Geochemical Mineral Exploration: Should We Use Enrichment Factors or Log-Ratios?

The notion of enrichment factor (EF) has been proposed about 40 years ago as a measure for considering the source of elements in the atmosphere of remote regions (Chester and Stoner 1973; Peirson et al. 1974; Zoller et al. 1974; Duce et al. 1975). The general formula for estimating EFs is (cf. Reimann and de Caritat 2005): EF _crust El = [(El)_sample/(X)_sample]/[(El)_crust/(X)_crust] where El is an element under consideration, X is a reference element, the square brackets indicate element concentration, and the subscripts “crust” or “sample” refer to the medium from which element concentration was measured. The use of EFs has subsequently been extended to a variety of earth materials to discern between natural and anthropogenic sources for elements. However, Reimann and De Caritat (2000, 2005) concluded that this extended usage of EFs is “at odds with the original concept” and they recommended that such indiscriminate use of EFs should be avoided.

In the geochemical mineral exploration literature in the last 10 years or so, there have been some extended applications of EFs to geochemical mineral exploration (Chandrajith et al. 2001; El-Makky and Sediek 2012; Gong et al. 2013; Yaylali-Abanuz 2013; Liu et al. 2014; Wang et al. 2013; Hosseini-Dinani et al. 2015; Chen et al. 2016). In the realm of compositional data analysis (Aitchison 1984; Aitchison and Egozcue 2005), EFs are, unlike uni-element concentrations, not affected by the so-called closure problem because they are ratios and unitless (see equation above). However, unlike log-ratios, EFs are not formal solutions to the closure problem (Aitchison 1986; Egozcue et al. 2003). In geochemical anomaly mapping for mineral exploration, to the best of the author’s knowledge, it has not been demonstrated yet whether using EFs is better than using log-ratios or vice versa. Therefore, this study aims to fill this knowledge gap by comparing and contrasting, through spatial statistical analysis, results of using EFs and log-ratios in a case study to map significant (i.e., deposit-related) geochemical anomalies.

The study area—the Giyani greenstone belt (GGB)—is the same area studied by Carranza et al. (2015) and Sadeghi et al. (2015). This area is suitable for this study because (a) there is a high-quality soil geochemical dataset, which can be used for comparing and contrasting the performances of using EFs and log-ratios in mapping significant geochemical anomalies, and (b) it contains several known gold deposits/occurrences, which can be used to validate the mapped geochemical anomalies.

The GGB is situated at the northeastern corner of the Kaapvaal Craton (Fig. 1), wherein the Archean rocks are dominated by 3640 Ma granitoid gneisses (Armstrong et al. 1990) and various 2650 Ma granitoids (Barton and Van Reenen 1992). The GGB, measuring ~70 km long and ~15 km wide and is divided at its southwestern half into the southern Lwaji branch and northern Khavagari branch (Fig. 2), is made up mostly of mafic–ultramafic rocks with minor intercalations of felsic schists, pelitic metasediments, and iron formations (Prinsloo 1977; McCourt and Van Reenen 1992; Brandl et al. 2006). The supracrustal rocks (i.e., the Giyani Group) in the GGB are flanked to the south by younger granite and to the north by the migmatized Klein Letaba Gneiss (SACS 1980). The northwestern boundary of the GGB roughly coincides with or forms part of the oblique to reverse south-verging, north-dipping regional-scale Hout River Shear Zone (HRSZ) (Fig. 1), which forms a boundary between the northern Kaapvaal Craton and the South Marginal Zone (SMZ) of the Limpopo Belt (De Wit et al. 1992; McCourt and Van Reenen 1992; McCourt and Vearncombe 1992; Roering et al. 1992; Rollinson 1993).

Simplified geological map of northeastern Kaapvaal Craton, Giyani area, and part of the Limpopo Belt (modified from Rollinson 1993). Greenstone belts: G Giyani; M Murchison; P Pietersburg, HRSZ Hout River Shear Zone, TSZ Triangle Shear Zone

Full size image

Simplified geological map of the Giyani area, modified from Sadeghi et al. (2015). Linear features are fault/shear zones, adopted from McCourt and Van Reenen (1992). Unfilled circles are active/inactive gold mines and dots are gold prospects, compiled from the database of the Council for Geoscience of South Africa

Full size image

The GGB has been subjected to complex polyphase deformation (cf. De Wit et al. 1992; McCourt and Van Reenen 1992): (i) an older penetrative deformation (D1); (ii) a younger non-penetrative deformation (D2); and (iii) the latest deformation event (D3) characterized by discrete strike-slip shear zones. The D1 phase resulted in north-trending regional schistosity and gave rise to ENE–WSW and E–W-striking, north-dipping oblique to reverse shear zones, and associated reclined sheath folds as well as well-developed mineral lineations. The D2 phase was superimposed on D1 structures, and can be recognized by either horizontal crinkle lineations or eastward plunging folds of the regional foliation. The D3 phase resulted in discrete strike-slip shear zones at the margins of the GGB post-dating granitoid intrusion. McCourt and Van Reenen (1992) suggest that the steeply dipping sinistral brittle–ductile shear zones (D3) and ultramylonite along the tectonic margin of the high-grade retrograde granulite (to the north), and the lower grade rocks of the GGB, are a part of the progressive D2 deformation (late-D2).

In the database of the Council for Geoscience of South Africa, there are 55 known gold occurrences in the GGB, of which six are active mines and the rest are inactive mines and prospects (Ward and Wilson 1998). In these mines/prospects, the characteristics of the gold deposits (cf. Pretorius et al. 1988; Van Reenen et al. 1994; Sieber 1991; Gan and Van Reenen 1995, 1997; Stefan 1997) are typical of orogenic gold deposits (cf. Groves et al. 1998; Goldfarb et al. 2001). The gold deposits associated with (Ehlers 1985; Gains et al. 1986): (a) quartz veins with minor sulfides; (b) banded-iron formations (BIF); (c) quartz–sulfide replacement veins; or (d) carbonate (calcite) veins. Gold in most deposits is closely associated with sulfides in quartz veins but in some deposits gold occurs as free-milling inclusions in silicates (Pretorius et al. 1988; Sieber 1991; Van Reenen et al. 1994). The sulfides mainly comprise pyrrhotite, chalcopyrite, pyrite, and arsenopyrite, with the last being the most predominant in BIF-hosted deposits. The sulfide mineralogy of the major active/inactive mines is similar despite strong differences in host lithology (Gan and Van Reenen 1995, 1997; Pretorius et al. 1988; Stefan 1997; Van Reenen et al. 1994). Although most parts of the GGB may show prograde metamorphism, greenstone remnants at most gold deposits/occurrences exhibit features indicating that gold mineralization in the GGB is mainly associated with fluid-related retrogression of upper amphibolite facies lithologies (cf. Weilers 1956; Pretorius et al. 1988; Gan and Van Reenen 1995, 1997).

Most of the known gold deposits in the GGB are situated close to the HRSZ and are localized in east–west-trending, steeply northward dipping ductile satellite shear structures of this major shear zone (Figs. 1 and 2) (McCourt and Van Reenen 1992; Van Reenen et al. 1994, 2014). However, most of the gold occurrences are hosted in mafic–ultramafic metavolcanics as well as BIF in anastomosing small shear zones in the immediate footwall of the HRSZ and in mafic–ultramafic metavolcanics in the hanging wall (i.e., the SMZ; Fig. 1) (Pretorius et al. 1988; Sieber 1991; Gan and Van Reenen 1995, 1997; Stefan 1997; Van Reenen et al. 1994). In particular, gold mineralization is concentrated along foliations in shear structures and ore shoots plunge as the mineral-elongation lineations do, implying a direct relationship between the gold mineralization and the southward-directed D2 thrusting (McCourt and van Reenen 1992). In rare instances, gold mineralization is hosted in granitoid gneisses and pegmatites that occur along reverse ductile shear zones (De Wit et al. 1992; McCourt and van Reenen 1992), which cut mafic–ultramafic metavolcanic rocks and BIFs.

Soil Sampling and Geo-Analysis

The South African Council for Geosciences (CGS) has conducted in 2007–2008 a high-density geochemical soil sampling of the Giyani 1:100,000 scale map sheet area (Fig. 3a). A total of 2725 soil samples (~5 kg/sample) have been collected from the top 25 cm of the soil at a sampling density of 1 sample/km² (Maritz et al. 2010). The soil geochemical data have been used by Sadeghi et al. (2015) for mapping of deposit-related anomalies in the GGB. The analytical data that were used in this study are concentrations of 31 elements.

Giyani area (a) soil sample locations; (b) ternary image of ratios of trace element concentrations in soil. Polylines in (b) are outlines of lithologic units (cf. Fig. 2)

Full size image

The following 28 trace elements were analyzed by inductively coupled plasma mass spectrometry (ICP–MS) after samples of the <75 μm soil fraction were digested in HF–HClO₄ (Maritz et al. 2010): Li (2.9), Be (0.06), Sc (0.28), V (0.73), Cr (30.58), Mn (0.0003), Fe (0.02), Co (0.16), Cu (21.73), Zn (19.98), Ga (0.18), Rb (0.06), Sr (0.81), Y (0.02), Zr (0.54), Mo (0.41), Ag (0.45), Cd (0.03), Sb (0.03), Te (0.02), Cs (0.07), Ba (8.65), Ta (0.01), Tl (0.01), Pb (0.51), Bi (0.04), Th (0.01), U (0.01), As (1.5). The following three elements were analyzed by direct current arc emission spectrography (DC-AES) after samples of the <75 μm soil fraction were decomposed with HCl/H₂O₂, pre-concentrated with activated charcoal/SnCl₂ and subsequently ashed (Elsenbroek 1995): Au (0.0005), Pd (0.009), and Pt (0.009). The numbers in parentheses are the lower detection limits (DL) in ppm of each element.

The ICP-MS analysis, which was undertaken at the CGS laboratory in Pretoria, South Africa, had an average relative standard deviation of 7% for duplicate measurements (Maritz et al. 2010). The precision of the DC-AES analysis, which was undertaken at the Henan Laboratory, Peoples Republic of China, was better than 10% based on duplicate measurements (Martiya Sadeghi and Alazar Billay, pers. comm.). The quality of the data is considered excellent, as the spatial distributions of ratios of certain elements using the uni-element data portray the underlying lithology quite well (Fig. 3b). The Sr/Rb ratio reflects compositional variation and/or the degree of metamorphism of granitic rocks. Gneisses in the northern parts of area show higher Sr/Rb ratios compared to granitoids in the southern parts of the area. The Ga/V ratio discriminates mafic–ultramafic rocks from granitic rocks. The greenstone (mafic–ultramafic) terrain in the area is characterized by very low Ga/V ratios, whereas the granitic terrains in the area are characterized by very high Ga/V ratios. Within the greenstone terrain, the ultramafic rocks exhibit slightly lower Ga/V ratios compared to the mafic rocks. The log Cr/Zr ratio depicts variations in various rock types with negative, near zero, and positive values reflecting granitic, mafic, and ultramafic rocks, respectively.

Dealing with Censored Geochemical Data

The goal of geochemical data analysis is not only to map deposit-related anomalies but also to identify geological/geochemical processes based on statistical and spatial variations in a dataset (e.g., El-Makky 2011; El-Makky and Sediek 2012; He et al. 2013; Luz et al. 2014). However, models of geochemical landscapes are influenced not only by geogenic as well as anthropogenic sources of elements concentrations but also by censored values (i.e., values below analytical DL). In practice, censored values are commonly substituted by a value of ½ the DL, which usually produces suitable results when there are only few of such values. The data used for this study are the censored values of As (685 samples), Au (4 samples), Pd (4 samples), and Pt (4 samples). The percentage of censored values of As (~40% of total samples) is quite high, but Sadeghi et al. (2015), who used the same data, found that, by including in the analysis the As data with censored values replaced by ½DL and by excluding in the analysis the As data, the high percentage of censored As values did not undermine interpretation and mapping of deposit-related anomalies.

Derivation of EFs

Of the various trace elements, Rb (Koinig et al. 2003; Chen et al. 2006), Sc (Weiss et al. 1997; Shotyk et al. 2002), and Zr (Koinig et al. 2003) are the most commonly used reference trace elements (X) for obtaining EFs (see equation in the Introduction) because they are deemed to be geochemically stable, conservative in most geochemical environments, and hosted by resistant minerals. To help decide which of these three elements (Rb, Sc, and Zr) should be used as X for obtaining EFs in this study, the robust coefficient of variation (CV _r) defined by Reimann and de Caritat (2005) was used to determine the variability (as a proxy measure of stability) of each of these three elements in soil in the area. The CV _r for Rb is 26.8%, Sc 37.6%, and Zr 21.3%. Therefore, Zr, with the smallest CV _r, was used as X for obtaining EFs in this study.

For the purpose of this study, the natural logarithms of EFs are taken and used for comparison with log-ratio-transformed data.

Log-Ratio Transformation of Geochemical Data

Because EFs are ratios (see equation above), they are not affected by the so-called closure problem in multivariate data analysis. The use of ratios in geochemistry, particularly in the study of igneous fractionation, has been well documented some five decades ago (Pearce 1968) and more recently by Stanley and Russell (1989a,b). The assumption in the use of ratios in geochemical modeling is that there is a “conserved” element in the system, which permits the use of ratios to model processes, and without this kind of control the use of ratios becomes problematic. Although straight ratios are not formal solutions to the closure problem because they range only in the “simplex” (Aitchison 1986), the use of logarithms “opens” ratios across the real number space. Therefore, in order to address the closure problem inherent in compositional (e.g., geochemical) data, three log-ratio transformations have been proposed, namely (1) additive log-ratio, denoted as alr (Aitchison 1986); (2) centered log-ratio, denoted as clr (Aitchison 1986); and (3) isometric log-ratio, denoted as ilr (Egozcue et al. 2003). Filzmoser et al. (2009) have discussed that, except for these three log-ratio transformations, any other transformation of compositional data is insufficient for statistical analyses.

However, for the purpose of this study, the data were subjected to ilr transformation only because (a) just as how EFs are calculated (see above), alr transformation involves simple ratios (see: Aitchison 1986); (b) although clr transformation is advantageous for preserving all of the variables, the clr-transformed data are collinear because the sum of clr variables per sample is zero and the resulting data matrix suffers from singularity problems in matrix inversion involved in methods of multivariate data analysis such as principal components analysis (Filzmoser et al. 2009); and (c) of the three log-ratio transformations, only the ilr transform represents an isometry (Filzmoser et al. 2009); that is, the “balanced” ratios represent new variables that are in an orthogonal space (i.e., with the so-called Aitchison geometry; Aitchison et al. 2000), in which standard statistical analyses can be applied. In this study, the ilr-transformed values were obtained using the CoDaPack software (Thio-Henestrosa and Comas 2016). For generating the ilr “balances”, the default sequential binary partition in CoDaPack was used because the specific processes related to soil geochemical dispersion in the area are poorly understood (cf. Maritz et al. 2010; Sadeghi et al. 2015).

Interpolation of the Data

There are numerous publications on geochemical anomaly mapping in which point data of soil uni-element concentrations have been transformed, typically using standard weighted moving average interpolation methods, into continuous fields. The best way to transform discrete point soil geochemical data into a continuous field geochemical landscape model is probably through the use of geostatistics, whereby semivariogram analysis allows modeling of the spatial field and provides justification for interpolation through a method such as kriging. In this study, bidirectional semivariograms were generated for indicator (i.e., Au) and pathfinder (e.g., As) elements because the gold mineralization is associated with the NE–SW-trending greenstone lithologies (Fig. 2), and so the spatial distributions of the indicator and pathfinder elements are also likely anisotropic. For example, the bidirectional semivariograms for the raw data for either Au or As show a relatively longer range for values that are NE–SW of each other than for values that are NW–SE of each other (Fig. 4), indicating the presence of anisotropy, which can be modeled by anisotropic kriging with parameters of the semivariogram models per element (Fig. 5). Therefore, the point soil geochemical data used in the analyses in this study were interpolated by anisotropic kriging based on parameters obtained from bidirectional semivariograms.

Bidirectional (NE–SW and NW–SE) semivariograms for (a) log_e-transformed soil Au data and (b) log_e-transformed soil As data

Full size image

Spatial distributions of element concentrations in soil modeled by anisotropic kriging with parameters derived from the bidirectional semivariograms (Fig. 4) of (a) log_e-transformed Au data (nugget = 0.64; sill = 0.97; anisotropy ratio = 1.8); (b) log_e-transformed As data (nugget = 7.5; sill = 10.5; anisotropy ratio = 1.5). The anisotropy ratio per element is the ratio of the larger semivariogram range to the smaller semivariogram range. Small un-filled circles on the maps are locations of known gold deposits/occurrences (cf. Fig. 2)

Full size image

Uni-element Analysis

For comparing and contrasting the usefulness of EFs and log-ratios for mapping of deposit-related geochemical anomalies in the area, data for Au as indicator element and data for As as pathfinder element were analyzed and discussed below. Data for other potential pathfinder elements were also analyzed but are not discussed or shown here due to restriction of printed space, although the results of analyses for the other potential pathfinder elements are generally similar to those for As (see below). Interpolated maps for Au, derived by anisotropic kriging of log_e-transformed EF for Au (hereafter denoted as ln-EF _Au) and ilr-transformed values for Au (hereafter denoted as ilr_Au), were compared and contrasted with each other. Likewise, interpolated maps for As, derived by anisotropic kriging of log_e-transformed EF for As (hereafter denoted as ln-EF _As) and ilr-transformed values for As (hereafter denoted as ilr_Au), were compared and contrasted with each other.

Multi-element Analysis

The method of robust principal components analysis (RPCA), proposed by Filzmoser et al. 2009, was applied to EFs and ilr values for the 31 elements. The RPCA was used in this study because it is robust against the presence of outliers (for details, see Filzmoser et al. 2009), and the soil geochemical data in the area contain significant outliers especially for Au (Fig. 6). Another advantage of the RPCA is that, although results of its application to ilr-transformed data are not readily interpretable because such data do not represent a one-to-one transformation from the simplex to the standard Euclidean space, the derived loadings and scores are back-transformed to the clr space for better interpretation (Filzmoser et al. 2009). To retain only the statistically meaningful principal components (PCs) that can be extracted from the data, the Kaiser (1960) criterion (i.e., eigenvalue >1) was applied. Then, among the retained PCs, the PC which portrays a multi-element signature that reflects the presence of gold mineralization in the area was determined. Subsequently, continuous field maps of PCs portraying multi-element signatures of mineralization, from EFs and ilr-transformed data, were generated by anisotropic kriging for comparison and contrasting.

Boxplots of ln-EF _Au and ilr_Au datasets, indicating the presence of significant outliers. Unfilled circles are ‘mild’ outliers, while asterisks are ‘extreme’ outliers (Kotz and Johnson 1985, pp. 136–137)

Full size image

Spatial Correlation Analysis

To determine empirically whether a geochemical map is better or worse for mapping of deposit-related anomalies, the spatial correlation of each interpolated map with the known gold deposits/occurrences in the area is quantified by way of the following procedure (Carranza, 2011b).

1. 1.

   A graph, denoted as D(N), portraying the relative cumulative frequency distribution of decreasing map values is created per element (Fig. 7). This D(N) graph represents a distribution of element values at mostly non-deposit locations, which may be due to various but mostly background geochemical processes.

   

   Results of Kolmogorov–Smirnov (K–S) tests of spatial correlation between the known gold deposits/occurrences and (a) map of soil log_e-transformed Au data (Fig. 5a) and (b) map of soil log_e-transformed As data (Fig. 5b). In (b), part of the D(M)–D(N) graph falls below 0 along the y-axis because part of the D(M) graph corresponding to intermediate log_e As values lies below but close to the D(N) graph, indicating weak negative spatial correlation of intermediate log_e As values with the known gold deposits/occurrences in the area

   Full size image

2. 2.

   A second graph, denoted as D(M), portraying the relative cumulative frequency distribution of decreasing values at only the locations of the known gold deposits/occurrences is created per element (Fig. 7). This D(M) graph represents a distribution of element values at deposit locations, which are probably anomalous and associated with mineralization.

Decreasing map values are used in steps 1 and 2 because concentrations of indicator and pathfinder elements associated with certain type of mineral deposits are expected to comprise the upper tail of data distribution, and the aim of the K–S test here is to determine if values in the upper tail of a geochemical data distribution are spatially correlated with the known gold deposits/occurrences.

1. 3.

   A third graph, denoted as D(M)–D(N), portraying the difference D(M)–D(N) is created per element (Fig. 7). This D(M)–D(N) graph represents a Kolmogorov–Smirnov (K–S) statistic, which determines if element values at deposit locations differ significantly or not from element values at non-deposit locations.

On the one hand, a positive and large D(M)–D(N) difference (i.e., the D(M) graph lies significantly above the D(N) graph) indicates that element values at deposit locations are significantly different from element values at non-deposit locations, and that a positive spatial correlation exists between the known mineral deposits/occurrences and the map values at (and around) such mineral deposits/occurrences. Thus, a strong positive spatial correlation exists between log_e-transformed Au values and the known gold deposits/occurrences in the area (Fig. 7a), indicating that high Au values at/around the known gold deposits/occurrences (Fig. 4a), are anomalous. On the other hand, a small D(M)–D(N) difference (i.e., the D(M) graph lies and/or fluctuates closely above and below the D(N) graph) indicates that element values at deposit locations are not significantly different from element values at non-deposit locations, and that no spatial correlation exists between the known mineral deposits/occurrences and the map values at (and around) such mineral deposits/occurrences. Thus, there is a lack of spatial correlation between log_e-transformed As values and the known gold deposits/occurrences in the area (Fig. 7b). This implies that the spatial distribution of log_e-transformed As values with respect to the known gold deposits/occurrences in the area is random, and so the map of log_e-transformed data is worthless for mapping of anomalies related to these deposits. Therefore, for comparing and contrasting the usefulness of EFs and ilr-transformed data for mapping of deposit-related geochemical anomalies in the area, the main criterion is that, between the maps of EF and ilr values per element (e.g., Au), the map with the higher/highest K–S curve portrays element concentrations having the stronger/strongest positive spatial correlation with the known gold deposits/occurrences (i.e., the better/best map for mapping of deposit-related anomalies).

Uni-element Analysis

The maps of ln-EF _Au and ilr_Au (Fig. 8) and the maps of ln-EF _As and ilr_As (Fig. 9) were generated by anisotropic kriging with parameters obtained from spherical models of their respective bidirectional semivariograms (Table 1; semivariograms not shown).

Giyani area: (a) soil ln-EF _Au; (b) soil ilr_Au; (c) results of K–S test. Small un-filled circles on the maps are locations of known gold deposits/occurrences (cf. Fig. 2). In (c), the graph for ln Au is the same as the D(M)–D(N) graph in Figure 7a

Full size image

Giyani area: (a) soil ln-EF _As; (b) soil ilr_As; (c) results of K–S test. Small un-filled circles on the maps are locations of known gold deposits/occurrences (cf. Fig. 2). In (c), the graph for ln As is the same as the D(M)–D(N) graph in Figure 7b

Full size image

On the one hand, the maps of ln-EF _Au and ilr_Au (Fig. 8), just like the map of log_e-transformed Au (Figs. 5a and 6a), have strong positive spatial correlation with the known gold deposits/occurrences, as indicated by their strong positive K–S values (Fig. 8c). The K–S graphs of these variables show that the highest 20% of log_e-transformed Au values have slightly stronger positive spatial correlation with the known gold deposits/occurrences in the area compared to the highest 20% of the ln-EF _Au and ilr_Au values (Fig. 8c). However, K–S graphs of these variables also show that the upper intermediate 20–50% of the ilr_Au values have much stronger positive spatial correlation with the known gold deposits/occurrences in the area compared to the upper intermediate 20-50% log_e-transformed Au and ln-EF _Au values. These results, especially considering the peaks of the K–S graphs as thresholds for anomaly mapping, indicate that the highest 20% of log_e-transformed Au, ln-EF _Au and ilr_Au values are likely anomalous and that the upper intermediate 20–50% of ilr_Au values are also probably anomalous but not the upper intermediate 20–50% of log_e-transformed Au and ln-EF _Au values. Thus, these results imply that using ilr_Au values for anomaly mapping will incur the least Type II (i.e., false negative) error compared to using log_e-transformed Au or ln-EF _Au values. Therefore, among these three maps for the indicator element Au, the map of ilr_Au is the best map for mapping of Au anomalies related to gold mineralization in the area.

On the other hand, the maps of ln-EF _As and ilr_As (Fig. 9), just like the map of log_e-transformed As (Figs. 5b and 6b), lack spatial correlation with the known gold deposits/occurrences, as indicated by their K–S values that vary closely around zero (Fig. 9c). This means that the soil geochemical data for As (whether log_e- or ilr-transformed or converted to EF) in the area are not satisfactory, making As not a useful pathfinder element in this case. Other elements like Bi, Cu, Pb, Sb, and Te are potential pathfinder elements for orogenic gold deposits (Eilu and Groves 2001), but the soil geochemical data for all these elements also lack spatial correlation with the known gold deposits/occurrences (results of analyses for these potential pathfinder elements are not shown but confirmed by the multi-element analyses described below).

Multi-element Analysis

The results of the RPCA of the log_e-transformed EFs derived from the soil geochemical data are given in Table 2. The PC1_ln-EF (accounting for at least 37% of the variance) represents a Fe–V–Mn–Cu–Zn–Sc–Y–Co–Cd–Pd–Pt–Cr association, which probably reflects soil derived from the greenstone lithologies or it may be due to scavenging of metals by Fe–Mn oxides in the weathering environment. The PC2_ln-EF (accounting for ~21% of the variance) represents a Zr–U–Th–Pb–Rb–Tl–Ba–Ga–Be–Sr–Ta association, which probably reflects soil derived from the granitoids or gneisses. The PC3_ln-EF (accounting for at least 7% of the variance) represents a Cs–Li–Bi–Be–Tl–Rb association, which probably reflects soil derived from some of the granites in the area. The PC4_ln-EF (accounting for at least 4% of the variance) represents a Pd–Pt–Au association, which probably reflects the gold mineralization hosted in the greenstone rocks in the area. The PC5_ln-EF (accounting for at least 3% of the variance) represents a Mo–Te association, which, together with the relatively high but non-significant loading on Bi, possibly reflects soil derived smaller granitic bodies; the relatively high but non-significant loading on Cr in this PC5 suggests possible contamination/mixing with soil derived from nearby greenstone rocks. The PC6_ln-EF (accounting for ~3% of the variance) represents a Sb–As association, which, together with the relatively high but non-significant loading on Au, possibly reflects enrichment of these elements linked with the gold mineralization in the area. Therefore, the results of the RPCA of the log_e-transformed EFs derived from the soil geochemical data adequately reflects the lithology and gold mineralization of the area. However, the significant PCs extracted generally show poor and non-significant correlation of Au with the potential pathfinder elements (i.e., As, Bi, Cu, Pb, Sb, and Te). Therefore, between the PC4_ln-EF (Pd–Pt–Au) and PC6_ln-EF (Sb–As), the former is deemed the multi-element signature that better reflects the gold mineralization in the area.

The results of the RPCA of the ilr-transformed soil geochemical data are given in Table 3. The PC1_ilr (accounting for ~32% of the variance) represents a Pd–V–Sb–Be–Zn–Mo–Li association that is antipathetic with a Rb–Bi–Zr–Ga association; the former probably reflects soil derived mainly from mafic–ultramafic rocks, the latter from granitoids. The PC2_ilr (accounting for ~13% of the variance) represents a Co–Fe–Sc–Be–Sb–Mo association that is antipathetic with Cu; the former (with negative loadings), together with the relatively high but non-significant positive loading on Mn, possibly reflects scavenging of metals by Fe–Mn oxides in the weathering environment, whereas Cu (with negative loading), together with the relatively high but non-significant negative loading on U, possibly reflects soil derived some of the granitic rocks in the area. The PC3_ilr (accounting for ~10% of the variance) represents a Pb–Tl–Ba–U–Zr association that is antipathetic with a Cr–Zn association; the former possibly reflects soil derived granitoids and gneisses, whereas the latter (with negative loadings), together with the relatively high but non-significant negative loading on Mn, possibly reflects scavenging of metals by Mn oxides in some parts of the area. The PC4_ilr (accounting for at least 6% of the variance) represents an As–Th–Bi association that is antipathetic with a Cd–Li association; the former (with positive loadings), together with the non-significant positive loading on U, possibly reflects soil derived from U-poor granitic rocks in the area, whereas the latter (with negative loadings), together with the non-significant negative loading on Mn, possibly reflects scavenging of Cd and Li by Mn oxides in certain parts of the area. The PC5_ilr (accounting for at least 4% of the variance) represents a Ta–Sr–V association that antipathetic with a Ga–Mn association; the former possibly reflects soil along the granitoid–greenstone contact zones (as Ta is more abundant in felsic rocks and V is more abundant in mafic–ultramafic rocks), whereas the latter possibly reflects scavenging of Ga by Mn oxides in clayey soil derived from weathering of feldspar-rich rocks (e.g., granitoids) in the area. The PC6_ilr (accounting for ~4%) represents a Te–Cs association, which possibly reflects soil derived from certain granitic rocks in the area. The PC7_ilr (accounting for at least 3% of the variance) represents a Au–Pt association, which probably represents the gold mineralization hosted in the greenstone rocks in the area. The PC8_ilr (accounting for ~3% of the variance) represents mainly Y, which, together with its positive but non-significant correlation with Rb and Sr, possibly reflects soil derived from granitic rocks in some parts of the area. Therefore, the results of the RPCA of the ilr-transformed soil geochemical data are interpretable with respect to the lithology of the area. However, the significant PCs extracted generally show poor and non-significant correlation of Au with the potential pathfinder elements (i.e., As, Bi, Cu, Pb, Sb, and Te). Nevertheless, the PC7_ilr (Au–Pt) is deemed the multi-element signature that reflects the gold mineralization in the area.

Therefore, for the purpose of this study, the maps of PC4_ln-EF and PC7_ilr were generated for comparison and contrasting. The maps of PC4_ln-EF and PC7_ilr (Fig. 10a and b) were generated by anisotropic kriging with parameters obtained from spherical models of their respective bidirectional semivariograms (Table 1; semivariograms not shown). The map of PC7_ilr (Au–Pt) strongly resembles the maps of log_e-transformed Au (Fig. 5), ln-EF _Au (Fig. 8a), and ilr_Au (Fig. 8b) because of the very high positive loading on Au in PC7_ilr (Table 3), whereas the map of PC4_ln-EF (Pd–Pt–Au) weakly resembles these maps because of the lower positive loading on Au compared to those on either Pd or Pt in PC4_ln-EF (Table 2). The K–S graphs for the PC4_ln-EF and PC7_ilr maps are strongly positive (Fig. 10c) but the K–S graph for the latter lies far above the K–S graph for the former, indicating that the known gold deposits/occurrences in the area have significantly stronger positive correlation with high values in the PC7_ilr map than with high values in the PC4_ln-EF map. Therefore, between these two maps, the PC7_ilr map is the better map for mapping of anomalies related with gold mineralization in the area.

Giyani area: (a) PC4 of ln-EFs derived from the soil geochemical data; (b) PC7 of ilr-transformed soil geochemical data; (c) results of K–S test. Small un-filled circles on the maps are locations of known gold deposits/occurrences (cf. Fig. 2)

Full size image

Typically, in most cases, analyses of data for pathfinder elements of primary gold deposits (e.g., orogenic gold) are useful for generating the regional field of gold mineralization but analyses of data for Au alone may be misleading because the “nugget” effect of gold makes modeling of spatial distribution of Au data difficult. In this case study, however, the uni-element analyses of soil geochemical data for As (and for each of the other potential pathfinder elements, although not shown here) did not yield useful results because the uni-element maps of log_e-transformed As (Fig. 5b), log_e-transformed enrichment factors of As (Fig. 9a), and ilr-transformed As (Fig. 9b) lack spatial correlation with the known gold deposits in the study area. This lack of spatial correlation, whether positive or negative, indicates that the spatial distribution of As (as well as the other potential pathfinder elements) in soil in the study area is random with respect to the known gold deposits/occurrences. As can be seen from these maps, the spatial distribution of high As values does not follow the spatial distribution of the known gold deposits/occurrences in the study area. This suggests that enrichment of As (as well as the other potential pathfinder elements) in soil in the study area is due to (a combination of) various processes, considering the protracted weathering history of the area since the Archean to the present. Unfortunately, the use of enrichment factors fails to highlight enrichment of As (and other potential pathfinder elements) that is due to gold mineralization in the study area. This means that, in the study area, the use of enrichment factors fails to account for variations in abundances of gold-deposit pathfinder elements in soil due to variations in parent lithology, regolith development, and various other factors that come into play. Fortunately, the soil geochemical data for Au in the study area have good accuracy and good precision. However, uni-element analysis of only Au data should be used very cautiously for anomaly mapping and so it must be accompanied by multi-element data analysis and spatial correlation analysis as well.

The robust principal components analyses of the log_e-transformed enrichment factors and the ilr-transformed soil geochemical data yielded similar multi-element associations (PC4_ln-EF, Pd–Pt–Au; PC7_ilr, Au–Pt) depicting the presence of gold mineralization in the study area. These multi-element associations can be visualized in the PC1–PC2 biplots (Fig. 11), which show (a) the correlation of Au with Pd and Pt in the log_e-transformed enrichment factors of the soil geochemical data and (b) the correlation of Au with Pt but not with Pd in the ilr-transformed soil geochemical data. However, the eigenvectors of the ilr-transformed data are spread in a full circle, whereas the eigenvectors of the ln-EFs mainly are mostly constrained in a semi-circle, suggesting that Au–Pt association represented by PC7_ilr is a more realistic signature of gold mineralization in the study compared to the Pd–Pt–Au association represented by PC4_ln-EF. This interpretation is supported by the spatial correlation analysis using the Kolmogorov–Smirnov statistic, which shows that the known gold deposits/occurrences in the study area have stronger positive correlation with the Au–Pt (PC7_ilr) signature than with the Pd–Pt–Au (PC4_ln-EF) signature.

Giyani area: biplots of PC1 versus PC2 of (a) ln-EFs derived from the soil geochemical data and (b) ilr-transformed soil geochemical data. Tiny gray crosses are eigenvalues, whereas arrows are eigenvectors. Arrows with the same colors represent correlated elements

Full size image

The analysis of spatial correlation between mineral deposits and anomalies described in this study is akin to the distance distribution analysis proposed by Berman (1977) and used by Bonham-Carter (Bonham-Carter 1985) and Carranza and Hale (2002) to quantify spatial correlation between mineral deposits and linear structures. In these previous studies, instead of decreasing map values, increasing map values (i.e., distances to linear structures) were used because if mineral deposits are associated with linear structures, the distances between them are expected to comprise the lower tail of distribution of distances from linear structures, and for this analysis the aim of the K–S test is to determine if values in the lower tail of a distance distribution are spatially correlated with mineral deposits (i.e., if mineral deposits occur proximal to linear structures). The spatial correlation analysis for the purpose of this study can also be achieved through the cumulative increasing approach to weights of evidence modeling (Bonham-Carter et al. 1989), as have been shown by Ziaii et al. (2011). However, weights of evidence modeling uses the parametric Student’s t test is, whereas the spatial correlation analysis described here uses the non-parametric Kolmogorov–Smirnov test (Yakir 2013), which is advantageous as it makes no assumption about the data distribution. In any case, analysis of spatial correlation between mineral deposits and geochemical data is crucial to deciding which geochemical map is the better/best one for mapping of significant (i.e., deposit-related) anomalies.

The results obtained in this study are mainly consistent with the findings of Carranza (2011a) that (a) using ilr-transformed uni-element data, compared to using log_e-transformed uni-element data (in this case ln-EF _Au), does not improve mapping of anomalies (of Au in this case) and (b) that using ilr-transformed multi-element data, compared to using log_e-transformed multi-element data (in this case ln-EFs), results in a map of multi-element anomalies with stronger spatial correlation with known deposits/occurrences. This study shows that, for mapping of significant anomalies, it is better to use ilr-transformed soil geochemical data than enrichment factors derived from soil geochemical data. Therefore, the map of the Au–Pt (PC7_ilr) signature (Fig. 10b) can now be combined with other relevant spatial evidence layers (cf. Carranza et al. 2015) to update map mineral prospectivity information in the area.

Finally, for criticisms similar to those made by Reimann and Caritat (2000, 2005) regarding the usage of enrichment factors in environmental studies, the use of enrichment factors in geochemical mineral exploration should be avoided. Instead, ilr-transformed geochemical data must be used.