Geochemical mineralization probability index (GMPI): A new approach to generate enhanced stream sediment geochemical evidential map for increasing probability of success in mineral potential mapping

Journal of Geochemical Exploration 115 (2012) 24–35

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Geochemical mineralization probability index (GMPI): A new approach to generate enhanced stream sediment geochemical evidential map for increasing probability of success in mineral potential mapping Mahyar Yousefi a,⁎, Abolghasem Kamkar-Rouhani a, Emmanuel John M. Carranza b a b

School of Mining, Petroleum and Geophysics, Shahrood University of Technology, P.O. Box 316, Shahrood, Iran Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, The Netherlands

a r t i c l e

i n f o

Article history: Received 17 November 2011 Accepted 4 February 2012 Available online 10 February 2012 Keywords: Stream sediment Geochemical evidential map Geochemical mineralization probability index Anomaly intensity Exploration success Mineral potential mapping

a b s t r a c t Integration of stream sediment geochemical data with other types of mineral exploration data, especially in knowledge-driven mineral potential mapping (MPM), is a challenging issue. In this regard, multivariate analyses (e.g., factor analysis) are generally used to extract significant anomalous geochemical signature of the mineral deposit-type sought. In this study, we used stepwise factor analysis to generate a geochemical mineralization probability index (GMPI) through a new approach to create stream sediment geochemical evidential maps. GMPI is a weight that can be mapped, and hence, can be used as an evidential map in MPM. Using stepwise factor analysis enhances recognition of anomalous geochemical signatures, increases geochemical anomaly intensity and increases the percentage of the total explained variability of data. With the GMPI, we developed a new data-driven fuzzification technique for (a) effective assignment of weights to stream sediment geochemical anomaly classes, and (b) improving the prediction rate of mineral potential maps and consequently increasing exploration success. Furthermore, the predictive capacity of each stream sediment geochemical sample for prospecting the deposit-type sought upstream of its location can be evaluated individually using GMPI. In addition, the GMPI can be used efficiently in knowledge-driven MPM as a new exploratory data analysis tool to generate a weighted evidential map in less explored areas. In this paper, we successfully demonstrated the application of GMPI to generate a reliable geochemical evidential map for porphyry-Cu potential mapping in an area in Kerman province, southeast of Iran. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Mineral potential mapping (MPM) is a multi-step process of generating evidential maps (i.e., extracting and weighting of features indicating the presence of the mineral deposit-type sought), combining evidential maps, and finally ranking promising target areas for further exploration. Knowledge- and data-driven methods are two types of approaches to assign evidential weights and combine various evidential maps for MPM (Bonham-Carter, 1994; Carranza, 2008). Integration of stream sediment geochemical data with other types of mineral exploration data in knowledge-driven MPM is a challenging issue that needs careful analysis of multi-element geochemical anomalies as evidence of the presence of the deposit-type sought. Analysis of stream sediment samples can reveal various geochemical associations, some of which can be considered as surficial geochemical signature of the deposit-type sought. A fundamental problem with regard to stream sediment geochemistry is to determine a multi-element ⁎ Corresponding author at: Shahrood University of Technology, P.O. Box 316, Shahrood, Iran. Tel.: +98 9113385443; fax: +98 273 3395509. E-mail address: M.Yousefi[email protected] (M. Yousefi). 0375-6742/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.gexplo.2012.02.002

anomalous signature of the deposit-type sought. Multivariate analyses are especially useful for that purpose because the relative importance of the combinations of geochemical variables can be evaluated. There are many studies that have used multivariate methods for analysis of geochemical exploration data (e.g., Chandrajith et al., 2001; Grunsky et al., 2009; Halfpenny and Mazzucchelli, 1999). Factor analysis, as one of the methods of multivariate analysis, has been widely used for interpretation of stream sediment geochemical data (e.g., Borovec, 1996; Helvoort et al., 2005; Kumru and Bakac, 2003; Reimann et al., 2002; Sun et al., 2009). The principal aim of factor analysis is to explain the variations in a multivariate data set by a few factors as possible and to detect hidden multivariate data structures (Johnson and Wichern, 2002; Krumbein and Graybill, 1965; Tripathi, 1979). Thus, theoretically, factor analysis is suitable for analysis of the variability inherent in a geochemical data set with many analyzed elements. Consequently, factor analysis is often applied as a tool for exploratory data analysis. Reimann et al. (2002) and Helvoort et al. (2005) state some of the most critical questions to be considered when performing factor analysis, namely: 1) How many factors should be extracted? 2) Which elements should be included in the factor model? 3) How can the information contained in many single element maps be presented in just a few factor maps?

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Fig. 1. Location of study area in Iran (a), and simplified geological map (b).

In this study, a large regional-scale geochemical data set containing many samples is used in an attempt to answer some fundamental questions with regard to the use of factor analysis in generating stream sediment geochemical evidential maps for MPM. Here, we applied stepwise factor analysis to enhance geochemical anomalies and to generate weighted geochemical evidential maps, so as to increase the prediction rate of mineral potential maps. If an enhanced geochemical evidential map is combined with other evidential maps (e.g., geological and geophysical evidential maps) in MPM, it provides more reliable target areas for further exploration of the deposit-type sought. Hence, the probability of success in MPM is increased. In MPM, especially in knowledge-driven modeling techniques, there are still some challenging aspects in generating stream sediment geochemical evidential maps with strong predictive capacity. The weighting of geochemical anomaly classes, for example, is a challenging aspect discussed in this paper. Therefore, the aim of this paper is to develop a new approach to generate stream sediment geochemical evidential map for integration with other evidential maps in MPM. In this approach, we introduced a geochemical mineralization probability index (GMPI), which is consistent with the concept of probability, whereby a method for weighting classes of geochemical anomalies has been adapted using stepwise factor analysis and the theory of probability. In this study, we selected an area in the Kerman province, southeast of Iran, as a case study. Geochemical analyses of 1804 stream

sediment samples for ten elements (Cu, Au, Mo, Zn, Pb, As, Sb, Ni, Cr, Co), collected by the Geological Survey of Iran (GSI), have been used to test the proposed approach using the GMPI. In all geochemical data distribution maps described in this paper, the cumulative percentile equivalent to 95% frequency has been considered as a reference value/threshold to evaluate and compare the efficiency of the methods discussed in this research. Table 1 Rotated component matrix of factor analysis in first step: loadings in bold represent the selected factors based on threshold of 0.6 (the absolute threshold value). Component

Zn Pb Cu As Sb Mo Au Ni Cr Co Eigen-value Variance (%) Cumulative variance (%)

F1

F2

F3

F4

.132 −.445 .017 .122 −.419 −.178 −.105 .842 .813 .785 3.192 31.9 31.9

.872 .794 .337 −.109 .559 .212 −.108 −.170 −.268 .250 1.896 18.9 50.8

.048 .012 .209 .867 −.553 .766 −.112 −.137 .325 −.048 1.647 16.5 67.3

.121 −.033 .751 −.065 .179 .162 .806 −.207 −.198 .398 1.112 11.1 78.4

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Fig. 2. Component plot in rotated space in first step of factor analysis.

A predictive model of mineral prospectivity must pertain to only one type of mineral deposit (Carranza, 2008). This paper focuses on porphyry-Cu deposits. This type of mineral deposit has been discussed in many publications (e.g., Boomeri et al., 2009; Cline and Bodnar, 1991; Cooke et al., 2005; Guangsheng et al., 2007; Gustafson and Hunt, 1975; Sillitoe, 1993; Singer et al., 2005). There are many studies that have attempted to explore and to characterize porphyry-Cu deposits. According to previous exploration works and several published papers about porphyry-Cu deposits, the suite of important geochemical indicator elements for prospecting this type of mineral deposit is Cu–Au–Mo–Zn–Pb–As–Sb–Ag–Fe–S (e.g. Cooke et al., 2005; Halter et al., 2004; Landtwing et al., 2005; Liu and Peng, 2003; Singer et al., 2005; Sotnikov et al., 2007; Weixuan et al., 2007; Xiaoming et al., 2007; Yang et al., 2009). The GMPI representing the presence of porphyry-Cu deposits can be used in combination with other evidential maps compiled in a GIS (Geographic Information System) for MPM. Each of the stages to generate a map of GMPI as a weighted geochemical evidential map, which can be used in MPM, is discussed here with demonstrations of its applications to generate geochemical evidential map of potential for porphyry-Cu deposits in the case study area. 2. The study area and porphyry-Cu mineralization Porphyry-Cu deposits are formed from post-magmatic hydrothermal fluids related to granitoid porphyritic intrusive rocks commonly having silicate alteration and with Cu, Mo, Pb, Zn and S geochemical

halos (Arribas, 1995; Singer et al., 2005). Magmatic-hydrothermal processes associated with porphyry-Cu deposits have been investigated in great detail (e.g., Cline and Bodnar, 1991; Dilles, 1987; Gustafson and Hunt, 1975; Hezarkhani et al., 1999; Sillitoe, 1993). These deposits are believed to form usually in island- and continental-arc settings (Billa et al., 2004; Cooke et al., 2005; Mitchell, 1973; Sillitoe, 1972), and are considered as among the most important primary sources of Cu (Halter et al., 2004). These deposits can be classified, according to the composition and association of ore elements, as (Guangsheng et al., 2007): (a) porphyry-Cu deposit, (b) porphyry Cu-Au deposit, and (c) porphyry Cu-Mo deposit. These three types of porphyry-Cu deposits, which are all found in Iran, can occur in similar geological settings and can be present in local and regional metallogenic belts. The study area with a surface of ca. 5000 km2 covering two 1:100,000 scale quadrangle maps, named Sarduiyeh and Baft, in the Kerman Province, is situated in the southern part of the Urumieh–Dokhtar Volcanic Belt (Fig. 1a). This belt has great potential for porphyry-Cu deposits as far as the geology and exploration of the belt suggest (e.g., Atapour and Aftabi, 2007; Boomeri et al., 2009; Hezarkhani, 2006a, 2006b; Ranjbar et al., 2004; Tangestani and Moore, 2002a). The Urumieh– Dokhtar Volcanic Belt was formed as a result of the subduction of the Arabian Plate beneath central Iran during the Alpine orogeny (Berberian and King, 1981; Hezarkhani, 2006a; Niazi and Asoudeh, 1978). The lithostratigraphic units of the study area are categorized in eight classes (Fig. 1b). Paleozoic metamorphic rocks, including phyllites, sericitic schists and marbles, and Cretaceous mélanges, including diabases, spilitic tuffs, cherts, serpentinites, harzburgites, sandstones, gabbros and keratophyres, are the oldest lithologic units in the study area. Eocene volcanic rocks are represented by pyroclastics, trachyandesites, trachybasalts, andesite-basalts, andesite lavas, tuffaceous sediments, rhyolites, rhyolite tuffs, agglomerate tuffs, agglomerates, ignimbrites, basaltic rocks and andesites. Sedimentary rocks of Eocene age in the volcano-sedimentary complex consist mainly of sandstones, siltstones, conglomerates and limestones. Intrusive rocks include granodiorites, quartz-diorites, diorites, dioriteporphyry, granite-porphyry and granites with ages of Cretaceous, Eocene, Oligocene–Miocene and Neogene. Oligocene–Miocene sediments consist mainly of conglomerates, siltstones and sandstones. Neogene volcanic rocks mainly include pyroclastics, andesitic agglomerates, dacites, rhyodacites and andesites, which overly Eocene volcano-sedimentary rocks. Quaternary alluvial deposits, terraces, clays and gravel fans are the youngest lithologic units in the study area (Dimitrijevic, 1973; Dimitrijevic and Djokovic, 1973; Sridic et al., 1972; Zolanj et al., 1972). In the study area, there are 32 known occurrences of porphyry-Cu deposits. We used these deposits as a set of testing samples to evaluate efficiency of the GMPI for prospecting unknown porphyry-Cu deposits and to provide empirical proof for increasing the prediction rate of mineral potential maps using GMPI versus using ordinary factor analysis.

Fig. 3. Distribution map of factor score F1 (Ni-Cr-Co): percentile in symbol form (left) and interpolated values (right).

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Fig. 4. Distribution map of factor score F2 (Zn-Pb): percentile in symbol form (left) and interpolated values (right).

Fig. 5. Distribution map of factor score F3 (As-Mo): percentile in symbol form (left) and interpolated values (right).

3. Methods 3.1. Stepwise factor analysis Just like many other statistical techniques, factor analysis requires normal (or symmetric) distribution of data. However, it is now well known among geochemists that regional geochemical data practically never show a normal distribution (Reimann and Filzmoser, 2000). In addition, stream sediment geochemical data are compositional data (Filzmoser et al., 2009), meaning that they represent a closed number system in which individual variables are not independent of each other but are parts of a whole (Carranza, 2011; Filzmoser et al., 2009). Filzmoser et al. (2009) examined both logratio- and ln-transformed geochemical data and proved that logratio-transformation can yield approximately symmetric data distributions compared to ln-transformation. Filzmoser et al. (2009) and several researchers (e.g., Aitchison and Egozcue, 2005; Reimann et al., 2008; Templ et al., 2008) have discussed the theoretical advantage of isometric logratio (ilr) transformation (Egozcue et al., 2003) over other logratio-transformations for the statistical analysis of geochemical data sets. Carranza (2011) has demonstrated that ilr-

transformation, compared to ln-transformation, for the case of stream sediment geochemical data, improves the enhancement of anomalous multi-element associations reflecting the presence of mineralization. In the present study, we examined ln- and ilr-transformed data. We found that ilr-transformation results in approximately symmetric distributions for the stream sediment element data in the study area. Consequently, we used the ilr-transformed data of Cu, Au, Mo, Zn, Pb, As, Sb, Ni, Cr and Co in factor analysis. We used the principal component analysis (PCA) for extraction of factors. Furthermore, we applied varimax rotation of factors (Kaiser, 1958). Then, we used a two-step factor analysis to extract components representing anomalous multi-element geochemical signatures of the deposit-type sought. In the first step, factor analysis has yielded four rotated components, each with eigenvalues greater than 1 (Table 1). Factor F1 represents a Ni–Cr–Co association, factor F2 represents a Zn–Pb association, factor F3 represents an As–Mo association and factor F4 represents a Cu– Au association. For better illustration of extracted factors, the factor plot in rotated space is shown in Fig. 2. Factor analysis allows us to calculate a single value for each factor. For example, instead of analyzing separate element maps, we can

Fig. 6. Distribution map of factor score F4 (Cu-Au): percentile in symbol form (left) and interpolated values (right).

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Table 2 Rotated component matrix of factor analysis in second step of factor analysis: loadings in bold represent the selected factors based on threshold of 0.6 (the absolute threshold value). Component

Zn Pb Cu As Mo Au Eigen-value Variance (%) Cumulative variance (%)

F1

F2

F3

.850 .888 .278 −.161 .227 −.048 1.961 32.7 32.7

.025 .022 .276 .861 .795 −.139 1.386 23.1 55.8

.141 .018 .698 −.097 .164 .880 1.110 18.5 74.3

establish a linear relationship (factor) among variables and plot a single map (factor score (FS) map) showing the distribution of such relationship. Because of the presence of indicator elements Cu and Au, the factor F4 is considered an anomalous multi-element geochemical signature reflecting the presence of porphyry-Cu deposits. Hence, locations with high F4 FSs can be defined as exploration targets for porphyry-Cu deposits. Distribution maps of FSF1 (Ni–Cr–Co), FSF2 (Zn–Pb), FSF3 (As–Mo), and FSF4 (Cu–Au) are represented as symbol plots and interpolated values (Figs. 3, 4, 5 and 6, respectively). Because the purpose of this study is to compare the results of GMPI method and ordinary factor analysis, we considered the cumulative percentile of 95% as the threshold value for separating anomaly and background samples in a distribution map of GMPI. Each of the distribution maps for FSF1, FSF2, FSF3 and FSF4 (Figs. 3–6) illustrates some small areas as promising exploration targets (those with values greater than the 95% cumulative percentile) as anomalies of a multi-element association that may or may not overlap with anomalies of other multi-element associations. Considering these geochemical distribution maps, the following important questions can be posed. The first question is: If a mineral potential map is obtained by combining individual FS maps into a single geochemical predictive map, which locations of the study area should be selected as target areas for further exploration of the deposit-type sought? We posed this question because in factor analysis the usual practice is to employ just one of the factors obtained, but useful information can be lost by omitting other factors. If we use all components, each with eigenvalues greater than 1, another question can be raised. That is: Which method(s) can be used to properly combine the FS maps? In addition to the foregoing questions, some problems still remain because of the mathematical basis of factor analysis as follows. In calculating the FS for each sample, here factors F1, F2, F3 and F4, the value of concentration of other elements can have negative influence on FS. This means that in a certain factor, elements with positive association are distinguished but there are some other elements having positive associations with other factors or have negative association with any of the factors even if such elements were used in calculating FSs of each sample based on the mathematical function of factor analysis (Table 1). An attempt is made to answer the question with regard to which elements have the largest influences on the results of factor analysis, and which area should be selected for further exploration. To answer the questions above, we can reduce the number of factors and increase the anomaly intensity using stepwise factor analysis. Increasing anomaly intensity means that the number of adjacent anomalous samples in a catchment has increased with respect to the total number of anomalous samples in the study area. In order to achieve this, the data for Ni, Cr and Co, which have strong positive correlations in factor F1, were omitted in the second factor analysis because the Ni–Cr–Co association is likely due largely to a lithologic

Fig. 7. Component plot in rotated space in second step of factor analysis.

unit (i.e., mélange) having no relationship to porphyry-Cu deposits in the study area (Fig. 3). In the second factor analysis, the data for Sb, which do not have positive associations with elemental data in each of the four factors, are omitted as well. Then, results of the second factor analysis of the remaining geochemical data were used to calculate new FSs for each sample. The rotated component matrix and the component plot in rotated space for the second factor analysis are shown in Table 2 and Fig. 7. Factor F1 represents a Zn–Pb association, factor F2 indicates a strong positive association between As and Mo, and factor F3 shows a Cu–Au association. According to Tables 1 and 2, the total variance relevant to the CuAu association, which is a significant indicator of porphyry-Cu deposits, has been increased from 11.11% in the first factor analysis to 18.5% in the second factor analysis. Likewise, the total variances relevant to the Zn–Pb and As–Mo associations increased from 18.9% and 16.5% in the first factor analysis to 32.7% and 23.1%, respectively, in the second factor analysis. Considering the results of the stepwise factor analysis, the number of factors has been reduced from four (in the first factor analysis, Table 1) to three (in the second factor analysis, Table 2). Consequently, through stepwise factor analysis whereby poor indicator geochemical components and elements are removed from the data, not only the number of factors (variables) has been decreased but also the total variance related to each factor has been increased. Moreover, separation of three variables (F1, F2 and F3) has been enhanced (Fig. 7). Hence, stepwise factor analysis is more effective than ordinary factor analysis in identifying and extracting significant indicator variables, and in increasing the variance explained by each factor. After the first factor analysis using all elemental data, elements that are poor and good indicators of the presence of porphyry-Cu mineralization can be

Table 3 The GMPI values corresponding to cumulative percentiles of 99%, 97.5%, 95%, 90%, 84% and 50% frequency for Cu-Au, As-Mo and Zn-Pb indicator components. Percentile

GMPIZn-Pb

GMPIAs-Mo

GMPICu-Au

99% 97.5% 95% 90% 84% 50%

0.938 0.863 0.80 0.736 0.676 0.476

0.917 0.873 0.833 0.784 0.731 0.508

0.971 0.926 0.866 0.774 0.694 0.459

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Fig. 8. GMPI distribution map for Zn-Pb indicator component: percentile of GMPI in symbol form (left) and interpolated GMPI values (right).

Fig. 9. GMPI distribution map for As-Mo indicator component: percentile of GMPI in symbol form (left) and interpolated GMPI values (right).

omitted and retained, respectively, in the second factor analysis. Thus, all of the components in the second factor analysis can be called ‘indicator components’. Accordingly, the elements Zn, Pb, As, Mo, Au and Cu are good indicators of the presence of porphyry-Cu mineralization in the study area. Examples of using these elements for studying porphyry-Cu mineralization can be found in several publications (e.g., Arribas, 1995; Cooke et al., 2005; Halter et al., 2004; Landtwing et al., 2005; Liu and Peng, 2003; Singer et al., 2005; Sotnikov et al., 2007; Weixuan et al., 2007; Xiaoming et al., 2007; Yang et al., 2009).

3.2. GMPI of indicator components In each of the indicator components obtained in the second factor analysis, elements with positive associations are distinguished (Table 2) while other elements still have positive associations with other indicator components. Hence, a third factor analysis can be carried out to calculate new FSs for each stream sediment sample. In this study, the third factor analysis was carried out three times, each time

using just elements that are positively associated to an indicative component. Thus, three sets of FSs were obtained: 1 FSs of Au–Cu indicator component for each sample based on just Au and Cu input data; 2 FSs of As–Mo indicator component for each sample based on just As and Mo input data; 3 FSs of Zn–Pb indicator component for each sample based on just Zn and Pb input data. After the FSs of each sample, weights should be assigned to each sample to represent probability of the presence of the deposit-type sought upstream of the sample. The weights are here called the GMPI. In ordinary factor analysis, the response variable is continuous and unbounded, meaning that the predicted response variable can take on any value. However, values outside the [0, 1] range are inappropriate if the response variable relates to probability. Thus, ordinary factor analysis is inappropriate for studies wherein the response variable is binary (present or absent) because the predicted response

Fig. 10. GMPI distribution map for Cu-Au indicator component: percentile of GMPI in symbol form (left) and interpolated GMPI values (right).

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M. Yousefi et al. / Journal of Geochemical Exploration 115 (2012) 24–35 Table 4 Final GMPI values of porphyry copper mineralization for cumulative percentile of 99%, 97.5%, 95%, 90%, 84% and 50% frequency calculated based on the final data set of GMPI values in Eqs. (5)a–(5)h. Percentile Percentile Percentile Percentile Percentile Percentile 99% 97.5% 95% 90% 84% 50% GMPIPorphyry Cu 0.975

0.938

0.888

0.839

0.660

0.477

where Fs is the factor score of each sample per indicator component obtained in a factor analysis. Thus, to calculate the GMPI of indicator components, i.e. Zn–Pb, As–Mo and Cu–Au components for stream sediment geochemical samples, the following equations are used. GMPIZnPb ¼

eFsZnPb 1 þ eFsZnPb

ð2Þ

GMPIAsMo ¼

eFsAsMo 1 þ eFsAsMo

ð3Þ

GMPICuAu ¼

eFsCuAu 1 þ eFsCuAu

ð4Þ

The GMPI is, therefore, a fuzzy weight of each stream sediment geochemical sample for each indicator component. In this way, the weights of different classes of evidential maps are calculated (not judged by the analyst) based on the FSs of samples per indicator component obtained in the stepwise factor analysis. Values of the GMPI corresponding to cumulative percentiles of 99%, 97.5%, 95%, 90%, 84% and 50% were determined for the Cu–Au, As–Mo and Zn–Pb indicator components (Table 3) for mapping purposes. In this paper, the distributions of GMPIs for the Zn–Pb, As–Mo and Cu–Au indicator

Fig. 12. GMPI distribution map of porphyry copper mineralization in symbol form based on threshold 0.888.

Fig. 11. Prediction rates of the GMPI distribution map, the first and second step factor score distribution maps with respect to the known porphyry copper occurrences in cumulative percentiles of 99%, 97.5%, 95%, 90%, 84% and 50% frequency for Zn–Pb (a), As– Mo (b) and Cu–Au (c) indicator components.

must be in the interval [0, 1]. In order to constrain the values of the predicted response variable within the unit interval [0, 1], Cox and Snell (1989) recommended to use a logistic model in order to represent the probability. Hence, to calculate the GMPI the logistic function has been used to fuzzify FSs of each sample per indicator component, thus:

GMPI ¼

eFs 1 þ eFs

ð1Þ

Fig. 13. Prediction rates of Cu mineral occurrences using different GMPI indicator components.

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components are represented as symbol plots and interpolated values (Figs. 8, 9 and 10, respectively). A value of the GMPI corresponding to cumulative percentile of 95% frequency was selected as the threshold value to separate anomalous and background samples, like in the FS distribution maps (Figs. 3–6). To demonstrate the superiority of the GMPIs over FSs from ordinary factor analysis, we compared the distribution maps of GMPIPb–Zn, GMPIAs–Mo and GMPICu–Au (Figs. 8, 9 and 10, respectively) with the corresponding FS distribution maps FSPb–Zn, FSAs–Mo and FSCu–Au obtained from the first factor analysis (Figs. 4, 5 and 6, respectively) and their prediction rates with respect to known porphyry-Cu occurrences (Fig. 11). The results of the comparisons show that some samples in a GMPI distribution map are classified as anomalous but in the corresponding FS distribution map those samples are classified as background, and vice versa. In Fig. 11a, the prediction rate of the GMPIZn–Pb map with respect to known porphyry-Cu occurrences is

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higher than that of the FSZn–Pb map obtained from either the first factor analysis or the second factor analysis. In Fig. 11b, the prediction rate of the GMPIAs–Mo map is higher than that of the FSAs–Mo map obtained from either the first factor analysis or the second factor analysis. In Fig. 11c, the prediction rate of the GMPICu–Au map is higher than that of the FSCu–Au map obtained from either the first factor analysis or the second factor analysis. It is also shown in Fig. 11 that the prediction rates of the FS maps obtained from the second factor analysis are generally higher than those of the FS maps obtained from the first factor analysis. In addition, the anomaly intensity has been increased, especially in the downstream of known mineral occurrences (compare Figs. 4 and 8, Figs. 5 and 9, and Figs. 6 and 10). These results illustrate the superiority of the GMPI approach over ordinary factor analysis in enhancing exploration success. Hence, the GMPIs based on an indicator component can be considered values of significant anomalous geochemical signatures for enhancing exploration success.

4. Results 4.1. GMPI of porphyry-Cu mineralization Although the GMPICu–Au is an effective multi-element signature of porphyry-Cu mineralization, the importance of the GMPIZn–Pb and GMPIAs–Mo to prospect this kind of mineralization should not be neglected as shown in Figs. 8–11. In fact the GMPIs of the indicator components (i.e., GMPIPb–Zn, GMPIAs–Mo and GMPICu–Au) are all important for prospecting porphyry-Cu deposits, but because of differences in chemical and physical mobility of the elements in stream sediments the elements do not have the same levels of anomaly in the same stream sediment sample. This means that for a certain porphyry-Cu deposit, samples with anomalous concentrations of every element are not located in the same positions downstream of that deposit. Therefore, with respect to a certain porphyry-Cu deposit, samples with anomalous values of GMPIPb–Zn, GMPIAs–Mo and GMPICu–Au are expected to be located differently downstream of that deposit. Therefore, an attempt should be made to find a way to use more indicator components of the deposit-type type sought as a general geochemical index. If just one of the GMPI of the three indicator components (i.e., GMPIPb–Zn, GMPIAs–Mo or GMPICu–Au) is used to generate a map of promising exploration target areas, the GMPI of the other two indicator components are omitted even if they are significant geochemical signatures of mineralization (see Fig. 11). Because anomalous area defined by each of the three GMPI distribution maps may or may not overlap (Figs. 8–10), one question arises: Which method(s) should be used to combine individual maps of GMPI into a single geochemical evidential map for MPM? That means we should find a way to combine the GMPIPb–Zn, GMPIAs–Mo and GMPICu–Au maps into a single geochemical evidential map. To make a binary map of promising areas (e.g., Bonham-Carter, 1994; Carranza, 2008), the high values in the GMPI maps, for example ≥95% cumulative percentile, can be extracted from each of three binary GMPI maps. Then “OR” or “AND” Boolean operator can be used to generate final promising areas of porphyry-Cu mineralization. However, the promising areas may be erroneously large or small while the fuzzy weights of each stream sediment sample are ignored. Hence, we experimented with the following mathematical expressions to derive the final integrated GMPI values of porphyry-Cu mineralization using the above-mentioned three indicator components for each stream sediment sample in different situations, thus:

GMPIðporphyryCuÞ

8 GMPI > > > GMPICuAu > > ZnPb > > > GMPIAsMo > > < AverageðGMPICuAu ; GMPIAsMo Þ ¼ > > AverageðGMPICuAu ; GMPIZnPb Þ > > > > AverageðGMPIZnPb ; GMPIAsMo Þ > > > AverageðGMPIZnPb ; GMPICuAu ; GMPIAsMo Þ > : AverageðGMPIZnPb ; GMPICuAu ; GMPIAsMo Þ

If If If If If If If If

GMPICuAu >¼ 0:866 and GMPIZnPb andb0:8 and GMPIAsMo b0:833 GMPIZnPb >¼ 0:8 and GMPICuAu b0:866 and GMPIAsMo b0:833 GMPIAsMo >¼ 0:833 and GMPIZnPb b0:8 and GMPICuAu b0:866 GMPICuAu >¼ 0:866 and GMPIZnPb b0:8 and GMPIAsMo >¼ 0:833 GMPICuAu >¼ 0:866 and GMPIZnPb >¼ 0:8 and GMPIAsMo b0:833 GMPICuAu b0:866 and GMPIZnPb >¼ 0:8 and GMPIAsMo >¼ 0:833 GMPICuAu >¼ 0:866 and GMPIZnPb >¼ 0:8 and GMPIAsMo >¼ 0:833 GMPICuAu b0:866 and GMPIZnPb b0:8 and GMPIAsMo b0:833

9 ðaÞ > > > ðbÞ > > > > ðcÞ > > > = ðdÞ ð5Þ ðeÞ > > > ðf Þ > > > > > ðgÞ > > ; ðhÞ

The foregoing equations for obtaining a final GMPI map of porphyry-Cu mineralization represent three different categories or situations. As a first situation, if for a sample one of the three GPMI values (i.e., GMPIPb-Zn, GMPIAs-Mo or GMPICu-Au) is ≥95% cumulative percentile while the other two GMPI values are b95% cumulative percentile, the final GMPI value of porphyry-Cu mineralization will be the same as the GMPI value that is ≥ 95% cumulative percentile [refer to Eqs. (5)a–(5)c]. This situation represents the outcome of using fuzzy “OR” operator. As a second situation, if for a sample one of the three GPMI values is b95% cumulative percentile while the other two GMPI values are ≥ 95% cumulative percentile, the final GMPI value of porphyry-Cu mineralization is equal to the average of the two GMPI values that are ≥ 95% cumulative percentile [refer to Eqs. (5)d–(5)f]. As a third situation, if for a sample all the three GMPI values are b95% cumulative percentile or ≥ 95% cumulative percentile, the final GMPI value of porphyry-Cu mineralization will be the average of all the three GMPI values [refer to Eqs. (5)g and (5)h]. The 95% cumulative percentile value of GMPIPb-Zn, GMPIAs-Mo and GMPICu-Au are given in Table 3 as 0.8, 0.833 and 0.866, respectively. Eqs. (5)a–(5)h can efficiently be used to evaluate the indicative degree of the presence of porphyry-Cu mineralization upstream from each stream sediment sample. To map the final GMPI values, we used values equal to 99%, 97.5%, 95%, 90%, 84% and 50% cumulative percentiles (Table 4). A final GMPI value of 0.888 corresponding to 95% cumulative percentile is used to generate the final GMPI distribution map for comparison with the FS maps obtained from ordinary factor analysis (Fig. 12). The 95% cumulative percentile has been considered in all distribution maps for comparison purposes. According to Fig. 12, the number of predicted known mineral occurrences upstream of anomalous samples is 17, equal to 53.12% of the known mineral occurrences. Thus, whereas the individual GMPIs (i.e., GMPIPb-Zn, GMPIAs-Mo and GMPICu-Au) are superior to FS maps obtained

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M. Yousefi et al. / Journal of Geochemical Exploration 115 (2012) 24–35

Table 5 Percentage of anomaly samples and prediction rate of mineral occurrences for the first and second steps of factor analysis, and GMPI approach, in cumulative percentile of 95% frequency.

Percentage of anomaly samples (%) Prediction rate of mineral occurrences (%)

F(Zn-Pb) in first step

F(Zn-Pb) in second step

(Zn − Pb)

GMPI

F(As-Mo) in first step

F(As-Mo) in second step

(As − Mo)

F(Cu-Au) in first step

F(Cu-Au) in second step

(Cu − Au)

GMPI of Porphyry Cu

3.93 18.75

3.66 28.12

4.98 46.87

4.93 21.87

4.88 21.87

4.98 25

3.66 28.12

3.77 31.25

4.98 40.62

5.04 53.12

GMPI

GMPI

from ordinary factor analysis (Fig. 11), the combination of the three indicator components into a single GMPI map using Eqs. (5)a–(5)h results in further enhancement of probability of success in MPM. To illustrate this point, we plotted the prediction of Cu mineral occurrences upstream of anomalous samples versus the 99%, 97.5%, 95%, 90%, 84% and 50% cumulative percentiles of the GMPIPb-Zn, GMPIAs-Mo, GMPICu-Au and final GMPI values (Fig. 13). According to Fig. 13, the prediction rates of the map of final GMPI values with respect to the known porphyry-Cu occurrences are higher than those of the individual GMPI maps. The superiority of the GMPI approach over factor analysis method is further shown in Table 5, which shows, using 95% cumulative percentile as basis for comparison, the percentages of anomalous samples and prediction rates of the FSs maps obtained from the first and second factor analyses, the individual GMPI maps and the map of final GMPI values. Table 5 demonstrates that the efficiency of geochemical evidential maps increases from the first factor analysis up to the final GMPI. 4.2. Separation of anomaly and background using GMPI To define a threshold for separation of anomalous and background samples based on the final GMPI values, we applied a graphical tool of exploratory data analysis (EDA) as follows. Because of the presence of mineral deposits (both discovered and undiscovered) in the study area, several outliers can be expected in the geochemical data (Ohta et al., 2005) as well as in the set of final GMPI values. Therefore, we used the histogram and the boxplot (Fig. 14) to determine the threshold to separate the outliers (e.g., Carranza, 2008; Reimann et al., 2005). The histogram of the final GMPI values (Fig. 14a) shows two major populations that can be separated by threshold value 0.8. The boxplot of the final GMPI values (Fig. 14b) shows several outliers greater than 0.86. Hence, according to the boxplot a threshold value of 0.86 can be used to separate anomalous and background samples to map areas with potential for porphyry-Cu deposits (Fig. 15). Based on a threshold final GMPI value of 0.86, the number of predicted known porphyry-Cu occurrences upstream of anomalous samples is 22. This represents about 69% of all the known porphyry-Cu occurrences in the study area. This prediction rate is higher than all of the prediction rates obtained based on the previous anomaly maps shown in this paper. Thus, the GMPI approach has given a much higher prediction rate of mineral occurrences than ordinary factor analysis. Hence, the GMPI approach is more powerful than factor analysis to extract geochemical evidence of target areas for further exploration. 5. Discussion Results of ordinary factor analysis generally include several factors that may indicate one or more anomalous geochemical associations, but the GMPI provides stronger distinction of significant anomalous geochemical signature of the deposit-type sought. Moreover, the GMPI of indicative components can be used for analysis of stream sediment geochemical data to generate probabilistic map as evidence of the presence of the deposit-type sought in an area. In the study area, the GMPI approach introduces some new promising areas that

have not been detected by individual indicator components (i.e., FS maps of F2, F3 and F4 in Figs. 4, 5 and 6, respectively). This is because in performing stepwise factor analysis, whereby non-indicator components and elements are omitted, significant indicator components are enhanced. Therefore, the GMPI approach provides for generation of reliable weighted geochemical evidential map of the deposit-type sought. Aside from increasing the prediction rate of mineral occurrences (Fig. 11, Table 5) and the intensity of geochemical anomalies (Figs. 4–6 compared with Figs. 8–10) and, consequently, enhancing exploration success (Figs. 11–13), the GMPI approach is a more

Fig. 14. Histogram (a) and boxplot (b) of the final GMPI values of porphyry copper mineralization.

M. Yousefi et al. / Journal of Geochemical Exploration 115 (2012) 24–35

Fig. 15. Distribution map of anomaly sample based on GMPI of porphyry copper mineralization in symbol form based on EDA, boxplot with thresholds 0.86.

powerful tool than ordinary factor analysis for weighting and fuzzification of stream sediment geochemical data to generate an enhanced geochemical evidential map for MPM. Six different forms of GMPI distribution maps (here, for porphyryCu potential mapping) can be generated (Fig. 16). Fig. 16a–c illustrate fuzzy GMPI distribution maps obtained by interpolation of GMPI values of samples. Fig. 16d shows a classified map based on ten

33

equal-interval cumulative percentiles of the GMPI values. Because the GMPI is a weight, the map shown in Fig. 16d can be used directly as a weighted geochemical evidential map in MPM, in which the lower or upper value of a class can be considered as the weight of that class. Fig. 16e and f illustrate, respectively, binary and ternary GMPI maps showing prioritized promising areas for further exploration. A map like that in Fig. 16e can be obtained using a GMPI threshold value obtained through EDA. A map like that in Fig. 16f can be obtained using 90% and 95% (or 97.5%) cumulative percentile as class limits. Alternatively, threshold GMPI values can be determined using the concentration-area fractal method to map various levels of background and anomaly in the study area (Cheng et al., 1994). However, it was not an objective in this study to determine which method of anomaly-background separation would perform best in using GMPI values. Maps like those shown in Figs. 16a–c can be used in: (a) fuzzy logic modeling (e.g., Carranza, 2002; Carranza and Hale, 2001; D'Ercole et al., 2000; Knox-Robinson, 2000; Nykänen et al., 2008; Porwal et al., 2003; Ranjbar and Honarmand, 2004; Rogge et al., 2006; Tangestani and Moore, 2003), in which the weight (e.g., GMPI) of any class in a geochemical evidential map (fuzzy membership) is

Fig. 16. Different forms of the GMPI distribution map: fuzzy distribution map of GMPI (a, b and c), classified map of GMPI, plotted based on ten ranges of percentile (d), binary map of GMPI (e), ternary map of GMPI (f).

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calculated based on data-driven approach, (b) analytical hierarchy process (AHP) modeling, as a weight for any class of geochemical evidential map (e.g., Carranza, 2008; De Araújo and Macedo, 2002; Hosseinali and Alesheikh, 2008; Moreira et al., 2003), (c) modeling with evidential belief functions (e.g., Carranza, 2002, 2008; Moon, 1990; Rogge et al., 2006; Tangestani and Moore, 2002b), in which the GMPI can be applied as the belief function, (d) wildcat MPM (Carranza, 2002, 2008; Carranza and Hale, 2002), in which the GMPI can be used for fuzzification of geochemical evidential maps. In all of the above methods for knowledgedriven MPM, the weight of any class of the geochemical evidential maps can be derived through the GMPI approach even in an area without any known mineral deposit occurrences. Each class of the map shown in Fig. 16d has a fuzzy weight and, thus, the map can be used in multivariate index overlay modeling (e.g., Billa et al., 2004; Bonham-Carter, 1994; Chico-Olmo et al., 2002; De Araújo and Macedo, 2002; Harris et al., 2001). The map shown in Fig. 16e can be used in binary index overlay modeling (Bonham-Carter, 1994; Carranza, 2002; Thiart and De Wit, 2000) and in Boolean logic modeling (BonhamCarter, 1994; Harris et al., 2001; Thiart and De Wit, 2000). All of the types of maps shown in Fig. 16, especially those in Fig. 16d–f can be used directly or with some modifications in data-driven MPM as weighted geochemical evidential maps. Generally, in MPM, GMPI is the weight of each geochemical sample with values in the range [0,1] for representing the probability of the presence of the deposit-type sought that can be mapped based on catchment analysis of each stream sediment sample, or the GMPI can be interpolated as continuous field values in the whole study area. 6. Conclusions Using stepwise factor analysis to generate GMPI (geochemical mineralization probability index), we developed a new approach for analysis and mapping of geochemical anomalies based on stream sediment element concentration data. Based on the results of this study, we could improve existing methods for recognizing significant anomalous multi-element geochemical signatures of the deposit-type sought and for weighting of stream sediment geochemical anomaly classes. Moreover, the significance of each sample for prospecting the deposit-type sought upstream of a sample can be evaluated using GMPI. Briefly, the following advantages of the GMPI approach have been demonstrated in this paper: 1. Non-indicator components and elements are recognized through stepwise factor analysis. 2. Stepwise factor analysis increases the percentage of total explained data variance by removal of non-indicator elements. 3. Anomaly intensity, especially near and around known mineral deposit occurrences, is enhanced in the GMPI approach compared to ordinary factor analysis. 4. The prediction rate of a GMPI map with respect to known mineral deposit occurrences is generally higher than factor score maps obtained through ordinary factor analysis. In addition, the GMPI approach can be used in knowledge-driven mineral potential mapping as a new exploratory data analysis tool to generate a weighted evidential map. Finally, the GMPI approach is worthwhile as it results in a geochemical evidential map that enhances the probability of success in mineral potential mapping, as compared to a geochemical evidential map obtained through ordinary factor analysis. Acknowledgements The authors thank Madan Pars Asia (MPA) consulting engineering company, especially Dr. Krimi, and Mr. Sahebzamani for supplying necessary data to do this research work. The authors express special thank to Mr. Esfehanipoor for some protection.

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