The use of evidential belief functions for mineral potential mapping in the Nanling belt, South China

Abstract

In this study, the evidential belief functions (EBFs) were applied for mapping tungsten polymetallic potential in the Nanling belt, South China. Seven evidential layers (e.g., geological, geochemical, and geophysical) related to tungsten polymetallic deposits were extracted from a multi-source geospatial database. The relationships between evidential layers and the target deposits were quantified using EBFs model. Four EBF maps (belief map, disbelief map, uncertainty map, and plausibility map) are generated by integrating seven evidential layers which provide meaningful interpretations for tungsten polymetallic potential. On the final predictive map, the study area was divided into three target zones of high potential, moderate potential, and low potential areas, among which high potential and moderate potential areas accounted for 17.8% of the total area, containing 81% of the total deposits. To evaluate the success rate accuracy, the receiver operating characteristic (ROC) curves and the area under the curves (AUC) for the belief map were calculated. The area under the curve is 0.81 which indicates that the capability for correctly classifying the areas with existing mineral deposits is satisfactory. The results of this study indicate that the EBFs were effectively used for mapping mineral potential and for managing uncertainties associated with evidential layers.

Graphical abstract

Keywords

Dempster-Shafer theory of evidence / GIS / uncertainty / tungsten polymetallic deposit / ROC curve

1 Introduction

Mineral potential mapping is one of the fields in mineral resource evaluation that is able to take great advantage of GIS technology as a substitution for traditional working methods (Nykänen and Ojala, 2007). During the past thirty years, many GIS-based mathematical/statistical models were developed to quantitatively integrate spatially referenced datasets for mineral potential mapping. As stated by Luo and Dimitrakopoulos (2003), these approaches are often employed to (a) maximize the extraction of information from the data; (b) effectively combine diverse information; (c) provide tools to quantify inherent uncertainties; (d) rank potential targets; and (e) reduce data processing and evaluation time. Notable approaches include logistic regression (Agterberg et al., 1993; Carranza and Hale, 2001a; Porwal et al., 2010), weights of evidence (WofE) model (Bonham-Carter et al., 1989; Agterberg, 1992; Cheng and Agterberg, 1999; Agterberg and Cheng, 2002; Carranza, 2004; Cheng, 2012), fuzzy logic model (Carranza and Hale, 2001b; Luo and Dimitrakopoulos, 2003; Porwal et al., 2003a; Abedi et al., 2013; Liu et al., 2014a), artificial neural network model (Porwal et al., 2003b; Behnia 2007; Leite and Filho, 2009; Oh and Lee, 2010), and evidence belief functions (An et al., 1994a, b; Carranza and Hale, 2003; Carranza et al., 2005, 2008a, b; Carranza, 2014). These models have been successfully applied to mineral potential assessment. Among these mathematical/statistical models, WofE model is the most popular method for mineral prospectivity lysis because of its intuitive implementation and easy interpretability. However, one of the disadvantages of the model is its inability to analyze multiclass evidential layers which may result in the loss of important information. In addition, the WofE model cannot be effectively used to evaluate uncertainties caused by ore-controlling factors. Relative to the WofE model, there are several advantages for using the evidential belief functions (EBFs) model in the application of mineral potential mapping, such as (a) favorable targets can be easily integrated using Dempster’s rule of combination; (b) uncertainties related to mineral exploration can be evaluated; and (c) spatial associations between evidential layers and target deposits can be quantified.

During the past two decades, the findings and prospective breakthroughs in the Nanling tungsten polymetallic metallogenic belt have been given a high degree of attention in both China and abroad. Previous studies in the belt mainly focused on metallogenic dynamics, geochronology, geochemistry, isotopes, and other typical deposits (e.g., Yuan et al., 1993; Peng et al., 2006; Hsieh et al., 2008; Li et al., 2009; Shu et al., 2011; Hu et al., 2012). In addition, conventional methods for tungsten polymetallic potential assessment in the study area were mainly based on personal experience and interpretation of available geological, geochemical, or geophysical data (e.g., Qin, 1987; Chen et al., 1990; Chi et al., 2012).

In the present study, EBFs model is used to integrate multi-source geospatial datasets with GIS techniques for mapping tungsten polymetallic potential. We organize this paper as follows. First, we introduce the EBFs (after An et al., 1994a, b), their geological data representation, and Dempster’s rule of combination by data–driven techniques (after An et al., 1994a; Carranza and Hale, 2003). Next, we describe the geologic setting and tungsten polymetallic mineralization in the study area. We then explain the results derived from the data-driven EBFs model, including the spatial associations between target deposits and certain classes of spatial data, mineral potential maps, and predictive accuracy. Finally, we discuss the significance of results and give our conclusions.

2 Evidential belief functions

The Dempster–Shafer theory of evidence, first developed by Dempster (1967, 1968) and then by Shafer (1976), is a generalization of Bayesian theory and upper and lower probabilities. The Dempster–Shafer theory of evidence provides a framework for estimation of EBFs according to Dempster’s rule of combination. The EBFs consist of degree of belief (Bel), degree of disbelief (Dis), degree of uncertainty (Unc), and degree of plausibility (Pls). The combined belief, plausibility, disbelief, and uncertainty can each be separately mapped (Carranza and Hale, 2003; Carranza et al., 2008a). The Bel and Pls represent a conservative estimate and an optimistic estimate, respectively, that the evidence supports a proposition. One advantage of EBFs is that it allows the user to represent uncertainty (or ignorance), because the interval between lower belief function and upper plausibility function can be considered as a confidence band, thus Unc = Pls−Bel. Disbelief (Dis) is the belief of the false proposition based on given evidential data, calculated as 1−Pls (or 1 −Bel−Unc), thus Bel + Unc + Pls =1. The following brief review of the Dempster–Shafer theory of evidence is synthesized from An et al. (1994a, b), Carranza and Hale (2003).

Let Θ be a frame of discernment or a set of all geological possibilities, for the mineral target proposition exists such that Θ = {A₁, A₂,…, A_n}. Then, each proposition is completely defined by a subset of H that contains exactly those geological possibilities where the proposition is true (Carranza and Hale, 2003). A function called a basic probability assignment or mass function is defined as m: 2^Θ→[0,1], where

(1)m\left(\phi \right)=\mathrm{0},

and

(2){\displaystyle \sum _{A\in \mathrm{\Theta }}m\left(A\right)}=\mathrm{1},

where A is a subset of Θ. The m(A) is called the A’s basic probability number as a measure of belief committed to A. Eqs. (1) and (2) mean that no belief should be committed to an empty set φ and the convention that one’s total belief has a measure of one. The total belief committed to a proposition H is given by

(3)\mathit{B}\mathit{e}\mathit{l}\left(H\right)={\displaystyle \sum _{A\subset H}m\left(A\right)}.

A function Bel: 2^Θ→[0,1] is a belief function over frame Θ, if and only if it satisfies the following conditions:

(4)\mathit{B}\mathit{e}\mathit{l}\left(\phi \right)=\mathrm{0},

(5)\mathit{B}\mathit{e}\mathit{l}\left(\mathrm{\Theta }\right)=\mathrm{1},

and for every positive integer n and every collection A₁, A₂,…, A_n of a subset of Θ

(6)\mathit{B}\mathit{e}\mathit{l}\left(A_{\mathrm{1}}\cup A_{\mathrm{2}}\cup \cdots \cup A_n\right)\ge \sum _{I\subset \left\{\mathrm{1},\mathrm{2},...,n\right\},I\ne \phi }{\left(-\mathrm{1}\right)}^{\left|I\right|+\mathrm{1}}\mathit{B}\mathit{e}\mathit{l}\left({\cap }_{i\in I}{A}_i\right).

A plausibility function Pls: 2^Θ→[0,1] is defined using the belief function Bel as

(7)\mathit{P}\mathit{l}\mathit{s}=\mathrm{1}-\mathit{B}\mathit{e}\mathit{l}\left(\overline{H}\right),={\displaystyle \sum _{A\subset \mathrm{\Theta }}m\left(A\right)}-{\displaystyle \sum _{A\subset \overline{H}}m\left(A\right)}={\displaystyle \sum _{A\cap H\ne \phi }m\left(A\right)}.

For every H⊂Θ, where \overline{H} is the negation of H. The belief and plausibility functions are the lower and upper envelopes of a class of probability assignments about H so that Bel(H)≦Pls(H), which can be viewed when comparing Eqs. (3) and (7). The degree of uncertainty about H is thus represented by the difference Pls(H) −Bel(H). When the degree of uncertainty equals 0,

(8)\mathit{B}\mathit{e}\mathit{l}\left(H\right)+\mathit{B}\mathit{e}\mathit{l}\left(\overline{H}\right)=\mathrm{1},

which is a Bayesian probability (An et al., 1994b).

Dempster’s rule of combination is a generalized scheme of Bayesian inference to aggregate evidence provided by disparate sources. Now suppose that m₁ and m₂ are the basic probability assignments based on entirely distinct bodies of evidence D₁ and D₂. The belief functions Bel₁ and Bel₂ for the basic probability assignments m₁ and m₂ can be combined to generate a new belief function. For all A₁, A₂,…, A_n∈2^Θ, Dempster’s rule produces a new probability assignment defined by m(φ)=0 and

(9)m\left(H\right)={\displaystyle \frac{\mathrm{1}}{\mathrm{1}-k}}{\displaystyle \sum _{A_i\cap B_j=H\mathrm{;}i,j}{m}_{\mathrm{1}}\left(A_i\right)m_{\mathrm{2}}\left(B_j\right)},

where

(10)

For all non-empty H⊂Θ, Eq. (9) is called the orthogonal sum of m₁ and m₂. The denominator (1−k) is a normalizing factor to compensate for the measure of belief committed to the empty set. Only two belief functions are combined at a time; hence, other belief functions that represent D₃,…, D_n can be combined one after another. The k in Eq. (9) is the total probability that is interpreted as a measurement of conflict between different sources for subsets of Θ. It represents a measure of conflict between two bodies of evidence. When k equals 1, the two bodies of evidence are completely contradictory, and the orthogonal sum of their basic probability assignments does not exist.

3 Geological data representation and Dempster’s rule of combination

The EBFs have been used in knowledge-driven approaches for mineral potential mapping (Moon, 1989; An et al., 1992). Procedures for data-driven estimations of EBFs described by Chung and Fabbri (1993) and An et al. (1994b) are suitable when both mineralized and non-mineralized locations are sufficiently known. Carranza and Hale (2003) proposed similar but different data-driven estimation procedures. The following brief review of data-driven EBF estimations is from Carranza and Hale (2003), and Carranza et al. (2005, 2008a, b).

Suppose an exploration area T consists of N(T) total number of unit cells or pixels and mineral deposits D occur in N(D) number of pixels. Suppose further that X_i (i = 1, 2, …, n) evidence maps, with C_ij (j = 1, 2, …, m) classes of evidence, have been created for certain deposit recognition criteria. The values of Be{l}_{C_{ij}} and Di{s}_{C_{ij}} are derived. The equation for data-driven estimation of Be{l}_{C_{ij}}is:

(11)Be{l}_{C_{ij}}={\displaystyle \frac{W_{C_{ij}D}}{{\displaystyle \sum _{j=\mathrm{1}}^m{W}_{C_{ij}D}}}},

where

W_{C_{ij}D}={\displaystyle \frac{{\displaystyle \frac{N\left(C_{ij}\cap D\right)}{N\left(C_{ij}\right)}}}{{\displaystyle \frac{N\left(D\right)-N\left(C_{ij}\cap D\right)}{N\left(T\right)-N\left(C_{ij}\right)}}}}.

The W_{C_{ij}D} in Eq. (11) is the ratio of the conditional probability that D exists given presence of C_ij to the conditional probability that D exists given absence of C_ij. The W_{C_{ij}D}, thus, is the weight of C_ij in terms of D being more present than absent as may be expected due to chance. Thus, the degree of belief for C_ij, Be{l}_{C_{ij}} as defined in Eq. (11), is the relative strength of W_{C_{ij}D} for every j^thC_ij class of evidence in map X_i. The equation for data-driven estimation of Di{s}_{C_{ij}} is

(12)Di{s}_{C_{ij}}={\displaystyle \frac{W_{C_{ij}\overline{D}}}{{\displaystyle \sum _{j=\mathrm{1}}^m{W}_{C_{ij}\overline{D}}}}},

where

W_{C_{ij}\overline{D}}={\displaystyle \frac{{\displaystyle \frac{N\left(C_{ij}\right)-N\left(C_{ij}\cap D\right)}{N\left(C_{ij}\right)}}}{{\displaystyle \frac{N\left(T\right)-N\left(D\right)-\left[N\left(C_{ij}\right)-N\left(C_{ij}\cap D\right)\right]}{N\left(T\right)-N\left(C_{ij}\right)}}}},

thus

(13)Un{c}_{C_{ij}}=\mathrm{1}-Be{l}_{C_{ij}}-Di{s}_{C_{ij}}.

The W_{C_{ij}\overline{D}} in Eq. (12) is the ratio of the conditional probability that D does not exist given presence of C_ij to the conditional probability that D does not exist given absence of C_ij. The W_{C_{ij}\overline{D}} is thus the weight of C_ij in terms of D being more absent than present as may be expected due to chance. Thus, the degree of belief for C_ij, Di{s}_{C_{ij}}, as defined in Eq. (12), is the relative strength W_{C_{ij}\overline{D}} for every j^thC_ij class of evidence in map X_i.

The formulas for combining EBFs of two evidence maps (X₁, X₂), according to an OR operation, which are usually employed for mineral potential mapping (An et al., 1994a) are given:

(14)Be{l}_{X_{\mathrm{1}}{X}_{\mathrm{2}}}={\displaystyle \frac{Be{l}_{X_{\mathrm{1}}}Be{l}_{X_{\mathrm{2}}}+Be{l}_{X_{\mathrm{1}}}Un{c}_{X_{\mathrm{2}}}+Un{c}_{X_{\mathrm{1}}}Be{l}_{X_{\mathrm{2}}}}{\beta }},

(15)Di{s}_{X_{\mathrm{1}}{X}_{\mathrm{2}}}={\displaystyle \frac{Di{s}_{X_{\mathrm{1}}}Di{s}_{X_{\mathrm{2}}}+Di{s}_{X_{\mathrm{1}}}Un{c}_{X_{\mathrm{2}}}+Un{c}_{X_{\mathrm{1}}}Di{s}_{X_{\mathrm{2}}}}{\beta }},

(16)Un{c}_{X_{\mathrm{1}}{X}_{\mathrm{2}}}={\displaystyle \frac{Un{c}_{x_{\mathrm{1}}}Un{c}_{x_{\mathrm{2}}}}{\beta }},

and

(17)\beta =\mathrm{1}-Be{l}_{X_{\mathrm{1}}}Di{s}_{X_{\mathrm{2}}}-Di{s}_{X_{\mathrm{1}}}Be{l}_{X_{\mathrm{2}}},

where \beta is a normalizing factor to ensure that Bel + Unc + Dis = 1. Eqs. (14) and (15) are both commutative and associative, so they result in a map of integrated Bel and integrated Dis, respectively. Only EBFs of two evidence maps can be combined each time. EBFs of maps X₃,…,X_n are combined one after another by repeated applications of either Eq. (13) or (14).

4 Geology and tungsten polymetallic mineralization

The Nanling tectono-magmatic belt, which covers over 187,000 km², lies between latitudes 23°22′28"N to 28°04′07"N and longitudes 110°40′39"E to 116°55′57"E in South China (Fig. 1). The exposed strata of this belt can be divided into three series. First, the Precambrian to Silurian slate, sandstone, and limestone constitute the basement of the study area. Second, cover rocks consist of different strata with ages ranging from Devonian to Triassic, comprising widely developed continental-marine paralic deposits that are distributed throughout the Nanling belt as large areas of ​​outcropping carbonate rocks and marlstone interbedded clastic depositions. Third, since the Jurassic-Cretaceous period, the representative deposits are rift basin clastics, volcanic rocks, and red beds (Mao et al., 2007).

Tungsten polymetallic mineralization in the Nanling belt occurred between the Caledonian and Yanshanian periods. The short time occurrence of the large scale Yanshanian ore-forming event means that the mineralization processes exhibit unexpectedness, uniqueness, and complexity, making the study area one of the most important tungsten metallogenic belts in the world (Mao et al., 2007; Li, 2011; Liu and Yu, 2011; Hu and Zhou, 2012; Liu et al., 2013a, b, 2014a, b, c). The extensive granitic rocks that evolved during the Yanshanian period are enriched in W and other metallic elements. Regarding lithology, alkali feldspar granites and syenogranites are the main mineralized rocks. Slates, phyllites, mudstone, clastic rocks, and carbonate in the basement are characterized by high background contents of tungsten and other metallic elements, and were primarily formed during the Sinian, Cambrian, Ordovician, Devonian and Permian periods (Chen et al., 1990; Hua et al, 2005; Hu and Zhou, 2012). A few genetic types of tungsten polymetallic mineralization can be identified in the region by multiple episodic mineralization and overprinting processes, such as skarn-, vein- and greisen-type tungsten polymetallic deposits (Mao et al., 2007). Different genetic types commonly occur together in most ore-fields and are significantly affected by granites and host rocks. In most cases, different host rocks determine different genetic types; for example, skarn-type or skarn greisen-type tungsten polymetallic deposits usually host in crystalline limestone and marble, and vein-type tungsten polymetallic deposits usually host in metamophic sandstone and slate near the lithostratigraphic contacts (Mao et al., 2009). Pei et al. (2009) proposed a universally-adapted tungsten polymetallic deposit model characterized by the contact structural system of magma emplacement. The contact structural system of magma emplacement provides important hydrothermal transported channels resulting in a wide range of tungsten polymetallic mineralization during multiple geological processes in the Nanling belt, South China.

5 Data

Five primary datasets were processed and combined by using EBFs model to evaluate tungsten polymetallic potential in the Nanling belt, including mineral deposits, lithostratigraphic contacts, aeromagnetic data, a fault system, and a geochemical multi-element association. Tungsten polymetallic deposits come from the National Mineral Deposit Database in 2006. The data were partially updated in 2010. A total of two hundred deposits are characterized by location, commodity, deposit type, size, and resource. All deposits were used as a training dataset for mineral potential mapping. A fault system was processed aided by GIS analysis. Map layers derived from the fault system include NE, NW, EW, and SN tending faults which were buffered with 1 km wide buffer bands and extended outward to a radius of 8 km,7 km, 12 km, and 10 km, respectively (Fig. 2). The study area is covered by 1,617 evenly distributed stream sediment samples which were collected from the Chinese Geological Survey (CGS). A geochemical multi-element association (F3: W–Sn–Mo–Bi–Be–Ag–Cd–Pb) was derived from a factor analysis (Liu et al., 2014c). The score map of F3 was classified into 10 classes based on quantile classification (Fig. 3(a)). The lithostratigraphic contacts between intrusive rocks and formations were extracted from a geology map. The contacts were buffered with 1 km wide buffer bands, and extended outward to a radius of 7 km (Fig. 3(b)). An aeromagnetic contour map collected from CGS was processed from earlier work (Fig. 3(c)).

6 Results

6.1 EBFs of evidential layers

Each class of seven evidential layers, such as E-W trending faults, S-N trending faults, SW-NE trending faults, SE-NW tending faults, F3, and aeromagnetic and lithostratigraphic contacts, were calculated by Eqs. (11)–(13). The results represented by the belief, disbelief and uncertainty are listed in Table 1. The EBF results indicate the inverse relationship between the degrees of belief and the degrees of uncertainty. A buffer distance within 1 km of contacts has the highest degree of belief and lowest degree of uncertainty, and contains 133 deposits, followed by F3 with a 90 to 100 percentile class containing 90 deposits. The results imply that tungsten polymetallic mineralization is mainly associated with proximal to lithostratigraphic contacts and F3. With respect to the derivative layers that resulted from the faults, the NW trending faults have a relatively higher degree of belief and a lower degree of uncertainty, followed by the NE trending faults. The distance from faults showed indirect relationships with deposit occurrences according to the degrees of belief. There were strong spatial relationships between the moderate aeromagnetic anomalies and the tungsten polymetallic deposits, because of the relatively higher degree of belief and lower degree of uncertainty between classes of 30 to 70 percentiles. Thus, lithostratigraphic contacts and F3 could have a greater contribution to the formation of tungsten polymetallic deposits than the other evidential layers.

6.2 Mineral potential mapping

The EBF maps were generated based on integrating evidential layers using Eqs. (14)–(17) which represent degrees of belief, disbelief, uncertainty, and plausibility, respectively (Fig. 4). Each map of integrated EBFs was classified into five classes by natural breaks. The disbelief map (Fig. 4(b)) complements the belief map by depicting areas that are potentially mineralized and otherwise. The uncertainty map (Fig. 4(c)) indicates lack of information or the presence of insufficient evidential data layers to provide support for the proposition that mineral deposits exist. The plausibility map (Fig. 4(d)) is somewhat similar to the belief map except the contrast as shown between lower and higher degrees is more apparent. In addition, the plausibility map shows mineral potential areas and presents more evidence t by integrating the degrees of belief and the degrees of uncertainty (Carranza and Hale, 2003). Figure 4 shows that zones with degrees of belief, disbelief, uncertainty, and plausibility primarily reflect the patterns of presence of proximity to mapped lithostratigraphic contacts and F3. The spatial distributions of degrees of belief and degrees of plausibility more strongly reflect the patterns due to the lithostratigraphic contacts and F3 than the patterns due to the other evidential layers (Figs. 4(a) and 4(d)). This implies that the lithostratigraphic contacts and F3 are more important as spatial controls of tungsten polymetallic mineralization in the study area than the other evidential layers.

The belief map (Fig. 4(a)), which clearly reflects the distribution of mineral deposits, was converted into the final mineral potential map. To determine the thresholds of the degrees of belief, the variations of cumulative tungsten polymetallic deposits with both cumulative percent of study area and with belief probabilities were plotted (Fig. 5). Two inflection points can be identified in curves (Fig. 5(a)). The threshold belief probabilities that correspond to the lower and to the upper inflection points on the curve in Fig. 5(a) are 0.6007 and 0.6788, respectively. The three target zones were then identified as high, moderate, and low potential areas (Fig. 5(b)). Low potential areas occupy 82.2% of the area and contain 19.5% of the deposits; moderate areas occupy 11.9% and contain 21.5% of the deposits; and high potential areas occupy 5.9% and contain 59% of the deposits.

The final tungsten polymetallic potential map was generated based on the belief map and Fig. 5 which provides a good understanding of the areas where minerals have been found in the past and of the geological situations in which future efforts should be focused (Fig. 6). Zones of high and moderate potential reflect the spatial coincidence of several of the more highly weighted ore-controlling factors. High potential areas are generally confined to intrusive rocks and their vicinities. Spatially, high potential areas objectively reflect the distribution of faults exhibiting SW–NE trending extensions. The final potential map shows that several areas where a number of deposits have been discovered have been well identified in the study area, such as place A and place B (Fig. 6).

The success rate method was used to evaluate the success rate accuracy (Chung and Fabbri, 1999, 2003; Lee and Pradhan, 2007). The receiver operating characteristic (ROC) curve was plotted on Fig. 7, and subsequently the area under the curve (AUC) was calculated. The AUC values provide the overall success rate which ranges from 0.5 to 1. A value equal to 0.5 indicates a random prediction accuracy, and a value equal to 1 indicates a perfect prediction accuracy (Lee and Dan, 2005). In the present study, the area under curve is 0.8061 which indicates that the capability for correctly classifying the areas with existing deposits is satisfactory.

7 Discussion and conclusions

The EBFs mode is employed to integrate multi-source geospatial datasets with GIS techniques for evaluating tungsten polymetallic potential and identifying interest areas associated with new mineral deposit discoveries in the Nanling belt, South China. Four EBF maps (belief map, disbelief map, uncertainty map, and plausibility map) were generated by integrating seven evidential layers. These maps can provide meaningful interpretations for tungsten polymetallic potential. The spatial associations of evidential layers with the target deposits are evaluated by using EBFs model. The results indicate that the degrees of belief of lithostratgraphic contacts within 1 km, and the degrees of F3 with a 90 to 100 percentile class, have a strong spatial association with tungsten polymetallic deposits, implying that those two evidential layers provide more contributions to the formation and location of tungsten polymetallic deposits than the other evidential layers.

In the present study, we have taken into account other evidential layers in addition to these seven evidential maps, to include density of faults and density of fault intersections. However, if all these evidential layers were integrated into the EBFs model, the resultant predictive map did not give a higher accurate rate under the test of ROC curve. Therefore, it is necessary that conditional independence (CI) between evidential layers be considered in the EBFs model, which could result in a lower accurate rate if there were strong spatial correlations between evidential layers; e.g., a strong spatial correlation may exist between faults and density of fault intersections. By multiple experiments, seven evidential layers are selected in the current study producing a more accurate rate when compared with other combinations according to the ROC curve.

The belief map is used to generate a final mineral potential map which provides a good understanding of areas where minerals have been found in the past and geological situations where efforts should be focused. The study area is classified into three zones based on the variations of cumulative deposits with both cumulative percent of study area and with belief probabilities. Favorable areas are characterized by moderate potential areas and by high potential areas occupying 17.8% of the total and containing 82.2% of the total tungsten polymetallic deposits. The success-rate curve is used to explain how well the integrated belief values predict the observed tungsten polymetallic deposits, and the results show that the success rate accuracy reaches to 80.61%.

Qualitative evaluation of extracted geospatial data signatures of the tungsten polymetallic deposits shows that the results are geologically reasonable. The signatures can be used as input to geological models and as exploration criteria for mineral potential mapping. The tungsten polymetallic potential map based on the belief map could be the basis for decision making. The high potential areas are related to clustered deposits that are associated with integrated signatures. The information provided by the mineral potential map could potentially assist geologists and mineral companies to reduce the risks of mineral exploration in the study area.

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