International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 The use of Dempster–Shafer model and GIS in integration of geoscientific data for porphyry copper potential mapping, north of Shahr-e-Babak, Iran Majid Hashemi Tangestani∗ , Farid Moore Department of Geology, Faculty of Sciences, Shiraz University, 71454 Shiraz, Iran Received in revised form 18 October 2001; accepted 19 February 2002 Abstract The Dempster–Shafer (D–S) belief theory, as a knowledge-driven approach for map combination, is used for porphyry copper potential mapping, in an under-explored area, north of Shahr-e-Babak, Iran. The evidential function provides a theoretical basis for uncertainty management in data integration in an exploration project. The results of this approach show that strong support is found in the west-central part of the study area, where porphyry copper deposits are known. Plausibility for the proposition is also high in the west-central parts and coincides with the zone having strong support. The uncertainty is low in the west-central parts where there are more efficient data layers with respect to the proposition. Uncertainty is high in the zones where either there are fewer data layers or the data cannot provide strong support for the proposition or its negation. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Belief; Combination; Evidential function; Exploration; GIS; Knowledge-driven; Plausibility; Support; Uncertainty 1. Introduction Exploration projects carried out in unexplored regions are mostly based on geoscientific information that are integrated and processed by the use of GIS-based decision making models. Although some of the mapbased approaches allow one to estimate probabilities based on known exploration target occurrences (Bonham-Carter et al., 1988; Rencz et al., 1994; Scott, 2000), recent advances in exploration models and decision support systems make it possible to quantify specific map information even when there are small ∗ Corresponding author. Tel.: +98-711-2284572; fax: +98-711-2280926. E-mail address: tangestani@geology.susc.ac.ir (M.H. Tangestani). known or no target mineral occurrences in an exploration area (An et al., 1991; An, 1992; Wright and Bonham-Carter, 1996). Because many regions in Iran are not well-explored and only a few occurrences or deposits are known, the Dempster–Shafer (D–S) belief approach could be tested and evaluated for porphyry copper potential mapping and new target-area recognition. The D–S belief theory (Dempster, 1968; Shafer, 1976) is an alternative mechanism to the fuzzy logic theory for knowledge representation and map combination. This method has been discussed in a mineral exploration context using a dataset (An, 1992; An et al., 1994a,b; Chung and Fabbri, 1993; Chung and Moon, 1991). Wright and Bonham-Carter (1996) applied the method to combine a variety of geophysical datasets to predict base metal and iron- 0303-2434/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 3 - 2 4 3 4 ( 0 2 ) 0 0 0 0 8 - 9 66 M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 formation deposits in an area north and west of the Rusty Lake–Snow Lake Greenstone Belts, Manitoba, Canada. Aminzadeh (1994) also describes the application of this model in oil exploration. 2. Belief function theory A detailed theoretical exposition and a formalization of the belief function approach can be found in Dempster (1968) and Shafer (1976). It is a knowledge-driven approach (Bonham-Carter, 1994), with some advantages and disadvantages as compared with fuzzy logic (Zadeh, 1965). For example, one advantage of this approach is that it allows the user to represent uncertainty in the knowledge representation, because the interval between support (lower belief function or a conservative estimate for a proposition) and plausibility (an optimistic assessment that the evidence supports a proposition) can be considered as a confidence band. Missing data also could be modeled in D–S approach by defining the plausibility as 1, the support as 0, so the uncertainty as 1. Evidences from two or more maps are combined using Dempster’s rule of combination (Wright and Bonham-Carter, 1996, and Eqs. (1)–(3) cited therein). The combined support, plausibility, disbelief, and uncertainty can each be separately mapped, although only two of these quantities are independent. This contrasts with the fuzzy logic output, which consists only of a single map—the combined fuzzy membership. The output map in fuzzy model only evaluates the favorability for porphyry copper mineralization in various levels for the study area, but the outputs in D–S model represent a conservative estimate of the favorability, an optimistic estimate of favorability, and related uncertainties in different images. Each map to be used as evidence to evaluate a proposition (e.g. “this cell contains a porphyry copper deposit”) is associated with a pair of belief functions, the support function and the plausibility function. In practice, these functions are usually held in map attribute tables, where each class on the map is associated with a support value and a plausibility value. Suppose we have map A, we will simply denote the value of the support due to A, as SupA , and the plausibility due to A, as PlsA . Because functions vary with the value (map class) of A, they can therefore be mapped in their own right by lookup operations from map A. For a given value of map A, the uncertainty is denoted as UncA , calculated as PlsA − SupA , and the disbelief, DisA = 1 − PlsA . Thus, the sum SupA + UncA + DisA = 1. The disbelief is the belief that the proposition is false, i.e. that a cell does not contain a porphyry copper deposit. Note that plausibility is greater than or equal to support. Where plausibility and support are equal, the uncertainty is zero, and Sup + Dis = 1, as in the probability approach. The relationship between these functions is well illustrated in Wright and Bonham-Carter (1996, Fig. 33). For each map used as evidence, two independent functions must be estimated, usually either the support and disbelief, or the support and plausibility, but in some cases, the uncertainty may be calculated with one of the other functions values. An et al. (1994a) and Chung and Fabbri (1993) discuss the estimation procedure. Given two maps A and B, with the support and disbelief functions for each, Dempster’s rule of combination for estimating the combined support, disbelief and uncertainty are shown in Eqs. (1)–(3) (Wright and Bonham-Carter, 1996). SptC = SptA SptB + SptA UncB + SptB UncA β (1) DisC = DisA DisB + DisA UncB + DisB UncA β (2) UncC = UncA UncB β (3) where the denominator for all three equations is calculated using Eq. (4): β = 1 − SptA DisB − DisA SptB (4) where β is a normalizing factor that ensures that Spt+ Dis + Unc = 1. 3. Geology and mineralization The study area (30◦ 19′ –30◦ 30′ N, and 55◦ 05′ – 55◦ 30′ E) is located north of Shahr-e-Babak town, in SW Kerman province (Fig. 1). It is situated within the southern part of the central Iranian volcano–sedimentary complex. The geological evolution of the area can be simplified as formation and M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 67 Fig. 1. Geological map of the study area in the north of Shahr-e-Babak, Kerman, Iran. folding of early Tertiary volcano–sedimentary rocks, and emplacement of late tertiary granodiorite, diorite, monzonite and tonalite in the volcano–sedimentary complex. A more detailed description of the geology of an area between Rafsanjan Belt in NE to Sirjan Belt in SW, is given by Dimitrijevic (1973). Eocene volcano–sedimentary rocks consist of alkalibasalt–andesite flows and tuffs, and volcaniclastic sediments. These are intersected with Pliocene and Eocene sandstones, marls, sandy calcarenites and conglomerates. The oldest and youngest exposures are upper cretaceous rocks and the quaternary alluvial deposits and gravel fans, respectively. Some well known copper and lead–zinc deposits and occurrences are shown in Fig. 1. Hydrothermal alterations, mainly in the form of chloritization, biotitization, sericitization, epidotization, carbonization, and silicification, developed in the intrusive and the volcanic rocks, are widespread over the area. The zonal pattern of alteration at Meiduk is concentric and almost symmetrically arranged around a tertiary porphyry intrusive. Potassic, phyllic, argillic, and propylitic alterations and silicification have been recognized at Meiduk (Amraie, 1991). Drill core observations indicate a relatively large core of potassic alteration surrounded by a thick shell of phyllic alteration. Later argillic alteration has been locally superimposed on the two earlier alteration zones. The superimposition has occurred in places where the surface water is driven down in contact with suitable minerals. Argillization is more prominent and extensive at higher elevations, at surface and especially in tunnels where acidic waters circulate more freely. Propylitic alteration seems to be entirely hosted by andesitic wall rocks and extends outward for hundreds of meters around phyllic alteration zone. Several deposits and numerous important mineral occurrences exist in the Kerman region, among which 68 M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 the copper deposits and occurrences are of prime importance. Two main types of mineralization are identified, porphyry-type and the vein-type mineralization. Porphyry-type mineralization is more important and is located in the vicinity of post-Eocene intrusive bodies in the Eocene volcanic–sedimentary complex. The vein-type mineralizations are controlled by faults of different trends and cut both the intrusives and extrusives. Meiduk and Sara are the most important porphyry copper deposits in the region, while the Chah–Mesi is a polymetallic deposit. The Meiduk porphyry copper deposit, situated near Meiduk village (Fig. 1) is hosted by Eocene andesitic and basaltic rocks. The main intrusive body responsible for mineralization alteration at Meiduk is an epizonal dioritic porphyry stock of Oligocene to Pliocene age (Bazin and Hubner, 1969). This deposit was mined in ancient times and is currently mined for its porphyry copper. The copper ore grade in the supergene zone varies between 1 and 3%, the average being 1.52% Cu. The supergene plus hypogene ore reserves amount to 20 million tonnes (Geological Survey of Iran, 1973). The Sara copper occurrence is located northwest of Meiduk deposit (Fig. 1). The geology and mineralization is very similar to that of Meiduk. Altered dioritic porphyrite, is exposed over an area of about 1.5 km2 and surrounded by weakly altered Eocene volcanites and pyroclastites. Geochemical measurements indicate copper concentrations of 120–500 ppm. The exploratory drilling in the altered intrusive confirmed the presence of porphyry-type copper mineralization. The ore grade was low, on average about 0.15% Cu, and no supergene enrichment was detected (Geological Survey of Iran, 1973). The Chah–Mesi polymetallic deposit is located at the east of the Meiduk village (Fig. 1).The rocks of this area are comprised of Eocene volcanic–sedimentary complex, subvolcanic intrusive bodies of intermediate composition, and quaternary deposits. Both volcanites and porphyrite intrusives are highly faulted and fractured. The richest mineralization occurs along a diagonal fault between Eocene volcanites and diorite–porphyrite intrusives. According to Omaljev (1972), average ore grade include 1.27% copper, 1.01% lead and 2.12% zinc with minor amounts of silver (10–150 ppm) and gold (up to 7 ppm). 4. Data input and pre-processing The most time-consuming step in most GIS projects is building the database. According to variations in data models, data structures, and data formats, the input layers may have many sizes and shapes. A digital geoscientific data to be used in porphyry copper mineralization mapping in the study area was established. A geological map of Shahr-e-Babak, compiled by Geological Survey of Iran at a scale of 1:100,000 was used as a source of lithologic and lineaments information. The bedrock geology was digitized as a series of polygons. In order to link each polygon to a lookup table containing attributes, a unique identifying number was given to it. There were 176 unique polygons that were regrouped into 24 geological categories so that each unit could be separately evaluated within the modelling process. A generalized version of the geological map is shown in Fig. 1. Remotely sensed data including aeromagnetic and Landsat Thematic Mapper (TM) were used as other sources of information on magnetic anomalies, part of structural features, and hydrothermal alteration haloes. Stream sediment geochemical data consisting of 335 individual sample points were also used in the analysis. For each sample, data on geographic coordinates, geological sheet number, and concentration of 14 elements were provided. Concentrations of six elements, (Cu, Pb, Zn, Mo, As, and Ag), were processed and used in this study as pathfinders for porphyry copper deposits. The raw data were run by Standard Package for Social Sciences (SPSS) software and basic statistics for the samples were computed. The anomalous and background values of each element were then calculated. Geochemical anomaly patterns for the elements noted above were generated using the Surfer software. The output files were then converted into DXF format of AutoCad and imported into PC Arc/Info to be edited and clipped for the study area. Database for the anomalies of elements were managed using Foxpro software and the final coverages were then converted to a raster format usable in GIS. Linear structural features interpreted from aeromagnetic data were combined with lineaments available in geological map to generate a lineament map. The interpreted lineaments were digitized and input into GIS as a vector file. The lines provided in this layer were classified and coded into four main classes according M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 to their direction. A geologic expert has considered the EW direction as a criterion for porphyry copper occurrence in the Kerman region (Dimitrijevic, 1973). In this form, weighting of lineament information by direction and distance to potential copper mineralization was possible. The EW lineaments were selected, combined with lineaments interpreted from aeromagnetic data with same direction and finally converted to a raster format. Porphyry copper deposits and occurrences have a direct spatial association with granitic to intermediate plutonic rocks (Guilbert and Park, 1986). These plutonic rocks may act as a source for the metallic elements and/or the hydrothermal fluids responsible for mobilizing metals. For these reasons, contacts of appropriate intrusive bodies were considered as an important input parameter. To enhance the alteration haloes around intrusive bodies, the Crósta technique for principal component analysis (Crósta and Moore, 1989) was applied on reflective bands of Landsat TM (Tangestani and Moore, 2001). Eigenvector loadings for some visible and infrared bands of TM, (bands 1, 3, 4, 5, and 7), showed that in each case of analysis the first principal component is an indication for albedo, and the third for vegetation. Features with lower importance such as iron oxides or hydroxyls are concentrated in subsequent principal components. PC4 of unstretched data transformation on bands 1, 4, 5, and 7 indicate the hydroxyl bearing areas around the porphyry intrusives. Some enhanced areas coincide with present porphyry deposits, and some indicate new exploration targets. PC4 of unstretched data transformation on bands 1, 3, 4, and 5 indicate that iron oxide stained areas coincide with sedimentary terrains and are not suitable for exploration. The results of principal component transformation on stretched TM bands were relatively similar using the unstretched bands, but the images were brighter and the distinction between lithological units was easier. The enhanced areas for hydroxyls were then digitized and input into GIS as an important binary predictor. A helicopter magnetic/electromagnetic/radiometric (HMER) survey was flown by Geonex Aerodat Incorporated over an area of 7000 km2 , in the Kerman province, south central part of Iran. The aim of the project was mainly exploration of porphyry and vein-type mineralization in the Kerman region. 69 Reford and Paterson (1994) have worked on a part of HMER data and concluded that the porphyry copper deposits in the Kerman region are associated with a distinct low magnetic, relative to the host rock, a high potassium and low resistivity. The pre-processing of aeromagnetic raster data was done previously in the GIS department of Geological Survey of Iran. The magnetic anomaly districts were classified in four magnetic intensity groups. The magnetic anomaly map, available as hard copy, was digitized and input into the model. 5. Assigning belief function values The assignment of belief function values for input layers can be performed by a statistical method if an exploration area is well surveyed and there are sufficient target occurrences. The assignments using a statistical method is based on traditional probability theory. When an exploration area is not well-studied, the assignments must rely mainly on the knowledge and expertise of exploration geologists (Wright and Bonham-Carter, 1996). For the study area, the assignment of the belief function values was made subjectively for the input maps listed in the Table 1. In practice, two problems are encountered at this stage. The first difficulty is the conceptualization of belief and disbelief. There is a tendency to think of disbelief as one minus the belief. It is often difficult to quantify an opinion indicating the difference between disbelief and uncertainty. For dealing with this problem, it is suggested to evaluate the support and plausibility for the proposition, which could readily be quantified, and to calculate the disbelief and uncertainty, using the mentioned equations (Wright and Bonham-Carter, 1996). The second problem is that if both two maps considered for integration have large support values, the combined support becomes close to 1. Further combination with other maps with high support values results in values even closer to 1 (and disbelief and uncertainty approaching zero), making the results difficult to interpret. Assigning the low values for support as listed in Table 1 can be suggested for dealing with this problem. The target proposition for the north of Shahr-eBabak area is: “there is a porphyry copper deposit”. The propositions for porphyry copper from the input 70 M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 Table 1 Dempster–Shafer functions for each map used as evidence of porphyry copper deposits in the north of Shahr-e-Babak, Iran Dataset Di Spti Disi Unci Plusi Ag concentration (ppm) >2.6 0.25 2.4–2.6 0.20 2.2–2.4 0.15 2.0–2.2 0.10 1.8–2.0 0.05 <1.8 0.05 0.05 0.06 0.07 0.08 0.09 0.10 0.70 0.74 0.78 0.82 0.86 0.85 0.95 0.94 0.93 0.92 0.91 0.90 As concentration (ppm) >41 0.25 37–41 0.20 33–37 0.15 29–33 0.10 <29 0.05 0.05 0.06 0.07 0.08 0.10 0.70 0.74 0.78 0.82 0.85 0.95 0.94 0.93 0.92 0.90 Cu concentration (ppm) >150 0.30 140–150 0.25 130–140 0.20 120–130 0.15 110–120 0.10 100–110 0.05 <100 0.05 0.05 0.05 0.06 0.07 0.08 0.09 0.10 0.65 0.70 0.74 0.78 0.82 0.86 0.85 0.95 0.95 0.94 0.93 0.92 0.91 0.90 Mo concentration >10 9–10 8–9 7–8 6–7 <6 (ppm) 0.30 0.25 0.20 0.15 0.10 0.05 0.05 0.06 0.07 0.08 0.09 0.10 0.65 0.69 0.73 0.77 0.81 0.85 0.95 0.94 0.93 0.92 0.91 0.90 Pb concentration (ppm) >140 0.20 130–140 0.18 120–130 0.16 110–120 0.14 100–110 0.12 90–100 0.10 80–90 0.10 <80 0.05 0.05 0.06 0.06 0.07 0.08 0.09 0.10 0.10 0.75 0.76 0.78 0.79 0.80 0.81 0.80 0.85 0.95 0.94 0.94 0.93 0.92 0.91 0.90 0.90 Zn concentration (ppm) >230 0.20 220–230 0.18 210–220 0.16 200–210 0.14 190–200 0.12 180–190 0.10 160–180 0.08 <160 0.05 0.05 0.06 0.06 0.07 0.07 0.08 0.09 0.10 0.75 0.76 0.78 0.79 0.81 0.82 0.83 0.85 0.95 0.94 0.94 0.93 0.93 0.92 0.91 0.90 Aeromagnetic data (density) Low 0.05 Medium 0.10 0.18 0.15 0.77 0.75 0.82 0.85 Table 1 (Continued ) Dataset Di Medium–high High Spti Disi Unci Plusi 0.15 0.10 0.75 0.90 0.20 0.05 0.75 0.95 Proximity to intrusive body (m) On body 0.00–100 100–200 200–300 300–400 400–500 >500 0.25 0.22 0.20 0.18 0.15 0.10 0.05 0.05 0.06 0.07 0.08 0.10 0.12 0.15 0.70 0.72 0.73 0.74 0.75 0.78 0.80 0.95 0.94 0.93 0.92 0.90 0.88 0.85 Proximity to EW lineaments (m) 0.00–100 100–200 200–300 300–400 400–500 >500 0.15 0.12 0.10 0.08 0.06 0.05 0.05 0.08 0.10 0.15 0.18 0.20 0.80 0.80 0.80 0.77 0.76 0.75 0.95 0.92 0.90 0.85 0.82 0.80 Proximity to alteration (m) On alteration 0.00–100 100–200 200–300 300–400 400–500 >500 0.25 0.22 0.20 0.18 0.15 0.10 0.05 0.05 0.06 0.07 0.08 0.10 0.12 0.15 0.70 0.72 0.73 0.74 0.75 0.78 0.80 0.95 0.94 0.93 0.92 0.90 0.88 0.85 Generalized geology Red tuffs Andesite and basalt Volcanics Trachyandesit and tachybasalt Pyroclastics Diorite Altered rocks Volcanic conglomerate Tuff sandstone Hornblend phenoandesite Lava Volcanic conglomerate and sandstone 0.10 0.15 0.15 0.18 0.05 0.22 0.22 0.05 0.10 0.22 0.18 0.10 0.15 0.10 0.10 0.10 0.15 0.05 0.05 0.15 0.15 0.05 0.10 0.15 0.75 0.75 0.75 0.72 0.80 0.73 0.73 0.80 0.75 0.73 0.72 0.75 0.85 0.90 0.90 0.90 0.85 0.95 0.95 0.85 0.85 0.95 0.90 0.85 maps, indicated by Di (i = 1, 2, . . . , 11), are: Sptci = a porphyry copper deposit exists from Di . Disci = a porphyry copper deposit does not exsits from Di . Uncci = 1 − Sptci − Disci . The values of Sptci , Disci , Uncci , and Plusci assigned to the attributes of Di , using a knowledgebased evaluation, are listed in Table 1. M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 71 Fig. 2. Support map for the porphyry copper deposits at the north of Shahr-e-Babak, Iran. The ordered legend is on the basis of increasing support. The locations of Meiduk and Sara porphyry copper deposits are also shown in this figure and in Figs. 3 and 4. 6. Interpreting output images The belief decision support module in IDRISI for Windows software generates three outputs, belief, plausibility, and belief interval. The output images are reclassified into 10 classes. The support image (Fig. 2) represents the degree to which the evidence provides concrete support for the proposition. It is important to interpret it with the plausibility and belief interval images. The plausibility image (Fig. 3) shows the degree to which the evidence does not refute the proposition. The relationship between the two output images is significant for evaluating what decisions to make about the gathering information. Even if concrete evidence for a proposition is poor, i.e. belief values are low, it is still possible to have high plausibility values in those areas. This would suggest possible spaces where enough information exists to make a concrete decision about the use of these spaces or the allocation of resources to them. At the very least, it suggests where to narrow down the selection of areas where the gathering of more evidence seems necessary possible. The uncertainty (Fig. 4) is the difference between plausibility and support and acts as a measure of uncertainty about a proposition. The belief functions are shown in colored plots. Fig. 2 shows the spatial distribution of the belief or support for porphyry copper. Strong support is found in the west-central part of the study area, where the Meiduk and Sara porphyry copper deposits are located. A nearly strong support is also found around the Abdar occurrence. Moderate support is extended in two patches east of Meiduk and as an extension located to the south of Meiduk deposit. Weak support (<5 in classified order) is found in both areas where the datasets provide weak support for the target proposition and where there are fewer spatial data layers, mostly at the east of area. Fig. 3 shows the spatial distribution of plausibility, or the maximum support for porphyry copper. Plausibility for the proposition is high in the west-central part of the study area and coincides with the areas with strong support. A small area with relatively high plausibility is also found east of the Abdar occurrence. Low plausibility are also mainly at the east of area. The uncertainty plot (Fig. 4) shows the degree to which the target proposition is uncertain. The uncertainty is low in the west-central 72 M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 Fig. 3. Plausibility map for the porphyry copper deposits to the north of Shahr-e-Babak, Iran. The ordered legend is on the basis of increasing plausibility. Fig. 4. Uncertainty map for the porphyry copper deposits at the north of Shahr-e-Babak. The ordered legend is on the basis of increasing uncertainty. M.H. Tangestani, F. Moore / International Journal of Applied Earth Observation and Geoinformation 4 (2002) 65–74 area where there are more efficient data layers with respect to the proposition. Uncertainty is high in the areas where either there are fewer data layers or the data cannot provide strong support for the proposition or its negation. 7. Conclusion The D–S belief method is a flexible approach which provides the possibility for representing uncertainty in the data, but the assignment of probabilities is cumbersome, e.g. in comparison to the fuzzy model. The D–S method produces output that include a conservative estimate of the belief (support), and optimistic estimate of belief (plausibility), and related uncertainties (ignorances). The evidential belief function provides an adequate basis to represent geoscience information. Field observations suggest that the highest plausibility and support shown in output images are well coincided on the known deposits of the area, and some new targets are also introduced for more detailed exploration projects. So, it is concluded that evidential belief function theory, as a knowledge-based approach, could be a useful model in areas such as Iran, that are not well-explored. Although the knowledge-based data evaluation approach using in present study relies on the knowledge and expertise of exploration geologists, it facilitates individual interpretations of Di (i = 1, 2, . . . , n) to be pooled together and to form a set of maps representing the target. Acknowledgements The authors would like to thank the research council of Shiraz University for providing the necessary funds for this research. Dr. Alimohammadi of the Tarbiat Modares University is also thanked for his help in computerized methodology. The authors would like to express their gratitude to Mr. Navaie of Geological Survey of Iran for providing geochemical and magnetic data for this research. References Aminzadeh, F., 1994. Application of fuzzy expert systems in integrated oil exploration. Comput. Electr. Eng. 20, 89–97. 73 Amraie, A., 1991. The study of mineralization and hydrothermal alteration at Meiduk porphyry copper deposit, M.Sc. thesis. Shiraz University, p. 125. An, P., 1992. 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