Introduction

Exploring and prioritizing mineralized areas for mining are complex operations, and their success may depend on multiple geoscientific datasets. Geoscientific datasets relevant for mineral exploration include satellite image products (remote sensing mineral maps), geophysical survey measurements (reduced to the magnetic pole, magnetic susceptibility, analytical signal, and radioelement maps), geochemical analyses (identification of anomalous copper areas with statistical methods), and geological maps (lithology, fault density, and fault distance buffers; John et al. 2010; Carranza 2011; Zhang et al. 2017). Integration of various geoscientific datasets simultaneously and together help to indicate high potential areas of mineralization and reduce the risk of mineral exploration (Harris et al. 2015). In order to explore porphyry copper deposits, it is essential to know their geological, geophysical, and geochemical characterizations. Copper mineralization within the study region has been formed within the fractures of intrusive units, which are hydrothermally altered and weathered (Nedimovic 1973; Zarasvandi et al. 2005; Atapour and Aftabi 2007; Asadi et al. 2014). Satellite imagery, magnetometry, gamma-ray spectroradiometry, stream sediments, lithological, and tectonic investigations are valuable tools for copper exploration (John et al. 2010) in this region (e.g., Rahimi et al. 2004; Shabankareh and Hezarkhani 2016; Maghsoudi Moud and Fathianpour 2016). Some of the lithological units such as Oligocene granite and granodiorite, and Miocene-Pliocene andesite are the host rocks for porphyry copper mineralization which could determine possible copper mineralization within the study region. Faults are the main conduits of ascending fluids, and they provide porous zones in which metals can be trapped (Safari et al. 2015; Mirzaie et al. 2015). A maximum distance of 1000 m from a fault has been reported for copper mineralization within the study region (Derakhshani and Mchrabi 2009). Therefore, the multiple-ring buffering technique and fault density could be used to determine the relationship within potentially mineralized zones. Hydrothermal alteration and gossan zones are keys to porphyry copper deposit exploration (Lowell and Guilbert 1970; Mars and Rowan 2006; Honarmand et al. 2011). Each zone has one or more specific minerals that could be mapped and explored via processing satellite images (Sabins 1999; Hosseinjani Zadeh et al. 2014), creating different potassium (K), equilibrium thorium (eTh), equilibrium uranium (eU) radioelement ratios, and processing magnetometry data (Dickson and Scott 1997; Honarmand 2016). Weathering and destruction of copper minerals, transportation, and subsequent deposition within stream sediments could make a catchment basin anomalous in copper element concentration. Stream sediment samples have been used to identify these anomalous catchment basins that potentially contain copper mineralization (e.g., Carranza 2008; Abdolmaleki et al. 2014).

Several and different types of copper mineralized areas and geoscientific datasets in the current study region made it appropriate for testing different mineral potential mapping (MPM) methods such as support vector machines and adaptive neuro-fuzzy inference systems (Shabankareh and Hezarkhani 2016; Shabankareh and Hezarkhani 2017). However, increasing the number of datasets may lead to discrepancies (Brown et al. 2000) between a decision-making group for having different strategies for the exploration target modeling. Also, a contradictory output of different exploration methods could complicate the decision-making process. Therefore, mineral exploration and prioritization performances are categorized as multi-criteria decision-making (MCDM) problems (Pazand et al. 2012). MCDM methods help exploration groups discover and prioritize areas based on their mineralization potential by considering relevant information in multiple geoscientific datasets. Analytical hierarchy process (AHP) and multi-criteria optimization and compromise solution (Vlsekriterijumska optimizacija I KOmpromisno Resenje in Serbian; VIKOR) are both methods for MCDM (Zeleny 2012). The MCDM techniques are categorized as one of the knowledge-driven methods (Carranza 2011).

MCDM methods have been used either individually or in a hybrid combination of MCDM forms for MPM and have shown successful outcomes. The AHP and fuzzy-AHP techniques have been used to compute optimized knowledge-driven weights for different geoscientific layers (e.g., Maghsoudi Moud and Fathianpour 2016; Zhang et al. 2017; Forson et al. 2020). Also, the AHP and fuzzy-AHP weights have been combined with other MCDM methods such as VIKOR for the MPM (Ghezelbash and Maghsoudi 2018; Khalifani et al. 2019; Pahlavani et al. 2020). The AHP uses a hierarchical systematic structure to include multiple attributes into a complicated decision-making problem (Saaty 1980). The problem involves different levels of goals (e.g., copper mineralization potential map) as the highest level, followed by criteria (geology, remote sensing, geophysics, and geochemistry) and sub-criteria (lithology, fault, hydrothermal alteration zones, magnetometry, radiometry, and stream sediment samples), and alternatives (image pixels) as to the lowest level. Each level’s elements are compared pair-wise with a component from the upper level, leading to the allocation of the relative importance of each criterion. The capability of measuring inconsistency is one of the advantages of using AHP to evaluate the reliability of judgments of decision-makers. The AHP is an easily applicable and precisely decisive method that provides a simple and flexible model by structuring the different levels. The difference between AHP and VIKOR is that the AHP weighs the geoscientific layers but does not rank the high potential areas. In contrast, VIKOR ranks high potential areas but does not weigh the geoscientific layers.

The VIKOR method (Opricovic 1998) was developed to solve a discrete decision-making problem with non-commensurable and conflicting criteria. This approach was performed by ranking and selecting various alternatives (in this study, image pixels of different geoscientific layers) to facilitate a final decision (Opricovic and Tzeng 2004). The ranking process is based on the closeness of a criterion to the ideal solution (closeness of each pixel to the highest and anomalous pixel value in each geoscientific layer). The VIKOR method consists of five steps, including making a decision matrix (geoscientific layers and their pixel values), normalizing and weighting the decision matrix, determining the best and the worst values for each criterion, measuring utility (S; relative pixel value difference between each pixel and the highest pixel value in a layer) and regret (R; maximum pixel value difference between each pixel and the highest pixel value in a layer) values for each criterion, computing the VIKOR decision parameter “v” and ordering the VIKOR values from the lowest as the best to the highest as the worst alternatives (Q; Opricovic 1998). This method is suitable for MPM when the geoscientific layers directly correlate with mineralization and deposition. Also, VIKOR uses linear normalization that is independent of the measurement units of each geoscientific layer. This characteristic helps to integrate geoscientific layers with different measuring units and values. The VIKOR method determines a compromise solution by providing a maximum group contribution and a minimum of individual opinion conflict (Opricovic and Tzeng 2004). Therefore, based on the target of this study, available datasets, and the characteristics mentioned earlier of the VIKOR method, it is recognized as a suitable method for exploration and prioritization of high potential areas of mineralization.

In most MPM projects, the weighting procedure for the geoscientific layers due to different opinions among the experts is a challenging issue. In the previous MPM-based studies through AHP-VIKOR, the employed geoscientific dataset weighting procedure has almost been derived from the AHP through pair-wise comparison (Ghezelbash and Maghsoudi 2018; Khalifani et al. 2019; Pahlavani et al. 2020). However, the fairness of assigned weights never has been assessed or compared with another method. Accordingly, the concern of unfairly dedicated weights affecting the VIKOR is not considered. This lack in the current study is motivated to compare the AHP-derived weights with the data-driven weight of evidence (WofE) weights for better evaluation. Furthermore, the decision parameter in VIKOR known as “v” almost is selected manually. However, the reason for choosing a value for the “v” was not supported, and its bias was depending upon the opinion of the project leader, thereby influencing the accuracy of mineral potential maps. Referring to these shortcomings, a mathematical modification using the expectation value was proposed and replaced with the manual selection. Moreover, most of the previous studies have been conducted on a local scale (≤ 1:100,000), and still, there is a gap in the examined performance and accuracy analysis of the integrated AHP-VIKOR in regional scale explorations. The previous local-scale studies have used visible-near infrared (VNIR), short-wave infrared (SWIR) satellite images, 1:100,000 stream sediment geochemical analysis results, 1:100,000 geological shapefiles, and in some cases low-resolution airborne magnetometry (with 7.5-km space lining; e.g., Pazand et al. 2012; Ghezelbash and Maghsoudi 2018; Khalifani et al. 2019; Pahlavani et al. 2020). In this study, we will add thermal infrared (TIR), high-resolution airborne magnetometry, and high-resolution airborne gamma-ray spectroradiometry (with 200-m space lining) to the above-mentioned datasets to improve the possibility of copper exploration. As this region has been used for the copper mineralization potential mapping, the modified AHP-VIKOR copper potential map can be easily compared with the previous studies to determine the advantages and disadvantages of the AHP-VIKOR in the MPM.

This paper presents potential copper mineralization mapping and ranking in the southeastern part of Iran using a modified AHP-VIKOR method and implementing different integrated geoscientific layers. The calculated weights for each assumed causative factor were achieved through incorporated AHP with WofE methods. The results demonstrated the presented modified AHP-VIKOR method’s applicability in mapping and ranking the high potential areas of copper mineralization, specially porphyry deposits.

Geology of the study region

The Kerman Cenozoic-Magmatic Arc (KCMA) is located within the southeastern part of the Urumieh-Dokhtar Magmatic Belt (UDMB; Fig. 1). The study area comprises the northern half of the KCMA (NKCMA; Fig. 1). The NKCMA has the highest density of copper mineralized areas, especially the porphyry type, throughout the UDMB (Zarasvandi et al. 2005). Several areas within the NKCMA, including Sar Cheshmeh, Meiduk, and Darreh Zar, are turned into mines, which shows the potential of the NKCMA for high-grade/tonnage copper ± gold/molybdenum mineralization and the prospectivity of the NKCMA for further exploration. The study region includes different types of copper deposits such as porphyry, vein, and polymetallic. Among the mentioned deposition types, porphyry copper deposits are the main sources of copper mining due to their relatively cheap mining operations and long lifetime (Ghorbani 2013). These deposits have large volumes (from a few million tons to a few billion tons) and low copper grades (0.2–0.4%). In these deposits, sulfide minerals, especially copper-bearing sulfides (i.e., chalcopyrite, chalcocite, covellite, and bornite), are distributed in hydrothermally altered host rocks. In hydrothermal alteration zones, the potassic alteration zone is located within the center of a porphyry system and is surrounded by phyllic, argillic, silicification, and propylitic zones, respectively. Generally, phyllic, argillic, and propylitic alterations could be observed widely at the surface of mineralized areas depending on weathering conditions, whereas potassic zones are usually hidden underneath overlaying phyllic and argillic alteration zones. Within the mineralized areas of the region, thin silicification veins are observed near the surface. Copper, gold, and molybdenum mineralization could be found between potassic and phyllic, and sometimes within argillic, and silicification zones, while lead, zinc, silver, manganese, cadmium, and bismuth mineralization are reported at propylitic zones (Edwards 2012). The ratio of pyrite to chalcopyrite in the potassic zone is on averagely 3:1 and within the phyllic zone this ratio increases to 12:1 while this ratio reaches 23:1 within the argillic zone (Lowell and Guilbert 1970). However, economic and mineable mineralization within the porphyry deposits is mostly observed within potassic and phyllic alteration zones which are covered by a gossan zone on the surface due to the weathering and oxidation of sulfide minerals. The porphyry copper deposits that are formed due to the continental margin subduction processes are classified as monzonitic porphyry deposits and belong to the Cenozoic and the Mesozoic era (Cooke et al. 2005).

Fig. 1
figure 1

Lithological map of the study region (1:100,000 scale; compiled from Bazin and Hübner 1969) with the location of copper mineralization (Nedimovic 1973; Honarmand et al. 2011; Asadi et al. 2014). Mines or copper deposits and occurrences are shown as solid black dots and solid white diamonds

Full size image

Sar Cheshmeh is a porphyry copper deposit, with 1.7 billion tons of copper above the cut-off grade of 0.6% (Atapour and Aftabi 2007). It has the highest copper ore reserve in Iran and contains copper-bearing minerals such as malachite, azurite, cuprite, chrysocolla, chalcopyrite, chalcocite, covellite, and bornite. It also contains the molybdenum mineral of molybdenite (with the cut-off grade of 0.03%) and 0.06 g/t gold (Waterman and Hamilton 1975). Darreh Zar is another porphyry copper deposit within the region, with 500 million tons of copper above the cut-off grade of 0.35% and copper minerals of cuprite, malachite, azurite, chrysocolla, covellite, chalcocite, and chalcopyrite (Parsapoor et al. 2017). Moreover, the Meiduk porphyry copper deposit within the study region contains 180 million tons of copper above the cut-off grade of 0.84% and copper minerals of chalcopyrite, chalcocite, covellite, and bornite. The area also contains molybdenite with a cut-off grade of 0.007%, and 1.8 ppm silver (Taghipour et al. 2008). The study region has a mountainous topography with many catchment basins, making the region suitable for stream sediment geochemical studies. The climate is typically continental and arid, with hot summers and cold winters with mostly sunny days. Minimal vegetation coverage of shrubs and bushes and occasional trees and the presence of outcrops have made the study region appropriate for geological, remote sensing, and gamma-ray radiometry investigations.

During the Oligocene period, granite, granodiorite, diorite, and quartz-diorite as intrusions intruded units within the Eocene volcanic complex (Dimitrijevic 1973). After the magmatic activities ceased in the late Eocene, fluids containing precious metals (e.g., copper, gold, and molybdenum) began to rise within these intrusion units during the Oligo-Miocene and led to the formation of copper ± gold/molybdenum mineralization and hydrothermal alteration zones in the Miocene. Copper mineralization was formed within potassic, phyllic, argillic, and silicification alteration zones (Yousefi et al. 2018). Due to weathering, gossan zones were formed on top of the previously mentioned hydrothermal alteration zones (Atapour and Aftabi 2007). The geoscientific layers were used and processed to map the copper mineralization as indications of gossan zones, hydrothermal alteration zones, and intrusion units.

Data and methods

The following sections describe the processing and preparation of each geoscientific layer for copper mineralization potential mapping. The geoscientific datasets that were considered to provide clues to the location of mineralization were prepared and processed. A group of geoscience professionals specializing in copper exploration, as decision-makers, were surveyed to weigh the geoscientific datasets using the AHP method. The AHP weights assigned by these experts were compared with weights derived from the weight of evidence (WofE) method to assess the fairness of the knowledge-driven assignment of weights by AHP. The AHP weights were applied to the geoscientific layers. The weighted layers were integrated using the VIKOR method to create a copper mineralization potential map. Since the criteria were weighted with the AHP and integrated with the VIKOR method, this combined method is called the AHP-VIKOR. The copper mineralization potential map was classified using the real value-area (RV-A) fractal method. The accuracy of the AHP-VIKOR mineral potential map was assessed using a confusion matrix. The AHP-VIKOR pixel values of very high potential areas of copper mineralization were used to rank them. The mapping and ranking results were compared to ore type, ore grade, and ore tonnage of already discovered deposits. The results demonstrated that the AHP-VIKOR is a useful and reliable method for exploring and prioritizing mineralized areas.

Lithology

Eight 1:100,000 scale geological maps of Dehaj, Anar, Robat, Shahr-e-Babak, Rafsanjan 1 and 2, Chahrgonbad, and Pariz that were vectored by the Geological Survey of Iran (GSI) used to create a single lithological map (Rahimi et al. 2004).

Faults

We made 200-, 400-, 600-, 800-, and 1000-m multiple ring buffers for the faults derived from 1:100,000 scale geological maps (Bazin and Hübner 1969; Honarmand et al. 2011). The 200-m interval was chosen as the most optimized buffer value based on the spatial resolution of the available datasets and the work of Hengl (2006). The areas with a higher density of faulted zones have the most probability of copper mineralization. The fault layer provided by the GSI was used to create a lineament density faults map within the ArcMap environment (Appendix Fig. 4a; Zhang et al. 2017).

Remote sensing

Six scenes of cloud-free Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images acquired during summer (from July 7th to July 25th, 2002 and 2003) were downloaded from the Earthdata website (https://earthdata.nasa.gov/). Visible and near-infrared (VNIR), short-wave infrared (SWIR), and thermal infrared (TIR) images were already preprocessed and converted into surface reflectance data for the VNIR and SWIR (Thome et al. 1999), and surface emissivity for the TIR images. Before downloading, the crosstalk correction (Iwasaki and Tonooka 2005) was also already applied as part of this preprocessing to the SWIR images by the Earthdata center. We downloaded the summer images because in this season, due to high solar elevation, and sparse vegetation cover, ASTER images are expected to have higher accuracy for alteration mapping (Shahriari et al. 2015). Surface reflectance Sentinel-2 imageries, which were atmospherically and geometrically corrected, were downloaded from the Copernicus Open Access Hub portal of the European Space Agency (ESA Copernicus 2017; https://www.esa.int/Applications/Observing_the_Earth/Copernicus).

Eighty-four ground spectra that were already obtained for satellite image pre-processing, processing, and validation from different copper mineralized areas (e.g., Sar Cheshmeh, Darreh Zar, Kader, Godekolevary, Iju, Serenu, Chahfiroozeh, Meiduk, Parkam, Abdar, and Kuh Panj) used in this study (Honarmand et al. 2011; Hosseinjani Zadeh et al. 2014; Seifi et al. 2017; Maghsoudi Moud et al. 2021a; Maghsoudi Moud et al. 2021b). The ground spectra were measured using a field spectrometer, an analytical spectral device (ASD) model 3 with a contact probe, and a high-contrast light bulb (https://www.malvernpanalytical.com/en/products/product-range/asd-range).

The level two surface reflectance and crosstalk corrected ASTER images were geo-referenced via the same acquisition date of the level one registered radiance at the sensor-orthorectified terrain corrected ASTER images. Bands five and nine of ASTER images have different reflectance values than in situ measurements (Mars and Rowan 2010; Shahriari et al. 2015). Band ratios 5/6 and 9/8 differences between the ASTER and the ground spectra were used to correct bands five and nine reflectance values of ASTER (Mars and Rowan 2010). We randomly selected and used half of the ground spectra (42) to correct bands five and nine. The rest of the spectra (42 spectra) were used as reference spectra for the Spectral Angle Mapper (SAM; Kruse et al. 1993) method for alteration mapping (Appendix Fig. 4b, c, and d). Kaolinite, alunite, and smectite spectra were categorized as minerals of argillic alteration zone (Lowell and Guilbert 1970); illite and muscovite spectra were classified as minerals of phyllic alteration zone; and chlorite and calcite spectra were classified as minerals of propylitic zone; goethite, hematite, jarosite, and limonite spectra were categorized as minerals of gossan zone (Atapour and Aftabi 2007). The SAM method compares the degree of similarities in radians between known reference spectra and unknown image spectra (Hecker et al. 2008). Inversed rule-images of the SAM were represented as hydrothermal alteration maps.

Band ratio 13/10 of the ASTER surface emissivity images was used to map silicification zones (Appendix Fig. 4e; Kalinowski and Oliver 2004). Band ratio 11/4 was applied on Sentinel 2 images to map gossan zones (Appendix Fig. 4f; van der Meer et al. 2014; van der Werff and van der Meer 2015).

Stream sediment geochemistry

The GSI collected sediment samples from the surface to a depth of 20 cm of the streams and analyzed the minus 80 mesh fraction. The inductively coupled plasma mass spectrometry (ICP-MS) was used to analyze fifteen elements, including copper, lead, zinc, chromium, nickel, cobalt, barium, arsenic, tin, silver, bismuth, antimony, tungsten, boron, and molybdenum (Parand 1998). Then, the analytical results were provided as an Excel file with the X and Y coordinates of sediment samples for each 1:100,000 geological sheet by the GSI. The Excel files were merged, and the results of 2207 stream sediment samples from eight 1:100,000 geological sheets were used to map geochemical copper anomalies.

Outlier data were discarded using the Mahalanobis distance method (Filzmoser et al. 2005). This method measures the distance of each point from other points. In this method, points with larger distance values than 95 percentiles are identified as outliers. Then, if less than 30% of samples for an element were lower than the limit of detection (LOD), the LOD values were replaced with 66% of LOD values. If more than 30% of samples for an element were LOD, that element was discarded from further processes (Martín-Fernández et al. 2012).

In geochemical exploration, there are two components: (a) syngenetic component which is related to source rock changes and (b) epigenetics which is related to mineralization. Stream sediment samples represent both of these components at the same time. Therefore, the samples might not be homogenous and could not be considered as one population for geochemical analysis. The type of outcropping bedrock as the syngenetic component plays the role of source for the sediments resulting from erosion in the sample catchment basin. The lithological variation in a source area could be large enough to change elemental concentration from a few ppm to a few hundred ppm. Therefore, due to the importance of the epigenetic component in geochemical exploration, lithological effects should be neutralized. Different methods have been used to remove the lithological effect from stream sediment samples including multiple regression and weighted mean (Carranza 2008). In this study, the weighted mean method was used to neutralize the lithological effect of the data (Eqs. 1 and 2):

$${M}_{j}={~}^{{\sum }_{i=1}^{n}{Y}_{i}{X}_{ij}}\!\left/ \!{~}_{{\sum }_{i=1}^{n}{X}_{ij}}\right.$$
(1)

where Yi is the measured stream sediment uni-element concentration, Xij is basin proportions, and Mj is a weighted mean uni-element concentration in each of the j (= 1, 2, …, m) lithological units in i (= 1, 2, …, n) sample catchment basins. Afterwards, the local background uni-element concentration Y’j due to j (= 1, 2, …, m) lithologic units in each sample catchment basin i (= 1, 2, …, n) is computable (Eq. 2):

$${Y^\prime}_{j}={~}^{{\sum }_{j=1}^{m}{M}_{j}{X}_{ij}}\!\left/ \!{~}_{{\sum }_{j=1}^{m}{X}_{ij}}\right.$$
(2)

The data were normalized using logarithmic transformation. Cluster analysis was applied on the data to select spatially and statistically correlated elements to copper (Gazley et al. 2015). Principal component analysis (PCA) was applied on the selected elements to map copper anomalies. The PCA sorts the data from the greatest to the least covariance in different PCs and helps decrease the dimension of the data (Wold et al. 1987). A PC with the highest copper loading and opposite loading between lead and zinc as copper pathfinder elements (McQueen 2005) with copper was chosen to map copper anomalies (Appendix Fig. 4g). In copper mineralized areas, copper is concentrated within the center of the mineralized area while lead and zinc show depletion (Wood and Trott 2017). This property was used to choose the best PC for copper concentration mapping.

Airborne geophysics

Airborne magnetometry and gamma-ray spectroradiometry helicopter-borne surveys were flown over the NKCMA by Geonex Aerodat Incorporated. The flight line spacing of 200 m with a 10-km tie line at 45- and 60-m altitudes was set to acquire magnetic and gamma-ray radiometry data (Ranjbar et al. 2011). Since most of the structures within the NKCMA have northwest-southeast trends, the flight lines were designed in a northeast-southwest direction. An altimeter and a global position system (GPS) on the helicopter recorded surveying altitude and coordination, respectively. A 16,780 cm3 downward-looking pack and a 4195 cm3 upward-looking crystal were used for EXPloranium GR-820 gamma-ray radiometer (Ranjbar et al. 2011). A high-sensitivity Scintrex cesium magnetometer sensor was used for the magnetic measurements (https://scintrexltd.com/product-category/airborne/). The measured data were preprocessed using different filters to enhance the signal-to-noise ratio (Reford and Paterson 1994). The processed data was provided in 1:50,000 scale sheets by the National Iranian Copper Industries Company (NICICo).

The ideal potassium content (anomalous radioelement potassium content that is characteristic for copper porphyry deposits), which was determined by using equivalent thorium concentration as lithological control, was computed to map potassic and phyllic alteration zones and reduce the effect of lithology ((Kmap average/Thmap average) × Thmap; Appendix Fig. 4h; de Quadros et al. 2003). The equivalent thorium over equivalent uranium ratio (eTh/eU) was used to map high potential areas of sulfide copper mineralization (Appendix Fig. 4i; Airo 2002).

Phyllic and argillic zones may have low magnetic susceptibility because of the oxidation processes, while potassic and propylitic zones have high magnetic intensity due to magnetite and/or pyrrhotite enrichment (John et al. 2010; Honarmand 2016). Reduction to the magnetic pole (RTP) was applied to correct the inclination effect of the magnetic field and locate high magnetic intensity values on top of the magnetic body (Appendix Fig. 4j; Nabighian et al. 2005). The analytic signal, a combination of horizontal and vertical derivations of magnetic intensity, was used to locate edges of magnetized lithological units that might be correlated with the concentration of magnetite and pyrrhotite within the potassic zones (Appendix Fig. 4k; Nabighian et al. 2005).

Data integration

The geoscientific layers used as input into AHP-VIKOR processing were first converted into raster format with the same pixel size, dimension, and coordinates to enable data integration. All geoscientific layer values were converted into normalized linear fuzzy values using ArcMap software to make all layers comparable. The normalized linear fuzzy function of ArcMap software transforms and normalizes the lowest value to zero, the highest value to one, and values between them to between zero and one to keep the continuity of values in this range. This method helps to have a gradual change in pixel values. Due to the different measurement units of the geoscientific layers, they have different values for each pixel. For instance, the RTP uses nanoTesla (nT) as its measuring unit, and the pixel values vary from − 800 to + 1200 nT, while ideal potassium content has a percentage value as its measuring unit with values varying from 0.1 to 2.5%. Using different measurement units with different pixel values variation for a decision-making matrix would lead to biased results in the MPM. Values of each pixel for the different data layers were extracted to create a decision matrix for the VIKOR method. Based on spatial resolutions of geoscientific layers, and the overall size of the study region and mineralized areas, we decided to select 100 × 100 m pixel size as the optimum pixel size for integration (for more details about optimum pixel size selection refer to Hengl 2006).

The diagnostic exploration features of copper deposits in the study region are mentioned in the “Introduction” section, such as hydrothermal alteration zones, higher lineament density, higher potassium radiometric content, higher copper content in the stream sediments, lower magnetic susceptibility, associated with intrusive bodies (John et al. 2010), which were considered to make a workflow for exploratory data integration for mapping areas of high potential for copper mineralization within the NKCMA. After weighing the geoscientific layers with the AHP method (refer to the “Weighting geoscientific layers with AHP” section), except for alteration layers, the layers with the same source, such as fault density and multiple ring buffer, RTP and analytic signal, and ideal potassium content and eTh/eU ratio, were combined using a logical “Fuzzy OR” operator (Bonham-Carter 1994). The “Fuzzy-OR” is a union operator between two or more sets. This operator selects the maximum membership between the sets and produces maps with the maximum values. Since each geoscientific layer was important for copper exploration, the “Fuzzy-OR” operator was selected to integrate layers. The AHP weighted-combined geoscientific layers were used for data integration with the VIKOR method.

Weighting geoscientific layers with WofE

Data-driven methods and knowledge-driven methods have been used for the MPM (e.g., Bonham-Carter 1989; Carranza 2011). Weight of evidence (WofE), artificial neural networks (ANN), and regression analysis are some of the data-driven methods that have been used for the MPM (refer to Carranza 2011). These methods, unlike knowledge-driven methods, are suitable for the MPM in well-explored areas with sufficient ground truth information by dividing the information into training, testing, and validation categories. Since the region is well-explored, the WofE-derived weights were compared with the AHP-derived weights in order to assess the fairness of the AHP-derived weights and to be able to focus on the performance of the VIKOR method in mapping and ranking mineralized areas. The WofE method uses the log-linear form of the Bayesian probability model to estimate the relative weights of each geoscientific layer. Detailed information on the WofE is presented in Bonham-Carter (1989). By subtracting W+ (importance of a geoscientific layer for the MPM when it is present) from W− (importance of a geoscientific layer for the MPM when it is absent), weight contrast “c” is computable. The “c” parameter for each geoscientific layer shows the weight and correlation of that layer with the copper mineralization potential map.

The RV-A fractal method (Shahriari et al. 2014) was applied to classify each geoscientific layer into two classes: (a) the low potential of mineralization (assigned value: 0) and (b) the high potential of mineralization (assigned value: 1). The RV-A fractal method computes a power-law relationship between cumulative pixel areas and pixel values above a certain threshold (Cheng and Li 2002). Each break (gradient change) in the RV-A fractal plot shows a different dimension assigned to a specific phenomenon, such as background or anomalous values in a mineral potential map. Any changes in a characteristic of a phenomenon lead to a break in the RV-A fractal plot and are considered to be a threshold value. The total number of pixels in the study region, the total number of pixels within mineral deposits, the number of high potential pixels for each geoscientific layer, and common pixels between mineralized areas and high potential pixels for each geoscientific layer were extracted using ILWIS 3.3 software. For the total number of pixels with mineralized areas, the threshold for each deposit was extracted based on the available information (e.g., Nedimovic 1973). These parameters were applied to the formula described by Bonham-Carter (1989) to compute the weights with the WofE method. The AHP weights were compared with the WofE weights to assess the fairness of the knowledge-driven assignment of weights by AHP.

Weighting geoscientific layers with AHP

A decision-making group consisting of five academic professors and five field geologists with experience in copper exploration within the NKCMA were asked to weigh lithological units by making a pair-wise comparison between them. The pair-wise comparison ranges from 9 (as criterion A is more important than criterion B) to 0 (as the same importance for both criteria) to 1/9 (as criterion B is more important than criterion A). The AHP-weighted lithological shapefile was converted into a raster layer (Appendix Fig. 4l; see the “Data integration” section) and normalized using the normalized linear fuzzy function. Also, the decision-makers weighted each buffer class with the AHP method based on the closeness of that buffer class to a fault (refer to the “Data integration” section). Finally, the vector layer was converted into a raster layer and normalized using the normalized linear fuzzy function. The AHP extension for ArcGIS (https://codesharing.arcgis.com/?dbid=13764) was used to build a hierarchy matrix and compute weights, as mentioned in the “Data integration” section.

The decision-making group was asked to make a pair-wise comparison between the geoscientific layers based on their relative importance in copper exploration and data quality. Each normalized geoscientific layer was multiplied by its corresponding AHP weight to create AHP-weighted geoscientific layers. Then, the AHP-weighted layers with the same source were combined as described in the “Data integration” section. It should be considered that the inconsistency ratio of the pair-wise comparisons must be lower than 0.1 to rely on comparison judgments. Inconsistency values higher than 0.1 show that the preference logic is incorrect, and some comparison cases are judged unfairly. For instance, let us imagine that the decision-making group prefers the phyllic alteration zone twice more than the argillic alteration zone in terms of copper mineralization potential. Also, the decision-making group prefers the argillic alteration zone three times more than the propylitic alteration zone. Therefore, we expect that the decision-making group prefers the phyllic alteration zone six times more than the propylitic zone. If this assumption is rejected in any condition, the judgments are not acceptable, and the inconsistency ratio increases.

Modified AHP-VIKOR and mineral prospectivity mapping

The AHP-VIKOR decision matrix consists of pixel values (alternatives) of combined geoscientific layers (criteria) after weighting with the AHP method. Each column represents an AHP weighted-combined geoscientific layer, and each row shows a pixel value in that corresponding layer considering its geographic coordination. Since all layers were normalized by linear fuzzy function and then weighted by the AHP, the normalization and weighting steps of the VIKOR algorithm were omitted. The lowest (the worst) and the highest (the best) are determinable for each layer. The utility (S) and regret (R) values are the relative distance in feature space between a pixel value within each layer with the best and the worst values within that layer. In the VIKOR (Opricovic 1998), the embedded parameter “v,” VIKOR decision parameter, which varies within the interval [0, 1], shows the agreement of the decision-making group in weighting each criterion. Accordingly, high “v” values VIKOR parameters (> 0.5) are interpreted for dedication when the decision-making group members’ weight for each criterion is similar and close, and the effectiveness of group decision is more critical and effective than the personal opinion (Opricovic 1998). However, low values (< 0.5) for the VIKOR parameter show that agreement between the decision-making group is low and personal decisions are more important than group decisions (Opricovic 1998). Assigning 0.5 to the “v” parameter shows equal importance for personal and group decisions (Opricovic 1998). This interpretation shows the value of 0.5 can easily be interpreted while it is not clear how the differences between other values, for example, 0.6 with 0.7 on a made decision, cannot be expounded. To solve this problem modification process on the “v” was carried out through the mathematical concept of the expectation value inspired by Abbaszadeh Shahri et al. (2022). The expectation value of “v,” EV(v)’s expectation value, reflects the generalized weighted average (population means value) of a random “v” over many opinions. Accordingly, the EV(v) expresses the center of the distribution of “v” and consequently denotes a central value that the results will tend to. The EV(Vi) in n population size of parameters is defined as Eq. (3):

$$EV\left(v\right)=\sum_{i=1}^{n}{v}_{i}p({v}_{i})$$
(3)

where the AHP weights are the probabilities p(vi) and vi are the AHP pair-wise comparison values of each decision-maker. For instance, the pair-wise comparison value between lithology and fault for decision-maker number 1 multiplied by the final AHP weight for lithology plus the same pair-wise comparison value for the second decision-maker multiplied by the final AHP weight for lithology. Since the EV(v) can be reformulated using the average of “v” values (\(\overline{v }\)) in the population in which EV(v) then expresses essentially the long-term average value of the v. Referring to the law of large numbers (Dekking et al. 2005), the \(\overline{v }\) converges to the EV(v) as the number of repetitions approaches infinity. Therefore, by growing the samples, the mean gets closer to the average of the whole population (Dekking et al. 2005). This leads to the equivalent center of mass of the distribution of “v” and thus mathematically can be interpreted as the number of Bernoulli trials needed to get one success. The variance of “v,” Var(v), can be determined by Eq. (4):

$$Var\left(v\right)=EV\left(v\right)-EV{(v)}^{2}$$
(4)

where it (Eq. 4) can be reformulated as Eq. (5):

$$Var(v)=EV{[(v-\overline{v })}^{2}]=\frac{1}{n}\sum_{i=1}^{n}(\frac{{v}_{i}-\overline{v}}{v })$$
(5)

where v plays the role of a normalizing operator that can control the size of Var(Vi) and changes in the made decision.

Finally, the VIKOR value (Q) shows the score of each pixel. The lower the VIKOR value (Q), the higher the copper mineralization potential and the priority rank. MATLAB software was used to code and run the VIKOR algorithm. For more information regarding the VIKOR method’s formula and assumptions please refer to Opricovic (1998).

The AHP pixel values of the combined geoscientific layers were extracted using ArcMap software’s raster to points function to create a decision matrix for mapping favorable areas of copper mineralization. The decision matrix consists of 10 criteria as the AHP weighted-combined geoscientific layers and 698,000 alternatives as pixels for each layer. The worst and the best pixel values for each criterion/combined geoscientific layer were determined. The “v” parameter was computed by using the above-mentioned expectation value theory. The utility (S) and the regret (R) values were determined using the equations described by Opricovic (1998). Finally, the VIKOR value (Q) was computed for each pixel.

The obtained copper mineralization favorability map is called AHP-VIKOR because the geoscientific criteria are weighted with the AHP method and integrated with the VIKOR method. Each pixel has an AHP-VIKOR value and coordination to be mapped. The RV-A fractal method (Shahriari et al. 2014) was applied to classify the AHP-VIKOR copper mineralization potential map. Each break in the logarithmic plot shows a threshold value that defines this method’s copper mineralization potential class. The copper potential map was classified as very high, high, moderate, low, very low potential and background based on the RV-A fractal method classes and the AHP-VIKOR pixel values.

Accuracy assessment of the modified AHP-VIKOR method

Several exploration studies have been done in the NKCMA that led to the discovery of several copper deposits in this region (e.g., Nedimovic 1973; Ghorbani 2013). The locations of the explored copper mineralized areas were collected from the previous studies and used as a database to evaluate the accuracy of the AHP-VIKOR copper potential map. The very high potential class (the highest class) was assigned to the location of mines and copper deposits, and the high potential class (the second highest class) was assigned to the location of copper occurrence to create a confusion matrix and compute the accuracy of the AHP-VIKOR copper potential map. The confusion matrix uses the number of correctly and incorrectly classified and unclassified classes based on ground information to compute the accuracy of a thematic map (Congalton and Green 2019).

Modified AHP-VIKOR for ranking deposits

The ranking of the very high potential areas of copper mineralization was done based on the average AHP-VIKOR pixel value of each very high potential area of copper mineralization and then sorted from the smallest VIKOR (Q) value to the highest. Based on the VIKOR method in ranking, the lower the AHP-VIKOR pixel value, the higher the rank of that area. The ranked results were compared with the ore grade and ore tonnage information of each deposit collected by Nedimovic (1973).

Results

The WofE-derived weights for the geoscientific layers

Table 1 shows the positive, negative, and contrast weights of the geoscientific layers derived from the WofE method. The table shows that lithology, gossan, phyllic, and argillic layers have the highest weights due to their direct and strong relationships with copper mineralization (Nedimovic, 1973; Atapour and Aftabi 2007), and magnetometry, silicification, and propylitic layers have the lowest weights due to their indirect and weak relationships with copper mineralization and low data quality. All geoscientific layers, except the propylitic alteration zone, have positive weights.

Table 1 Positive (W+), negative (W−), and contrast (c) weights were obtained from the WofE method
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The AHP-derived weights for the geoscientific layers

Table 2 shows the pair-wise comparison ratios and the weights of the geoscientific layers derived from the AHP method. The inconsistency ratio of the AHP pair-wise comparison matrix is 0.054, which is less than 0.1 and shows the reliability and fairness of the judgments of the decision-making group in pair-wise comparison. According to this table, phyllic, gossan, and argillic layers have the highest weights due to their strong and direct relationship to copper mineralization (Lowell and Guilbert 1970; Atapour and Aftabi 2007), and similar to the WofE weights, magnetometry, silicification, and propylitic layers have the lowest weights.

Table 2 Decision matrix of the AHP for pair-wise comparison of geoscientific layers
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RV-A fractal for classification

Figure 2 demonstrates five breaks within the RV-A fractal curve between 0.28–0.35, 0.35–0.51, 0.51–0.57, 0.57–0.67, and 0.67–0.84 AHP-VIKOR scores. The breaks refer to threshold values for non-mineralized (AHP-VIKOR score range: 0.67–0.84) as background, very low (0.57–0.67) as areas with a possibility of pyrite mineral distribution, low (0.51–0.57) as areas with a low probability of secondary copper mineralization occurrence and indication, moderate (0.35–0.51) as areas with a high probability of secondary copper mineralization occurrence and indication, high (0.28–0.35) as areas with a high probability of economic copper mineralization and deposition, and very high (0.23–0.28) as areas with the highest probability of economic copper mineralization and deposition potential areas. The RV-A fractal method helped select unbiased and optimum threshold values for classification as shown by the different slope gradients of the cumulative area versus the AHP-VIKOR pixel value.

Fig. 2
figure 2

The very high (red), high (orange), moderate (dark yellow), low (green), very low (light blue), and background (dark blue) threshold values were obtained from the RV-A fractal method

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Modified AHP-VIKOR prospectivity map

The applied AHP-VIKOR method on the combined geoscientific layers with the VIKOR decision parameter “v” equal to 0.6 obtained from the expectation value showed its capability in identifying high potential areas of porphyry copper mineralization (Sar Cheshmeh, Darreh Zar, Meiduk, God-e-Kolevary, Nowchun, Sar Kuh, Bagh Khoshk, and Iju) which are currently actively mining (Fig. 3). This study’s examination of areas currently being mined demonstrated the capability of the AHP-VIKOR method for MPM.

Fig. 3
figure 3

The copper mineralization potential map obtained from integrating geoscientific data via the modified AHP-VIKOR method shows (a) malachite and turquoise mineralization within the Chah Firouzeh mine, (b) open-pit mine at Meiduk, (c) hydrothermal veinlets with pyrite mineralization close to the Sar Cheshmeh city, (d) Sar Cheshmeh open-pit mine, and (e) iron oxide stockworks within the phyllic alteration zone of the Kuh Panj area

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Accuracy assessment of modified AHP-VIKOR

The confusion matrix consists of 24 deposits/mines and 26 copper mineralization occurrences. Among all mining areas, merely three districts of Palangi (9), Bondar Baghu (18), and Sar Bagh (19) were classified as high potential areas (rather than the very high potential areas), and the rest were classified as the very high potential areas of copper mineralization. The result showed 84% accuracy for the classified AHP-VIKOR copper mineralization potential map via the RV-A fractal method (Table 3). The accuracy of the classified AHP-VIKOR copper mineralization potential map indicates the high performance of the RV-A fractal method in classification and the AHP-VIKOR in MPM. The accuracy of the AHP-VIKOR copper mineralization potential map showed that this method is useful for the MPM on the regional and local scales (i.e., Ghezelbash and Maghsoudi 2018; Khalifani et al. 2019). The kappa coefficient (0.68) showed a high interrater correlation (McHugh 2012) between the very high potential areas with the location of mines and depositions and the high potential areas with the location of copper mineralization occurrence.

Table 3 Confusion matrix for accuracy assessment of the classified AHP-VIKOR copper mineralization potential map
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Ranking mineralized areas with the modified AHP-VIKOR

The average AHP-VIKOR scores of the very high potential areas of copper mineralization were sorted from the lowest to the highest to rank them. Table 4 shows the AHP-VIKOR ranking for the very high potential areas of copper mineralization. The results demonstrate that copper deposits which are currently actively mining are ranked within the first half of the table, except for Bondar Baghu, and are located above all copper mineralization occurrence areas while copper mineralization occurrence and indication areas are located within the lowest part of the table. The presence of high-grade high-tonnage deposits within the first ranks shows that the AHP-VIKOR is a useful method for further exploration operations and mining activities.

Table 4 Comparison of the AHP-VIKOR ranking result for prioritizing the high potential of copper mineralization with the available information (Nedimovic 1973; Taghipour et al. 2008; Mirnejad et al. 2013; Parsapoor et al. 2017)
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Discussion

Comparison of the AHP- and WofE-derived weights

Knowledge-driven methods such as the MCDM methods have been used in many MPM studies (i.e., Pazand et al. 2012; Najafi et al. 2014; Khalifani et al. 2019; Pahlavani et al. 2020). The strength of using MCDM methods for the MPM is the possibility of benefiting from the experience and knowledge of a decision-making group that has both academic and practical orientations. The output of these studies, regardless of the used knowledge-driven methods, depends on the experts’ weights. Therefore, their judgment directly affects the output, and it is possible that the weights are not optimal. Studying and understanding mineralization conditions within a region are necessary to give accurate weights. If sufficient information regarding mineralization conditions (such as geologic settings) is not provided to the decision-makers, it is difficult to achieve successful results. Therefore, having prior knowledge of the study region is a prerequisite for using the MCDM methods. However, the knowledge-driven methods do not require ground truth information to train, test, and validate a model. Comparing AHP-derived weights with the weights derived from a data-driven method such as the WofE would help managers and geoscientists map high potential areas of mineralization with higher confidence.

Comparing the order of geoscientific layers of the WofE with the AHP shows that all layers have the same order of importance except for the lithological layer. This shows that the judgments of the decision-making group were fair. Lithology has the highest rank and weight in the WofE method because, based on previous studies, granodiorite units within the NKCMA are positively correlated with copper mineralization within the region (Zarasvandi et al. 2005; Shafiei et al. 2009; Asadi et al. 2014). However, it is ranked as the fourth-highest weight with the AHP as the decision-making group believed that hydrothermal alteration zones are more important than the lithological units in copper mineralization. The hydrothermal alteration model of Lowell and Guilbert (1970) demonstrated that the phyllic alteration zone contains copper mineralization. Since the phyllic alteration zone is outcropping within the NKCMA, the phyllic alteration zones have the highest order and weight by AHP and the second-highest order by the WofE. After the phyllic alteration zone, the gossanous zones have the third-highest and second-highest weight with respect to the WofE and the AHP because the gossan zone forms due to the destruction and oxidation of sulfide minerals (Atapour and Aftabi 2007); and it has a direct relationship with the location of the ore deposit. The argillic alteration zone is ranked as the fourth-highest and third-highest weight for the WofE and AHP, respectively, due to its extensive development in the region, identifying high potential areas. Minor copper mineralization can also be formed in the argillic zone, as reported in some cases, such as Sar Cheshmeh (Waterman and Hamilton 1975).

The copper content of stream sediments is related to copper concentration distributed within watersheds. However, the concentration of elements in stream sediments can be contaminated or diluted through the corresponding streams and do not reflect the true values on top of each lithological unit (Abdolmaleki et al. 2014). Therefore, compared to other geoscientific layers such as alteration zones, the stream sediment layer has lower importance and was ranked fifth for both the WofE and the AHP. Gamma-ray data helped to identify outcrops of phyllic and potassic alteration zones. However, as fewer details are observable with the gamma-ray data compared to the hydrothermal alteration maps derived from satellite imagery, it ranked as the sixth-highest weight for the WofE and the AHP. Previous studies demonstrated that mostly strike-slip faults are associated with copper mineralization (Mirzaie et al. 2015). However, the region also consists of normal and reverse faults, not mostly related to copper mineralization. Therefore, the fault layer has the fourth-lowest weight and rank for the WofE and the AHP. Compared to other exploratory data and the data quality, the RTP and analytic magnetic signal layers (as magnetometry layers) ranked as the third-lowest weight and rank in both the WofE and the AHP methods. Except for porphyry alteration zones that developed on the surface (e.g., Sar Cheshmeh and Darreh Zar), low magnetic intensity variation decreased the importance of magnetic measurement in the pair-wise comparison. Siliceous rocks are related to high copper grades and have less than the 5-m thickness (since they formed within the fractures of faults) in mineralized areas within the NKCMA (Atapour 2001). The emissivity images of ASTER with 90 m by 90 m pixel size can lead to uncertainty in siliceous rocks mapping, thus having the second-lowest weight and rank for both WofE and AHP. Propylitic alteration is extensively developed within the whole region and within the many lithological units such as Eocene andesite-basalt lava flows that are not related to copper mineralization. Thus, it has the lowest importance in prospecting high potential areas. The propylitic zone shows inverse weight signs for the WofE method, which means that the propylitic alteration zone does not correlate with the copper mineralization. This study showed that our decision-making group’s weights were similar to the weights derived from the WofE method on the regional scale. Therefore, the AHP-VIKOR mineral map and rank are not affected by the weights and reflect the AHP-VIKOR’s performance in mapping and ranking.

Performance and accuracy of modified AHP-VIKOR in MPM

One of the main goals of this study was to assess the accuracy and ability of the MCDM methods, particularly AHP-VIKOR, for MPM at the regional scale. Previously, the MCDM methods such as AHP and VIKOR have been merely used for the MPM at a local scale (1:100,000), and their performances at a regional scale (> 1:100,000) were not assessed (Ghezelbash and Maghsoudi 2018; Khalifani et al. 2019). Previous studies manually selected a value for the “v” parameter, and the assigned value would affect the final AHP-VIKOR map. In most cases, 0.5 was chosen for the “v” parameter to equalize the group and individual impact in VIKOR outcomes (Ghezelbash and Maghsoudi 2018; Khalifani et al. 2019). At the same time, it could be inaccurate, and there was no scale or logic for selecting other values. The “v” parameter was automated and determined a logic value based on the concept of the expectation value and the AHP pair-wise comparisons. The result for the “v” parameter, which was equal to 0.6, showed that the group decision is more important than personal and individual ideas in weighting. The accuracy assessment results demonstrated 84% accuracy by correlating 21 out of 24 depositions and mines as the very high potential areas of copper mineralization. The remaining areas (three areas) have vein-type copper mineralization, and they may be classified as high potential areas rather than very high potential areas because of data quality (spatial resolution) and pixel size of geoscientific layers. Therefore, this shows that the modified AHP-VIKOR is a useful technique for porphyry copper exploration with the regional scale datasets. The accuracy of the AHP-VIKOR method indicates that the RV-A fractal method, the dedicated weights for each geoscientific layer, the used geoscientific layers, and the assumed copper mineralization model were sufficient and useful for the identification of high potential areas. Comparing our work with previous research suggests that the accuracy of the modified AHP-VIKOR is slightly higher than the previously used AHP-VIKOR for the MPM due to the optimized assignment value for the “v” value, more geoscientific layers, and fairly assigned AHP weights (80–82% accuracy for the works of Khalifani et al. 2019; Pahlavani et al. 2020). Also, comparing the operation of the AHP-VIKOR as a knowledge-driven method with the support vector machine (SVM; Shabankareh and Hezarkhani 2017) and adaptive neuro-fuzzy inference system (ANFIS, Shabankareh and Hezarkhani 2016) in copper mineralization potential mapping in the same region demonstrated that the AHP-VIKOR discovers the copper mineralized areas, especially porphyry copper deposits, with higher accuracy (the accuracy with the SVM method: 78.3% and with the ANFIS method: 65%) and can rank the discovered areas for further exploration and mining operation activities. However, it should be mentioned that compared to Shabankareh and Hezarkhani (2017), we used more geoscientific layers, including gamma-ray datasets, as one of the useful exploration methods that improve MPM accuracy.

From a geological perspective, the background class within the AHP-VIKOR map (Fig. 3) indicates quaternary gravel fan units which are not hydrothermally altered, fractured, and weathered. Therefore, the chance of finding copper mineralization in these areas is very low. The very low potential areas within the AHP-VIKOR map are correlated with the limestone units that are altered to propylitic minerals such as calcite. There is a possibility of observing a randomly distributed pyrite (Lowell and Guilbert 1970). Low potential areas of copper mineralization within the AHP-VIKOR map are mostly correlated with the location of copper mineralization occurrence, such as randomly disturbed in the transition zone from propylitic to silicification. The moderate copper mineralization potential areas are associated with argillic alteration zones and andesite and basaltic units. In these areas, azurite, malachite, and pyrite could be observed. The high potential areas are located within the transition zone between argillic to phyllic and within the andesite and dacite units. These areas contain gossan zones minerals such as hematite, goethite, and jarosite, and other minerals such as malachite, azurite, pyrite, and chalcopyrite. The very high potential areas of copper mineralization are located within the phyllic-potassic-gossan zone and have dense mineralization of chalcopyrite, cuprite, native copper, azurite, and malachite.

Performance of modified AHP-VIKOR in ranking mineral deposits

The ability to rank criteria is the advantage of using MCDM methods for prioritizing explored deposits. The VIKOR method is based on proximity to the ideal point (best solution; closeness of each pixel to the highest and anomalous pixel values in each geoscientific layer) and does not consider the distance to the regret point (worst solution; maximum pixel value difference between each pixel and the highest pixel value in a layer). Therefore, this method is suitable for situations that the decision-makers want to make the most profit and least risk in any case which can be translated to the exploration of porphyry deposits due to their long life production and large ore tonnage.

The ranking result shows that the modified AHP-VIKOR sorts the porphyry deposits with high grades and tonnages (e.g., Sar Cheshmeh, Darreh Zar, Deh Siyahan, Nowchun, Chah Firouzeh, and Sar Kuh) as the highest priority for mining operation which is consistent with their current condition (mining). Sar Cheshmeh (13) as the highest rank contains the largest copper reserve (1.7 billion tons of Cu with the cut of grade of 0.6%) among all explored deposits within the NKCMA. The first six AHP-VIKOR ranks, including Sar Cheshmeh (13), Darreh Zar (14), Meiduk (6), Deh Siyahan (16), Nowchun (12), and Chah Firouzeh (23) are porphyry deposits with a million tons of ore reserve. God-e-Kolevary area which is currently mining is ranked higher than Iju and Bagh Khoshk porphyry deposits and their ranks are compatible with the corresponding copper ore tonnages. The God-e-Kolevary has a larger copper ore tonnage (46 million tons) than Iju (25 million tons) and Bagh Khoshk (27 million tons). A new area under the title of Raviz (22) has ranked in 12 place, which was not explored before and leads us to a new prospective area that needs further investigations such as rock sampling, ground geophysical survey, and drilling. Kuh Panj (21) porphyry district has the average copper grades of 0.7% and 0.2% (Nedimovic, 1973; Khosravi 2007) based on the drilling cores within the supergene and hypogene zones which are in mineable condition but due to the feasibility studies, the area has been remained unmined. The presence of Sereydoon (24), Kader (1), Abdar (8), Hosseinabad (10), Sar Bagh (19), Band-e-Bagh (20), Serenu (4), and Sara (5) areas with lower than 0.1% copper grade within the last lowest priorities showed that the non-economic areas are ranked as the latest rankings with the AHP-VIKOR method. The presence of three deposits of Sar Kuh (11), Bondar Baghu (18), and Palangi (9) in lower ranks would be related to their average low pixel values, which led to the lower ranks. The VIKOR method gives higher importance to the porphyry deposits, then to the vein-type deposits, and at the end to the copper occurrence areas in the ranking.

Summary and conclusion

This study has used the AHP to weigh different geoscientific layers and integrate them with the VIKOR to map and rank copper mineralized areas for exploration and mining activities. The AHP weights showed that geoscientific layers such as phyllic, gossan, argillic, and lithology that are directly correlated with copper mineralization have the highest weights. The WofE was used to evaluate the accuracy of the AHP-derived weights for geoscientific data layers. The comparison of the AHP and WofE weights showed that their geoscientific layer rankings are roughly similar, except for the lithology layer. The AHP and WofE could be used simultaneously to validate the decision-making group’s judgments. The expectation value concept optimizes and quantifies the decision-making parameter “v” of the VIKOR and in this study, group decision is more important than individual decisions. The real value-area (RV-A) fractal method was used to select the best threshold values to classify high potential areas and discriminate them from low potential and background areas. The modified AHP-VIKOR showed 84% accuracy for copper mineralization potential mapping. Also, the modified AHP-VIKOR showed that it is a useful method for ranking mineralized areas as it currently ranks mining and potential porphyry deposits as the highest priorities for exploration.