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: rahmati.miner@gmail.com

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

2954 Arab J Geosci (2015) 8:2953–2965

(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

Arab J Geosci (2015) 8:2953–2965 2955

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

2956 Arab J Geosci (2015) 8:2953–2965

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

Arab J Geosci (2015) 8:2953–2965 2957

Fig. 7 C–N fractal models of Fe 15.85–43.65 %

Fig. 8 C–N fractal models of Fe 43.65–57.54 %

2958 Arab J Geosci (2015) 8:2953–2965

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

Arab J Geosci (2015) 8:2953–2965 2959

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 %

2960 Arab J Geosci (2015) 8:2953–2965

Fig. 12 C–V fractal models of Fe 38.01–52.48 %

Fig. 13 C–V fractal models of Fe >52.48 %

Arab J Geosci (2015) 8:2953–2965 2961

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

2962 Arab J Geosci (2015) 8:2953–2965

Fig. 14 Histograms of raw and estimated data for Fe values

Arab J Geosci (2015) 8:2953–2965 2963

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.

References

Afzal P, Khakzad A, Moarefvand P, Rashidnejad Omran N, Esfandiari B,Fadakar Alghalandis Y (2010) Geochemical anomaly separation bymultifractal modeling in Kahang (GorGor) porphyry system.Central Iran. J Geochem Explor 104:34–46

Afzal P, Fadakar Alghalandis Y, Khakzad A, Moarefvand P, RashidnejadOmran N (2011) Delineation of mineralization zones in porphyryCu deposits by fractal concentration–volume modeling. J GeochemExplor 108:220–232

Agterberg FP (1995) Multifractal modeling of the sizes and grades ofgiant and supergiant deposits. Int Geol Rev 37:1–8

Agterberg FP, Cheng Q, Wright DF (1993) Fractal modeling of mineraldeposits. In: Elbrond J, Tang X (eds) 24th APCOM symposiumproceeding, Montreal, Canada, p 43–53

Agterberg FP, Cheng Q, Brown A, Good D (1996) Multifractal modelingof fractures in the Lac du Bonnet Batholith, Manitoba. ComputGeosci 22:497–507

Bai J, Porwal A, Hart C, Ford A, Yu L (2010) Mapping geochemicalsingularity using multifractal analysis: application to anomaly defi-nition on stream sediments data from Funin Sheet, Yunnan, China. JGeochem Explor 104:1–11

Bolviken B, Stokke PR, Feder J, Jossang T (1992) The fractal nature ofgeochemical landscapes. J Geochem Explor 43:91–109

Bonyadi Z, Davidson GJ, Mehrabi B, Meffre S, Ghazban F (2011)Significance of apatite REE depletion and monazite inclusions inthe brecciated Se–Chahun iron oxide–apatite deposit, Bafq district,Iran: insights from paragenesis and geochemistry. Chem Geol 281:253–269

Carranza EJM (2008) Geochemical anomaly and mineral prospectivitymapping in GIS. Handbook of exploration and environmental geo-chemistry, vol 11. Elsevier, Amsterdam, 351:pp

Carranza EJM (2009) Controls on mineral deposit occurrence inferredfrom analysis of their spatial pattern and spatial association withgeological features. Ore Geol Rev 35:383–400

Carranza EJM (2010) From predictive mapping of mineral prospectivityto quantitative estimation of number of undiscovered prospects.Resour Geol 61:30–51

Carranza EJM (2011) Analysis and mapping of geochemical anomaliesusing logratio transformed stream sediment data with censoredvalues. J Geochem Explor 110:167–185

Carranza EJM, Sadeghi M (2010) Predictive mapping of prospectivityand quantitative estimation of undiscovered VMS deposits inSkellefte district (Sweden). Ore Geol Rev 38:219–241

Carranza EJM, Owusu E, Hale M (2009) Mapping of prospectivity andestimation of number of undiscovered prospects for lode-gold,southwestern Ashanti Belt, Ghana. Mineral Deposita 44:915–938

Cheng Q (1999) Spatial and scaling modelling for geochemical anomalyseparation. J Geochem Explor 65:175–194

ChengQ (2000)Multifractal theory and geochemical element distributionpattern. Earth Sci- J China Univ Geosci 25(3):311–318

Cheng Q (2007) Mapping singularities with stream sediment geochemi-cal data for prediction of undiscovered mineral deposits in Gejiu,Yunnan Province, China. Ore Geol Rev 32:314–324

Cheng Q, Agterberg FP, Ballantyne SB (1994) The separation of geo-chemical anomalies from background by fractal methods. JGeochem Explor 51:109–130

Cox D, Singer D (1986) Mineral deposits models. U.S. GeologicalSurvey Bulletin.1693:pp

Daliran F, Heins-Guenter S (2005) Geology and metallogenesis of thephosphate and rare earth element resources of the Bafq iron-oredistrict, central Iran. Proceedings of the 20th World MiningCongress, Iran, pp 357–361

David M (1970) Geostatistical ore reserve estimation. Elsevier,Amsterdam, p 283

Davis JC (2002) Statistics and data analysis in geology, 3rd edn. JohnWiley & Sons Inc, New York

Deng J, Wang Q, Yang L, Wang Y, Gong Q, Liu H (2010) Delineationand explanation of geochemical anomalies using fractal models inthe Heqing area, Yunnan Province, China. J Geochem Explor 105:95–105

Förster HJ, Jafarzadeh A (1994) The Bafq mining district in Central Iran -a highly mineralized Infracambrian volcanic field. Econ Geol 89:1697–1721

Goncalves MA, Mateus A, Oliveira V (2001) Geochemical anomalyseparation by multifractal modeling. J Geochem Explor 72:91–114

2964 Arab J Geosci (2015) 8:2953–2965

Hassanpour S, Afzal P (2013) Application of concentration–number (C–N) multifractal modeling for geochemical anomaly separation inHaftcheshmeh porphyry system, NW Iran. Arab J Geosci 6:957–970

Hitzman MW, Oreskes N, Einaudi MT (1992) Geological characteristicsand tectonic setting of Proterozoic iron oxide (Cu-U-Au-REE) de-posits. Precambrian Res 58:241–287

Jami M (2005) Geology, geochemistry & evolution of Esfordi phosphate(iron deposit, Bafq Area—Central Iran), Unpublished Ph.D thesis,University of New South Wales 384: pp

JamiM, DunlopAC, Cohen DR (2007) Fluid inclusion and stable isotopestudy of the Esfordi apatite-magnetite deposit, Central Iran. EconGeol 102:1111–1128

Laznicka P (2005) Giant metallic deposits future sources of industrialmetals. Springer Berlin Heidelberg, p 732

Li C, Ma T, Shi J (2003) Application of a fractal method relatingconcentrations and distances for separation of geochemical anoma-lies from background. J Geochem Explor 77:167–175

Mandelbrot BB (1983) The fractal geometry of nature. W. H. Freeman,San Fransisco, p 468

Mohammadi A, Khakzad A, Rashidnejad Omran N, Mahvi MR,Moarefvand P, Afzal P (2013) Application of number-size (N-S)fractal model for separation of mineralized zones in Dareh-Ashki golddeposit, Muteh Complex, Central Iran. Arab J Geosci 6:4387–4398

Monecke T, Gemmell JB, Monecke J (2001) Fractal distributions of veinsin drill core from the Hellyer VHMS deposit, Australia: constraintson the origin and evolution of the mineralising system. MineraliumDeposita 36:406–415

Pirajno F (2009) Hydrothermal processes and mineral systems. Springer,The University of Western Australia, Perth

Sadeghi B, Moarefvand P, Afzal P, Yasrebi AB, Daneshvar Saein L(2012) Application of fractal models to outline mineralized zonesin the Zaghia iron ore deposit, Central Iran. J Geochem Explor 122:9–19

Samani BA (1988) Metallogeny of the Precambrian in Iran. PrecambrianRes 39:85–106

Shayestehfar MR, Zarrabi A, Sharafi A, Yazdi A (2006) Petrology,petrography and mineralographical studies of “Choghart Iron OreMine”, Bafgh area, Iran. Geochim Cosmochim Acta 70:A578

Spalla MI, Morotta AM, Gosso G (2010) Advances in interpretationof geological processes: refinement of multi-scale data andintegration in numerical modelling. Geological Society,London, 240: pp

Tukey JW (1977) Exploratory data analysis. Addison-Wesley, Reading,MA, p 688

Wang QF, Deng J, Liu H, Wang Y, Sun X, Wan L (2011) Fractalmodels for estimating local reserves with different minerali-zation qualities and spatial variations. J Geochem Explor108:196–208

Yasrebi A, Afzal P, Wetherelt A, Foster P, Esfehanipour R (2012)Correlation between geology and concentration-volume fractalmodels: significance for Cu and Mo mineralized zones separationin the Kahang porphyry deposit (Central Iran). Geol Carpath 642:153–163

Zuo R (2011) Decomposing of mixed pattern of arsenic using fractalmodel in Gangdese belt, Tibet, China. Appl Geochem 26:S271–S273

Zuo R, Cheng Q, Xia Q (2009) Application of fractal models to charac-terization of vertical distribution of geochemical element concentra-tion. J Geochem Explor 102:37–43

Arab J Geosci (2015) 8:2953–2965 2965