3. Criteria to retain optimal principal components ical issues (Carranza, 2009; Carranza and Sadeghi, 2010; Cheng, 2010; He et al., 2013; Luz et al., 2014; Shahriari et al., 2013; Wang et al., One of the concerns regarding the utilization of PCA is how to deter- 2010; Wang et al., 2011a, 2011b; Zhao et al., 2012, 2013; Zuo, 2011; mine the number of retainable PCs for further interpretation. To satisfy Zuo et al., 2012). Singularity theory (Cheng, 2007a) becomes a useful that, broadly discussed criteria includes Kaiser's rule (Kaiser, 1960), cu- tool in quantitative and qualitative characterization of geo-anomalies mulative percentage of total variation, Bartlett's test (Bartlett, 1950, caused by various geological processes. Taking geochemical distribution 1951), Scree test (Cattell, 1966), Horn's Parallel Analysis (Horn, 1965), as an example, a power-law relationship exists between a given area A and Minimum Average Partial (MAP) test (Velicer, 1976). Kaiser's rule and the elemental concentration C(A): proposed the criterion that retainable PCs should be with eigenvalues greater than 1 (i.e., λ ≥ 1). It also suggests that PCs with eigenvalues α i −1 ðÞ¼ 2 ð Þ less than 1 are not necessary to be further discussed since these PCs con- CA cA 7 tain less information than one of input variables. However, this criterion was queried due to only a few PCs were retained that may limit the uti- where c is a coefficient determining the magnitude of the power-law lization of PCA, because the last few PCs are often of interest (Zwick and function. The symbol stands for “expectation” implying the power–

Fig. 3. Spatial distribution of the spatially weighting factor. Euclidian distance of pixels from the intersections between the Yamansu Formation and felsic intrusions is currently used as the weighting factor in SWPCA. The farther is the pixel from the intersection the lower weighting value assigned to the pixel. The pixels located out of the extent of the Yamansu Formation are weighting 0. J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 113

Fig. 4. SWPCA model. In the SWPCA model, controlling factors (i.e., fault systems, the Yamansu Formation and felsic intrusions) and ore elements (Fe2O3, Co, Cu, Mn, Ni, Ti, V and Zn) are currently used as input variables. Weighting factor is defined in Fig. 3. law relationship usually holds true in a statistical sense (Cheng and calculated prior to the implementation of statistical analysis (i.e., PCA Zhao, 2011). If a log-transformation is applied to Eq. (7), it can be de- and SWPCA) for better delineation of geochemical signatures in the derived that: sert covered study area (Cheng, 2012; Zhao et al., 2012). Achieved singularity indices are the quantitative and qualitative characterization of LogCA½¼ðÞε c þ ðÞα−2 LogðÞε ð8Þ geochemical distributions, and describe the geochemical behaviors of their respective elements and oxides. The indices describe the spatial where ε is the size of the square area A, the singularity index α quantifies variations of concentration and are unitless. Moreover, calculation of the degree of singularity. In 2-dimension scenario, α varies roughly singularity indices results in an “open” data matrix that is suitable for in- around 2. Specifically, α b 2 termed as positive singularity implies en- version in multivariate data algorithms such as PCA. Therefore, current richment of elemental concentration in the given area; whereas α N 2 study does not further discuss log-ratio transformation before the im- termed as negative singularity implies depletion of elemental concen- plementation of PCA or SWPCA. tration. Since singularity theory had been introduced in many published studies, more detailed explanations are found in Cheng (2007a,b, 2010); Cheng and Zhao (2011), or other applications (Wang et al., 2011a, 4.1. SWPCA model 2011b; Wang et al., 2012; Wang et al., 2013a, 2013b; Xiao et al., 2012; Zhao et al., 2012, 2013; Zuo et al., 2009). Previous research indicates that the Fe mineralization can be sorted into four subclasses according to ore element assemblages: Fe deposits, 4. Potential mapping of Fe mineralization by SWPCA Fe–Mn deposits, Fe–V–Ti deposits, and Fe–Cu–Zn deposits (BGEDXP, 2009). Mapping of the spatial distributions of geo-anomalies of element Geochemical data often expressed as a close number system (i.e., 0– association is necessary for delineation of target areas. In this paper, 100%) is a typical compositional data. When statistical methods are ap- SWPCA is applied to stream sediment geochemical data to enhance plied to investigate compositional data, specific treatments like log-ratio geo-information associated with Fe mineralization in the eastern transformation are generally implemented to open the simplex prior to Tianshan district, China. The general process of SWPCA modeling in data analysis especially by multivariate methods (Buccianti, 2013; this area consists of input variable selection and definition of spatial Buccianti and Grunsky, 2014; Carranza, 2011; Egozcue et al., 2003; weights based on the metallogeny of volcanic-sedimentary Fe deposits. Grunsky et al., 2009; Grunsky et al., 2014; Wang et al., 2015a). In this The Fe-polymetallic mineralization in the eastern Tianshan district is paper, singularity indices for all elemental concentrations were generally controlled by three factors: fault systems, the Yamansu

Fig. 5. PCA results for recognition of fault systems by using singularity indices of geochemical data (i.e., As, Au, Hg, and Sb). A score map of PC1 overlaid withfaulttraces. 114 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121

Fig. 6. PCA results for recognition of the Carboniferous Yamansu Formation (C1y) by using singularity indices of geochemical data (Al2O3,CaO,Fe2O3,K2O, MgO, Na2O, SiO2,Ag,Cd,Cu,Zn, Co, Mn, V, As and Sb). A score map of PC1 overlaid with outcrops of the Carboniferous Yamansu Formation. volcanic strata and hydrothermal alteration associated with felsic intru- migration of Au. Under the effect of geo-processes (e.g., variations in sions. Most of the Fe deposits are located within the extent of the geo-stress, temperature, and physico-chemical condition), these ele- Yamansu Formation and were altered by hydrothermal fluids differen- ments tend to migrate with the hydrothermal fluids toward the surface tiated from felsic intrusions, based on which a spatially weighting factor and precipitate at favorable places. The places where migration ceased to highlight Fe mineralization is defined as follows. The first step is to may frequently be fracture zones or intersections of faults with different outline the intersections of The Yamansu Formation and felsic igneous directions (Yuan et al., 1979). In the eastern Tianshan district, the intrusions because the contact zones of these two features are optimal Kanggurtag–Huangshan shear zone (Fig. 1a) is the Au mineralization places for Fe mineralization. Secondly, Euclidean distances of the inter- belt, which corresponds with activation, migration and mineralization sections were created to determine a decay function for the weighting of Au and its paragenetic elements (As, Sb and Hg) in the fault systems. factor which means the further the location is from the intersection, The enrichment of these elements can produce geochemical anomalies the lower the weight assigned to the pixel. Thirdly, areas out of the at/near the surface, which may be linearly distributed along the fault Yamansu Formation, which do not possess great Fe mineralization po- traces and/or around the intersections of faults trending in different di- tential, were weighted as 0 and expelled from calculation of the correla- rections (Qian, 2009). tion coefficients (Fig. 3). Therefore, in the current SWPCA model (Fig. 4), Based on the tectono-geochemical properties of Au, As, Hg and Sb, the Euclidian buffer of the intersections between the Yamansu Forma- PCA was applied to integrate the geochemical anomalies of these ele- tion and the felsic intrusions confined within the extent of the Yamansu ments to recognize the spatial distribution of the fault systems Formation was used as the weighting factor. The spatial distributions of (Fig. 5). Comparing the PCs with the greatest eigenvalues, PC1 possesses the felsic igneous rocks, the fault systems, the Yamansu Formation, and 48% of the information contained in these four elements and is retained the geochemical distributions of ore elements (i.e., Fe, Co, Cu, Mn, Pb, Ti, for further interpretation (Table 1). According to the characteristics of V, and Zn) were used as input variables. By the SWPCA model, areas singularity indices, the four positively loaded elements in PC1 suitable for Fe-polymetallic mineralization associated with different (Table 1) imply the spatial distribution of the fault systems can be controlling factors can then be delineated. reflected by low PC1 scores. Overlaying with the fault traces derived from the geological database, the low PC1 scores are seen to be spatially 4.2. Identification of controlling factors coincident with the fault systems. Therefore, PC1 which reflects the spatial distribution of fault systems is accepted as an input layer for the 4.2.1. Fault system SWPCA model (Fig. 4). Stress difference is one of the main effects influencing hydrothermal fluid flow. Representing areas with abrupt decrease of geo-stress within 4.2.2. The Yamansu Formation geological bodies, the latticed fault systems, especially those with ten- Most of the Fe deposits in the eastern Tianshan district are hosted by sion fractures can produce a local decompression environment which Lower Carboniferous Yamansu volcanic strata which mainly consist of is beneficial to the convection of hydrothermal fluids. The hydrothermal submarine felsic–mafic lava, volcanoclastic rocks, terrigenous clastics, fluids extracted salts from the wall rocks and developed into brines and carbonate rocks (Hou et al., 2006; Ding, 1990; Xiao et al., 2004). during migration within the fault systems. This increase of salinity can Among these rock types, intermediate and mafic volcanic rocks are boost the solubility of metals (e.g., Hg, Sb, As, U, Pb, Zn, Cu, Ag, and believed to have provided ore sources. Therefore, rock forming oxides

V) in hydrothermal fluids. Being geochemically active fractions, Hg, Sb including Al2O3,CaO,Fe2O3,K2O, MgO, Na2O, and SiO2 are used to iden- and As are sensitive to variations in environment and are apt to be dis- tify the spatial distribution of the Yamansu volcanic strata. Minerals solved into or precipitated from the hydrothermal fluids. In addition, As with economic values in the Fe deposits include Fe-rich minerals and Sb are often paragenetically associated with Au. Acting as mineral- (e.g., magnetite, hematite and limonite) and other sulfide minerals izers, the geochemical behaviors of As, Sb and Hg can promote (e.g., chalcopyrite, galena, sphalerite, pyrrhotite, chessylite, and

Fig. 7. PCA results for recognition of the felsic and intermediate igneous rocks by using singularity indices of geochemical data (Al2O3,CaO,Fe2O3,K2O, MgO, Na2O, SiO2, Ba, Be, and Li). A score map of PC1 overlaid with outcrops of the intermediate and felsic and intermediate igneous rocks. J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 115

Fig. 8. Parameters of PCA and SWPCA results. The y-axis on the left side indicates the scree plots of eigenvalues of PCs and SWPCs; the y-axis on the right side displays the cumulative variance of PCs and SWPCs. molybdenite). The formation of these minerals in the Yamansu volcanic settings and absence of hydrothermal processes. Distinguishing the strata caused prominent enrichment of Ag, Cd, Cu, Zn, Co, Mn, V, which Yamansu Formation from other Carboniferous volcanic strata needs may represent geochemical anomalies of the corresponding elements more detailed work. In this paper, geochemical anomalies associated at/near surface (BGEDXP, 2009; Deng et al., 2006; Han et al., 2002; Lu with the Yamansu Formation discussed are conﬁned in the Aqishan– et al., 1995). Furthermore, as described in previous sections, because Yamansu volcanic belt. the eruption and sedimentation of volcanic lava were spatially controlled by the fault systems, the elements (i.e., As and Sb) formerly 4.2.3. Intermediate and felsic igneous rocks used to recognize the spatial distribution of fault traces are further ap- Hydrothermal processes are efﬁcient in enriching existing ores in plied to depict the extent of the Yamansu Formation which is linearly many cases. In the eastern Tianshan district, most of Fe deposits have stretched along the fault traces. Therefore, singularity indices of ele- been hydrothermally enriched and ore materials which were initially ments/oxides involved in identifying the Yamansu Formation are scattered in country rocks were accumulated by hydrothermal alter-

Al2O3, CaO, Fe2O3,K2O, MgO, Na2O, SiO2, Ag, Cd, Cu, Zn, Co, Mn, V, As ation (Ding, 1990). The hydrothermal ﬂuids were probably differentiat- and Sb. ed from felsic magma after the early stage of Fe mineralization.

Femic oxides (i.e., Fe2O3 and MgO) and felsic oxides (i.e., K2O, Na2O, Providing heat and hydrothermal fluids, felsic igneous rocks are be- and SiO2) are positively and negatively loaded on PC1, respectively, and lieved to be important for Fe exploration, especially in their contact PC1 possessing 43% of the total importance (Table 2). It corresponds to zones with carbonate rocks. To recognize the spatial distribution of the abundant representation of basalt, basalt tuff, breccias, dolerite, and the felsic igneous rocks, Ba, Be and Li were used in addition to the andesite in the Yamansu Formation. Loadings of the metallogenic ele- rock-forming oxides, because Ba and Be are abundant in felsic rocks ments (Ag, Cd, Cu, and Zn) with the same signs as femic oxides reflect whereas Li is abundant in maficrocks(BGEDXP, 2009). In our previous mineralization of these elements in basic igneous rocks in the Yamansu work (Zhao et al., 2012), felsic igneous rocks, especially those covered Formation. Iron family elements (i.e., Co, Mn and V) which show load- by overburden were identified. The results achieved previously are ings with the same signs as the femic oxides imply the concentration quoted for comparison (Fig. 7). PC1 with the greatest eigenvalue of corresponding elements in the Yamansu Formation. The semimetal (Table 3) accounting for 35% of the information contained by geochem- and mineralizer elements (i.e., As and Sb) presenting the same signs ical data was retained for analysis. Examining the loadings of all ele- as the femic oxides, metal metallogenic elements, and iron family elements/oxides (Table 3), the felsic components (i.e., Ba, Be, SiO2,K2O, ments means that in the Yamansu Formation they are located in linear Na2O) contribute negatively in PC1 whereas femic components (i.e., Li, and pinch-and-swell structures along the fault systems in the eastern Fe2O3, CaO and MgO) contribute positively in PC1. According to charac- Tianshan area. Except for K2O, Na2OandSiO2, all elements/oxides con- teristics of singularity indices, the high PC1 scores show the integration tribute positively to PC1. According to characteristics of singularity indi- results of felsic geochemical anomalies which can indicate the spatial ces, low PC1 scores (Fig. 6) delineate integrated geochemical anomalies distribution of the felsic igneous rocks (Fig. 7). of these elements and outline the spatial distribution of the Yamansu Formation. Compared with the geologic map (Fig. 1a), the Yamansu For- 4.3. Mapping of Fe mineralization mation is primarily distributed in the Aqishan–Yamansu volcanic belt, the outcrops of which well correspond to low values (Fig. 6). However, PCA and SWPCA were applied to map the potential of Fe mineraliza- in both the Xiaorequanzi area and Kanggur ductile shear zone, low PC1 tion in the eastern Tianshan district (Figs. 8–11). Loadings of elements/ scores are also observed. It is because of presences of other Carbonifer- oxides in both PC1 and SWPC1 present similar results. All input layers ous volcanic strata (e.g., Xiaorequanzi Formation) with very similar ele- are positively correlated (Fig. 9a), which implies that high scores of mentary composition as the Yamansu Formation. Infrequently occurred both PC1 (Fig. 9b) and SWPC1 (Fig. 9c) are suitable to reflect the Fe- Fe mineralization in these areas may be due to unsuitable tectonic polymetallic mineralization in the eastern Tianshan mineral district. 116 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121

Fig. 9. Results of PC1 and SWPC1. a. Loadings of selected input layers on PC1 and SWPC1. b. A score map of SWPC1 overlaid with outcrops of the Yamansu Formation. c. A score map of PC1 overlaid with outcrops of the Yamansu Formation.

However, different from the fault system and the Yamansu Formation, processes caused by hydrothermal ﬂuids differentiated from the felsic felsic igneous rocks spatially associated with the Fe mineralization in igneous rocks. an indirect way. Iron mineralization occurs in the outer contact zones Since patterns with low PC1 and SWPC1 scores correspond well rather than within felsic igneous rocks. Therefore, geochemical anoma- with known Fe deposits, it can be concluded that both PC1 and lies indicating the spatial distributions of felsic igneous rocks are nega- SWPC1 are indicative of Fe mineralization, especially for the volcanic tively associated with Fe mineralization. Felsic igneous rocks are sedimentary Fe mineralization in the Yamansu Formation. Areas indicated by low PC1 scores (Fig. 7) while the fault traces and the with high PC1 and SWPC1 scores in the Yamansu Formation but Yamansu Formation are coincident with their associated high PC1 without corresponding known Fe deposits can be delineated as scores (Figs. 5 and 6), respectively. These statistical results are in accor- targets for exploration of volcanic sedimentary Fe deposits. As dance with the regional Fe metallogenic model that the Fe mineraliza- explained previously, the purpose of employing a weighting factor tion are spatially distributed in and genetically associated with the in the SWPCA model is to highlight objective geo-information fault-controlled Yamansu Formation, and experienced alteration described by the ordinary PCA. From the results, SWPC1 scores J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 117

Fig. 10. Results of PC2 and SWPC2. a. Loadings of selected input layers on PC2 and SWPC2. b. A score map of SWPC2 overlaid with outcrops of the felsic intrusions. c. A score map of PC2 overlaid with outcrops of the felsic intrusions.

(Fig. 9b) show insigniﬁcant differences with PC1 scores (Fig. 9a), and its capability to interpret geo-anomalies is extended in the aspect of however, SWPC1 with greater contributions of the Yamansu Forma- number of retainable PCs. Several generally employed criteria to choose tion and Fe2O3 and less contribution of felsic igneous rocks is more retainable PCs were introduced in Section 3.3. In this paper, the cumula- methodologically reasonable than ordinary PC1. tive percentage of total variation (x%) which takes both statistical and geological senses into consideration is employed. A series of x% 5. Discussion (i.e., 70%, 75%, 80%, and 85%) were applied to cumulated importance of PCA and SWPCA (Table 4). Under the effect of weighting factor, the SWPCA, which was introduced as an extension of ordinary PCA, had eigenvectors of SWPCA can be seen as the rotation on that of PCA been utilized to enhance objective geo-anomalies in former studies, (Fig. 2). All SWPCs except the PC1 have higher eigenvalues than the weighting factors of which are usually deﬁned thoughtfully and with ordinary PCs. The number of retainable SWPCs is increased in compari- physical meanings. Utilization of SWPCA model is currently developed, son with PCA based on different thresholds (Table 4). Consequently, 118 J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121

Fig. 11. Results of PC3 and SWPC3. a. Loadings of selected input layers on PC3 and SWPC3. b. A score map of SWPC3 overlaid with outcrops of the felsic intrusions. c. A score map of PC3 overlaid with outcrops of the felsic intrusions.

more PCs with geological meanings are retained to support further intrusion (Fig. 11a). However, due to the limitations of their eigen- interpretation. values, PC2 and PC3 which are supportive of these conclusions cannot These retainable and interpretable SWPCs provide multiple or de- be retained only if the threshold of cumulative importance is set tailed descriptions for geological bodies and geo-processes. Loadings above 85%. On the contrary, eigenvalues of both SWPC2 and SWPC3 of input variables on both PC2 and PC3 exhibit physico-chemical mean- are greater than those of PC2 and PC3 (Fig. 8), and the first three compo- ings. Considering the characteristics of singularity indices, the associa- nents can be preserved just for the threshold reaches 80% (Table 4). tion of V, Ti, Ni, Fe, Co, as well as felsic igneous rocks in PC2 signifies Therefore, instead of lack of new information provided by ordinary mineralization of iron family elements in and/or related to felsic intru- PC2 and PC3, the geo-information described by SWPC2 and SWPC3 sions (Fig. 10a); the association of Zn, Fe, Cu, Mn, and felsic intrusions can be used to indicate mineralization of iron family elements (Fe–V– signifies mineralization of Fe–Cu–Zn–Mn in and/or related to felsic Ti–Ni–Co) and Fe–Cu–Zn–Mn in felsic intrusions, respectively. Iron J. Zhao et al. / Journal of Geochemical Exploration 164 (2016) 107–121 119 family elements in SWPC2 contribute negatively. Consequently, the pat- References terns with high SWPC2 scores represent the spatial distribution of min- Abdi, H., Williams, L.J., 2010. Principal component analysis. 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