ORIGINAL PAPER
Application of concentration–number and concentration–volumefractal models to delineate mineralized zones in the Sheytoor irondeposit, Central Iran
Abulfazl Rahmati & Peyman Afzal &Seyed Amir Abrishamifar & Behnam Sadeghi
Received: 29 October 2013 /Accepted: 7 February 2014 /Published online: 7 March 2014# Saudi Society for Geosciences 2014
Abstract The aim of this study is to delineate Fe-mineralizedzones utilizing concentration–number (C–N) and concentra-tion–volume (C–V) fractal models in the Sheytoor iron de-posit located in Central Iran. The C–N model reveals fourmineralized zones characterized by Fe thresholds of 15.85,43.65, and 57.54 %, which represent wall rocks (Fe<15.85 %), weakly mineralized zones (15.85–43.65 %), mod-erately mineralized zones (43.65–57.54 %), and highly min-eralized zones (Fe >57.54 %). Results obtained by the C–Vmodel depicted four Fe-mineralized zones defined by Fethresholds of 26.3, 38.01, and 52.48 %, with zones <26.3 %Fe representing non-mineralized wall rocks and zones>52.48 % Fe show highly mineralized zones. Both the C–Nand C–V multifractal models indicate that highly and moder-ately mineralized zones are situated in the central and NE partsof the area. Their results were compared with the geologicalmodel using logratio matrix. Thus, the results show that thehighly and moderately mineralized zones derived via the C–Nmodel are more accurate than the C–V model.
Keywords Fractal models . Concentration–number (C–N) .
Concentration–volume (C–V) . Fe-mineralized zones .
Sheytoor
Introduction
The identification and recognition of different mineralizedzones and non-mineralized wall rocks are always the main
purpose in the economic geology and mineral exploration.The conventional geological methods were used formineralographical and petrographical studies (Cox andSinger 1986; Hitzman et al. 1992; Laznicka 2005; Pirajno2009; Shayestehfar et al. 2006). However, mathematicalmethods such as statistical analysis have been extensivelyutilized to support that purpose since the 1950s (Tukey1977; Davis 2002).
Mathematical modeling based on fractal/multifractal theo-ry (Mandelbrot 1983) has wide applications in the geosciencesand mineral exploration since the 1980s, e.g., Agterberg et al.(1993), Agterberg (1995), Bolviken et al. (1992) Cheng et al.(1994), Cheng (2000), Monecke et al. (2001), Zuo et al.(2009), Deng et al. (2010), and Afzal et al. (2011). Severalfractal/multifractal models have been proposed recently, e.g.,concentration–area (C–A; Cheng et al. 1994), concentration–distance (C–D; Li et al. 2003), concentration–volume (C–V;Afzal et al. 2011), and concentration–number (C–N;Hassanpour and Afzal 2013) on 2D and 3D data. Fractalmodels provide log-log plots with straight line segments fittedto the graph have some break points that are thresholds (Afzalet al. 2010, 2011; Bai et al. 2010; Carranza 2008, 2009, 2010;Carranza et al. 2009; Carranza and Sadeghi 2010; Cheng 1999,2007; Goncalves et al. 2001; Wang et al. 2011; Zuo 2011;Mohammadi et al. 2013).
In this paper, C–N and C–V multifractal models were usedfor separating various iron-mineralized zones in the Sheytoordeposit (Central Iran), and the results are compared with theresults of geological modeling.
Geological setting of the Sheytoor iron deposit
The Sheytoor iron deposit in the Bafq district is located 70 kmeast of Bafq city, Central Iran. The Bafq district is situated in ametallogenic area in Iran with other mines such as Choghart
A. Rahmati (*) : P. Afzal : S. A. Abrishamifar :B. SadeghiDepartment of Mining Engineering, Faculty of Engineering,South Tehran Branch, Islamic Azad University, Tehran, Irane-mail: [email protected]
P. AfzalCamborne School of Mines, University of Exeter, Penryn, UK
Arab J Geosci (2015) 8:2953–2965DOI 10.1007/s12517-014-1330-1
Fig. 1 Geological map of the Sheytoor area
Fig. 2 3D models of the Sheytoor iron ore deposit
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(iron), Esfordi (phosphate-magnetite), Koushk (lead and zinc),and Chadormalu (iron and apatite). In this district, there are alsoPrecambrian complexes with mineralizations of U, Th, V, Mn,Mo, Ti, Ba, apatite, rare earth elements (REEs), stratiform Pb-
Zn massive sulfides, and various types of Fe ore (Samani 1988;Förster and Jafarzadeh 1994; Daliran and Heins-Guenter 2005;Jami 2005; Jami et al. 2007; Bonyadi et al. 2011; Sadeghi et al.2012). Most parts of the Sheytoor iron deposit are covered by
Fig. 3 3D geological model of high and low concentration zones
Fig. 4 Histogram of Feconcentrations inlithogeochemical samples fromthe Sheytoor deposit
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alluvium. The north to northwestern and central parts of thedistrict are mainly made of up limestones and dolomites. Inaddition, only a few areas are metasomatic. Some outcropsof iron are in the central and southeastern regions. In con-trast, the main areas in the south were made up of granites,whereas the north to south in the eastern part of the districtis made up of sandstones (Fig. 1). The existence of the Feminerals magnetite and hematite are utilized to classify high-
grade and low-grade ores, respectively. The terms of “high-low” have been utilized in order to explain the Fe minerals,within the deposit.
Based on subsurface data consisting of collar coordi-nates of each drillcore, azimuth and dip (orientation),lithology, and mineralogy we generated a 3D geologicalmodel of the Sheytoor iron deposit using theRockworks™ v.15 software (Fig. 2). According to thisgeological model, the major part of the surface is madeup of lime and alluvium. Moreover, high- and low-gradeore zones are located in the center and NE parts of thearea. Obviously, the overlap between high-grade(magnetite) and low-grade (hematite) ores in the deepand semi-deep parts is observable in the center, south-ern, and eastern parts of the area (Fig. 3).
Table 1 Characteristicsof the semi-variograms atthe Sheytoor deposit
Characteristics Quantities
Nugget effects 90.3 %2
Sill 231.3 %2
Range 83.2 m
Fig. 5 Horizontal (a) and Vertical (b) semi-variogram of Fe data in the Sheytoor deposit
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Fractal models
C–N fractal model
The number–size (N–S) fractal model, which was orig-inally proposed by Mandelbrot (1983), can be used todescribe the distribution of geochemical populationswithout pre-processing of data. Based on that model,the C–N fractal model was proposed by Hassanpourand Afzal (2013) for analyzing the raw data of geolog-ical models. This model displays relations between geo-logical attributes (e.g., ore elements in this paper) andtheir cumulative frequency of samples. The model isexpressed by the following formula (Deng et al. 2010;Mandelbrot 1983; Sadeghi et al. 2012; Mohammadiet al. 2013):
N ≥ρð Þ∝Fρ−D ð1Þ
where ρ indicates element concentration, N(≥ρ) denotes cu-mulative number of samples with concentration values greaterthan or equal to ρ, F is a constant, and D is the scalingexponent or fractal dimension of the distribution of element
concentrations. According to Mandelbrot (1983) and Denget al. (2010), log-log plots ofN(≥ρ) versus ρ show straight linesegments with different slopes −D corresponding to differentconcentration intervals. This method is based on the fact thatthe number of samples reduces by increasing concentrationsof them.
C–V fractal model
The C–V fractal model was proposed byAfzal et al. (2011) fordelineation of different mineralized zones and wall rocks inIranian porphyry-Cu deposits. This model can be expressed asthe following (Yasrebi et al. 2012):
V ρ≤υð Þ∝ρ−α1 ; V ρ≤υð Þ∝ρ−α2 ð2Þ
where V(ρ≤υ) and V(ρ≥υ) denote two volumes with concen-tration values less than or equal to and greater than or equal tothe contour value ρ, υ represents the thresholds values thatoutline boundaries between different mineralized zones andwall rocks, and α1 and α2 are characteristic exponents. Toassess V(ρ≤υ) and V(ρ≥υ) in this study, the borehole data ofore element concentrations were interpolated usinggeostatistical estimation methods.
Discussion
From 37 boreholes, 832 lithogeochemical samples were col-lected and analyzed by XRF for various elements related to Fe
Fig. 6 C–N log-log plot for Fe concentrations in the Sheytoor deposit
Table 2 Zones in theSheytoor deposit basedon three thresholds of Fecontents defined fromthe C–N fractal model
Fe (%) Mineralized zones
<15.85 Wall rocks
15.85–43.65 Weakly mineralized
43.65–57.54 Moderately mineralized
>57.54 Highly mineralized
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Fig. 7 C–N fractal models of Fe 15.85–43.65 %
Fig. 8 C–N fractal models of Fe 43.65–57.54 %
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mineralization. A multimodal distribution is illustrated by thehistogram of Fe data with mean value of 34.03 % (Fig. 4). Thehorizontal and vertical experimental semi-variograms for theFe data in this deposit are similar and represent a range andnugget effect of 82 m and 90.3 %2, respectively (Table 1;Fig. 5).
C–N fractal modeling
The raw data were used for the C–N fractal modeling,and the relation between concentration and number wasshown in a log-log plot. Considering that abrupt chang-es in the slopes of conformed straight line segments
Fig. 9 C–N fractal models of Fe >57 %
Fig. 10 C–V log-log plot for Feconcentrations in the Sheytoordeposit
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fitted to the log-log plot represent boundaries betweenmineralized zones (Agterberg et al. 1996; Spalla et al.2010), four concentration populations were separated(Fig. 6). The first Fe threshold is 15.85 %, and valuesof <15.85 % Fe refer to wall rocks and weakly miner-alized zones. The Fe values of 15.85–43.65 % denotelow-grade mineralized zones. The Fe values of 43.65–57.54 % denote moderately mineral ized zones(representing a combination of low- and high-gradeores), whereas values of >57.54 % Fe pertain to highlymineralized zone (magnetite ore; Table 2; Figs. 7, 8,and 9). Moderately mineralized zones are located in thecentral and SW parts of the area, and just a small partof the deposit in the center is indicated to be Fe highlymineralized zone (Fig. 9).
C–V fractal modeling
The Fe distribution in the Sheytoor iron deposit was modeledby 10m×10m×10m voxels, which were concluded based onthe geometrical properties of the deposit and grid drillingdimensions (David 1970), with ordinary kriging using theDatamine Studio software. Using the 3D model of Fe distri-bution in the Sheytoor iron deposit, the C–V log-log plot wasprepared using amounts of concentrations and their occupiedvolumes, then some straight line segments were fitted to it,and consequently, three threshold values and four populationswere obtained (Fig. 10). The first Fe threshold is 26.3 %, andvalues of <26.3 % Fe refer to wall rocks. The second Fethreshold is 38.01 %, and values of 26.3–38.01 % Fe denoteweakly mineralized zones. The third Fe threshold is 52.48 %,and values of 38.01–52.48 % Fe refer to moderately mineral-ized zones, whereas values of >52.48 % Fe relate to highlymineralized zone (Table 3). According to these results, it wasfound that the low concentration zones are located in thecenter, east, and SE parts of the study area. Moderately min-eralized zones are situated in several parts of the center andeast of the area; however, only in the center part are the highlymineralized zones (Figs. 11, 12, and 13).
Table 3 Zones in theSheytoor deposit basedon three thresholds of Fecontents defined fromthe C–V fractal model
Fe (%) Mineralized zones
<26.3 Wall rocks
26.3–38.01 Weakly mineralized
38.01–52.48 Moderately mineralized
>52.48 Highly mineralized
Fig. 11 C–V fractal models of Fe 26.3–38.01 %
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Fig. 12 C–V fractal models of Fe 38.01–52.48 %
Fig. 13 C–V fractal models of Fe >52.48 %
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Comparison of results derived via fractal modelsand geological model of the deposit
Results of C–N and C–V modeling of the Sheytoor irondeposit are compared to the 3D geological model of thedeposit constructed by utilizing the RockWorks™ v.15software. There is good correlation between both thegeological and C–N fractal models for low and moder-ately mineralized zones. This was proved by a matrix ofnumber of overlapping voxels in the geological and C–N fractal models (Carranza 2011; Fig. 9). This matrixassessed the type I error (T1E) and type II error (T2E),which are 0.73 and 0.15, respectively, and the overallaccuracy (OA) of the low and moderately mineralizedzones mapped by the C–N fractal model with respect tothe geological models is 0.82 (Table 4).
Comparison of the C–V fractal model with the geo-logical model shows that moderately mineralized zonesmapped by the former model has a lower accuracycompared to that of the C–N fractal model (Fig. 9;Table 6). The T1E and T2E values of the C–V fractalmodel with respect to the geological model are 0.62and 0.24, respectively, and the OA of the moderatelymineralized zones mapped by the C–V fractal modelwith respect to the geological model is 0.74 (Table 5).
With respect to highly mineralized zones in the geo-logical model, high-grade zones mapped by the C–Nfractal model have better accuracy than those mappedby the C–V fractal model. The T1E and T2E and OAvalues are 0.99, 0.0008, and 0.95, respectively, for C–Nfractal modeling (Table 6); whereas, for the C–V model,the T1E and T2E are 0.94 and 0.018, respectively, andOA is 0.93 (Table 7).
The C–N and C–V fractal modeling carried out werebased on raw and estimated data, respectively. For bet-ter comparison between the results obtained by thefractal models, statistical parameters of raw and estimat-ed data were calculated and compared, as shown inTable 8. Additionally, histograms of raw and estimateddata were generated which have shown multimodal dis-tribution (Fig. 14). Fe mean for raw and estimated data
Table 8 Comparisonbetween statistical pa-rameters of raw and esti-mated data
Parameter Raw data Estimated data
Data no. 832 1136
Max. 63.82 57.71
Min. 1.08 13.24
Range 62.63 44.44
Mean 34.02 37.14
Median 32.92 36.54
Variance 234.19 85.85
Table 7 Logratio matrix of the high-grade ore zones using C–V fractalmethod
Outside zones Inside zones
405 B 62 A Inside zones
21,208 D 1,074 C Outside zones
0.018739 T2E 0.945423 T1E
0.934986 OA
Table 4 Logratio matrix of the moderate-grade ore zones using C–Nfractal method
Outside zones Inside zones
3,170 B 303 A Inside zones
18,443 D 833 C Outside zones
0.146671 T2E 0.733275 T1E
0.824036 OA
Table 5 Logratio matrix of the moderate-grade ore zones using C–Vfractal method
Outside zones Inside zones
5,291 B 432 A Inside zones
16,322 D 704 C Outside zones
0.244806 T2E 0.619718 T1E
0.736472 OA
Table 6 Logratio matrix of the high-grade ore zones using C–N fractalmethod
Outside zones Inside zones
19 B 1 A Inside zones
21,594 D 1,135 C Outside zones
0.000879 T2E 0.99912 T1E
0.949272 OA
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is 34 and 37 %, respectively. Moreover, the variance ofestimated data is lower than raw data (Table 8) whichreveals that the C–V fractal modeling has smaller rangeof data. The lower difference between maximum andminimum of estimated data caused the thresholds de-rived via C–V fractal model to be closer together.
Conclusions
In this paper, the concentration–number (C–N) and concen-tration–volume (C–V) fractal/multifractal models were uti-lized to delineate different Fe-mineralized zones in theSheytoor iron deposit in the Bafq district, Central Iran. Boththe C–N and C–V fractal models indicate high-grade Fe-mineralized zones in the NE part of the deposit. The thresholdFe values for highly mineralized zones are 57.54 and 52.48 %based on the C–N and C–V fractal models, respectively.Models of moderately mineralized zones in the central andNE parts of the deposit contain 43.65–57.54 % Fe accordingto the C–Nmodel, and 38.01–52.48 % Fe according to the C–V model. The C–N model reveals weakly mineralized zonesand wall rocks containing 15.85–43.65 and <15.85 % Fe,respectively. In contrast, the C–Vmodel shows that wall rockscontain <26.3 %, and weakly mineralized zones contain 26.3–38.01 % Fe.
According to the correlation between results derived byfractal and geological modeling from drillcores in theSheytoor iron deposit, highly mineralized zones mapped byfractal models, especially the C–N model, have a strongrelationship with high-grade iron ores in the 3D geologicalmodel, and moderately mineralized zones correlate with low-grade iron ores in the NE and central parts of the Sheytoor irondeposit. Comparison of the fractal and geological modelsillustrate that highly and moderately mineralized zones de-rived by C–N fractal model have better accuracy than the C–Vfractal model both with respect to the geological model.
Acknowledgments The authors would like to thank Mr. GholamrezaHashemi, manager of the Iranian iron exploration project in IranMineralsProduction & Supply Co. (IMPASCO), and Dr. M. R. Mahvi, executivemanager of International Minerals Engineering Consultant Co. (IMECO),for authorizing the employment of the Sheytoor exploration data.
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