Journal of Geochemical Exploration 134 (2013) 85–98

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Journal of Geochemical Exploration

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Quantitative assessment of mineral resources by combining geostatistics and fractalmethods in the Tongshan porphyry Cu deposit (China)

Gongwen Wang a,⁎, Zhenshan Pang b,⁎⁎, Jeff B. Boisvert c, Yinglong Hao a, Yuanxing Cao a, Jianan Qu a

a State Key laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Beijing 100083, Chinab Technical Guidance Center for Mineral Resources Exploration, MLR, Beijing 100120, Chinac Center for Computational Geostatistics, School of Mining and Petroleum Engineering, 3-133 Markin/CNRL, Natural Resources Engineering Facility, University of Alberta, Edmonton,Alberta T6G 2W2, Canada

⁎ Corresponding author. Tel.: +86 10 82323271.⁎⁎ Corresponding author. Tel.: +86 10 51632107.

E-mail addresses: gwwang@cugb.edu.cn (G. Wang), p

0375-6742/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.gexplo.2013.08.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 January 2013Accepted 5 August 2013Available online 14 August 2013

Keywords:3D geological modelingGeostatisticsHurst exponentC–V fractal model3D trend modelingTongshan porphyry-Cu deposit

Three-dimensional (3D) geological, geostatistical, and fractal/multifractal modeling are combined for the identi-fication of new exploration targets in the Tongshan porphyry Cu deposit (China): (1) A 3D geological model ofthe deposit includes the strata, faults, altered rocks, intrusive bodies, and three orebodies using geological map,cross-sections, borehole dataset, and magnetic inversion; (2) geostatistical analysis involves omnidirectionaland vertical semi-variogram calculations of the orebody, ordinary kriging interpolation of the orebody and 3Dtrendmodeling using the assay data; (3) fractalmodels consisting of Hurst exponent estimation of the continuityof verticalmineralization and its concentration–volume (C–V) fractalmodel separationmineralized zones in a 3Dblock model; and (4) interpretation and validation: magnetic inversion was utilized to constrain intrusive rockshape between cross-sections and additional interpret orebody geometry model by ordinary kriging interpola-tion method using Tongshan borehole dataset. The results indicate that (a) the Hurst exponent is useful foridentifying the vertical continuity of mineralization (with the range between 0 and 1200 m), (b) the C–V fractalmodel is useful for identifying thresholds of Cu values in oxidation-type, skarn-type, and magmatic-typeorebodies in the Tongshan deposit, and (c) the 3D geological and trend model can be combined to recognizepotential subsurface targets in the Tongshan deposit. The methods can be applied to estimate mineral resourcesthrough district-scale exploration.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Mineral exploration in a maturing mining district is challengingbecause it is accompanied by an increase in cost and risk of targetingdeposits at increasingly great depths, which requires more detaileddata and more expensive data acquisition methods (De Kemp et al.,2011;Houlding, 2000;Wanget al., 2011a,b). Combing geological knowl-edge andmathematical analysis aids in improving the understanding ofthe distribution of mineral resources at depth and the relationshipsamong strata, intrusive bodies, faults, and orebodies, which are impor-tant parameters for mineral exploration. The various types of kriging in-terpolation methods, both in 2D and 3D space, are key steps in mineralresource calculation and assessment. For example, kriging-based esti-mation techniques are generally important for the recognition of spatialdistribution patterns (Deutsch, 2002). Geostatistics has become increas-ingly popular for numericalmodeling and uncertainty assessment in theearth sciences (De Kemp et al., 2011; Deutsch, 2002; Deutsch andJournel, 1998; Leuangthong and Deutsch, 2004).

zs927@163.com (Z. Pang).

ghts reserved.

Three-dimensional geological modeling is an important technol-ogy in quantitative assessment and prediction of mineral resourceson a district scale, and conventional geostatistics has been developedto use 3D reverse estimation. Three-dimensional geological model-ing integrates geological, geochemical, and geophysical data for delin-eating of metallogenesis of mineral deposits and exploration targets ina 3D block model. Moreover, the variogram as a geostatistical tool canbe used to derive omnidirectional and vertical distributions of elementsin a mineral deposit and provides essential parameters for estimation/simulation and interpolation in a district-scale 3D block model(Houlding, 2000; Wilson et al., 2011). Given good supporting data,geostatistical tools are notably powerful when applied in a 3D GIS envi-ronment (De Kemp et al., 2011).

Since the 1980s, fractal andmultifractal models have been effective-ly applied to describe the distributions of geological objects (Agterberg,2012; Bansal et al., 2011; Carlson, 1991; Carranza et al., 2009; Cheng,1995, 2004; Cheng et al., 1994; Mandelbrot, 1983; Raines, 2008;Turcotte, 1997; Zuo et al., 2009a,b,c). Fractal and multifractal modelsare used to model geochemical or geophysical data (e.g., Afzal et al.,2010, 2012; Carranza, 2008, 2010a,b; Cheng, 2004; Daneshvar Saeinet al., 2012; Delavar et al., 2012; Sadeghi et al., 2012; Wang et al.,2011a,b; Zuo, 2011a,b, 2012; Zuo et al., 2009a, 2013) and have been

86 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

used to map geochemical and geophysical anomalies (Carranza andSadeghi, 2010; Cheng et al., 1994; Heidari et al., 2013; Wang et al.,2012a,b; Zuo et al., 2009a).

In this study, results obtained from 3D geological modeling of theTongshan porphyry Cu deposit and geostatistical and fractal methodsare combined to assess the mineral resources quantitatively and to de-lineate potential exploration targets at substantial depths, revise certaininterpretations of the Tongshan fault that were poorly correlated withborehole data, improve the understanding of the geological history ofthe Tongshan district, and serve as a guide during detailed exploration.The construction of the 3D geological model links sample observationsto geostatistical analysis and subsurface grade estimation using a bore-hole dataset.

2. Methodology

Results derived from the 3D geological, geostatistical, and fractal/multifractal modeling are combined in quantitative assessment ofmineral resources and delineation of potential targets in the Tongshanporphyry Cu deposit, China. The 3Dgeologicalmodel (the geological ob-jects include faults, alteration zones, orebodies, geophysical inversions,and intrusive rocks) of the Tongshan deposit was constructed using 94boreholes, 21 cross-sections, and 23,800 samples from the boreholedataset. The geostatistical analysis involved semi-variogram modelingof metal distribution in orebodies, ordinary kriging interpolation ofmetals in the orebodies and 3D trend modeling using KT3D.exe inGSLIB software (Deutsch and Journel, 1998). The fractal models whichwere used include (a) estimation of the Hurst exponent from theborehole dataset to model the continuity of mineralization and (b) ap-plication of the concentration–volume (C–V) fractal model to definean ore element threshold value to constrain the mineralization fluidcenter or a path in a 3D blockmodel (Afzal et al., 2011). These methodswere applied to identifying potential copper targets, which is the aim ofthis paper. For example, the Hurst exponent can be used to constrainsegments classified in KT3D.exe calculation for trend modeling,

Fig. 1. Schematic flow-chart for 3D modeling by in

parameters from omnidirectional and vertical semi-variograms ofmetal data are used in ordinary kriging interpolation analysis, and theordinary kriging interpolation results are subjected to C–V fractalanalysis for recognition of a Cu concentration center and the edges ofan orebody.

2.1. 3D geological modeling

The use of 3D models to better understand surface and subsurfacegeology is well-established (Calcagno et al., 2008; Fallara et al. 2006;Houlding, 1994; Kaufman and Martin, 2008; Lemon and Jones, 2003;Mallet, 2002). In this paper, the method we propose for 3D geologicalmodeling of the Tongshan porphyry Cu deposit involved the followingfour steps (Fig. 1):

(1) Step 1, geoscience data handling: acquiring, compiling, digitizingand standardizing the geological, geophysical, topographical,geochemical, and borehole datasets in a 3D coordinate system(x, y, z).

(2) Step 2, integration of the 2D geological data: importation of a dig-ital elevation model into the Micromine software (ASCII format)to model the topographic surface; importation of the boreholedataset (23,800 samples) including coordinates (x, y, z), dips,azimuths, depths, survey, geology, minerals, and alteration in-dexes into Micromine software; and integration of geologicalcontacts combining a 1:2000 scale geological map and 21 crosssections at a scale of 1: 2000 in AutoCAD.

(3) Step 3, 3D geological modeling: construction wireframe/geometrymodels of geological objects (Duobaoshan Formation, LuoheFormation, Tongshan fault, intrusive rocks, altered rocks, threeorebodies) using integration of the 2D geological data. Geologicalsurface models were built by contact curves and dip vectorsderived from the surface geological maps, cross-sections, anddigital elevation models. Geological subsurface objects were val-idated and interpreted by geophysical inversions and sparse

tegration of multiple types of geoscience data.

87G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

borehole data at depth. The contact relationship between twoobjects can be identified combing geological knowledge andwireframe Boolean operation model in Micromine software.When the 3D orebody wireframe/geometry model is completed,the 3D orebodymodel can be created using the borehole datasetand interpolation method. When the interpolation results ofgrade model between inverse distance weight (Wang andHuang, 2012) was compared to the ordinary kriging methods,we observed that the latter method created a better model ofthe geometry of mineralization associatedwith the zone of alter-ation in 3D space.

(4) Step 4, interpretation and validation: geological maps, the bore-hole dataset and magnetic inversion were used as additionalcontrol elements between the interpreted cross-sections; mag-netic inversion was utilized to constrain intrusive rock shape be-tween cross-sections and additional interpret Cu geometrymodel by ordinary kriging interpolationmethod using Tongshanborehole dataset; geological knowledge was used to analyze thepotential mineral targets (e.g., 3D buffer analysis was used toconstruct a 3D intrusive rock model for delineating the likelyporphyry Cumineralization zones, and 3Dmodels of the porphy-ry alteration rocks were used to identify the edges or center ofthe orebody).

2.2. Geostatistics analyses

2.2.1. Semi-variogram analysisA semi-variogram model is a mathematical expression that relates

semi-variance (γ) to distance and represents the measured variabilityof the available samples (Journel and Huijbregts, 1978). Semi-variogramanalysis provides a powerful technique for analyzing the adequacy ofthe available samples, specifically their spatial distribution and densityfor purposes of characterization (Houlding, 2000). One of the advan-tages of the analytical semi-variogram is that it provides a logicalbasis for deciding which of the available samples of a regional variableare relevant for estimation of a point in the subsurface (Houlding,2000). Semi-variograms serve a number of functions with respect toassessing characterization quality. These functions include providing ameasure of the adequacy of sampling, ameasure of the spatial variabilityof the samples, and the degree of correlation between the semi-variogram models employed for estimation and the measured spatialvariability.

The variations inmineral grademay not be the same in all directions(David, 1977). Therefore, omnidirectional and vertical analysis of semi-variograms is important for 3D orebody modeling and 3D mineraliza-tion trend modeling. The former is associated with interpolation, andthe latter is associated with selecting a search radius in a 3D space. Inthis study, both the Stanford Geostatistical Modeling Software (Remyet al., 2009) and the GSLIB (Deutsch and Journel, 1998) gamv.exevariogram program were used to analyze irregularly distributed bore-hole data in the 3D space. The vertical variogram is a combination ofall borehole data. The experimental variogram may show a trend inany one or more of the principal directions, and the trend can be easilyidentified as the experimental variogram continues to increase aboverandom variance as the lag distance.

2.2.2. 3D trend modelingTrends are deterministic or predictable patterns of the spatial distri-

bution of grade or petrophysical properties. Certain trends can be in-ferred from geological knowledge, and certain trends can be detectedby applying geostatistics tools (e.g., kriging) to well/borehole data(Deutsch and Journel, 1998). In certain cases where the mineralizationenvironment is well understood, trends can be detected using geologi-cal knowledge of the site of interest. In most cases, however, the dataare the sources of information for trend detection. Large-scale spatialfeatures can be detected during several stages of data analysis and

modeling. The most common and straightforward approach is to theseparate residual value (RV) into two components, the trend and theresidual:

Z uð Þ ¼ m uð Þ þ R uð Þ; ð1Þ

where Z is the original RV, m is the trend or mean component, R is theRV, and u denotes the location, commonly in the form of Cartesian coor-dinates (x, y, z).

The mean component is defined from all locations via a 3D trendmodel, while residual values are defined only for data locations.Geostatistical modeling is then only performed on residuals consideredto be stationary. Multiple realizations of residuals are generated andadded back to the single trend model to produce multiple realizationsof the original RV. There is no unique way to integrate these two trendsinto a consistent 3D trend model (Deutsch, 2002). However, one ap-proach can be used to scale the areal trend by the proportion of the ver-tical trend to the global mean:

m x; y; zð Þ ¼ mglobalm zð Þmglobal

!m x; yð Þmglobal

!: ð2Þ

This approach is straightforward and well-adapted to practice incases where limited data may make it difficult to develop a full 3Dtrendmodel. Inherent in Eq. (2) is an assumption of conditional indepen-dence of the vertical trend component within the horizontal plane andthe horizontal trend component in the vertical direction (Leuangthongand Deutsch, 2004).

The GSLIB program KT3D.exe is a particularly powerful modelingtool (Deutsch and Journel, 1998; Leuangthong and Deutsch, 2004).The program KT3D.exe provides a fairly advanced 3D kriging programfor blocks by simple kriging, ordinary kriging, or kriging with a polyno-mial trend model with up to nine monomial terms.

2.3. Fractal modeling

The fractal models are utilized to analyze spatial features in theTongshan deposit: (1) a Hurst exponent model is used to characterizethe continuity of mineralization along boreholes and identify the centerof the mineralization or the edge of orebody III; and (2) the C–V fractalmodel is used to distinguish supergene enrichment and hypogene zonesfrom oxidation-type zones and to separate skarn-type orebodies andporphyry-type orebodies based on the distribution of Cu grades in the3D block model.

2.3.1. Hurst exponent modelThe Hurst exponent proposed by Hurst (1951) is directly related to

the fractal dimension of a process and provides a measure of processroughness. The Hurst exponent is associated with a self-affine record,which measures the long-range dependence in a time series and pro-vides a measure of long-term nonlinearity. The values of H lie between0 and 1. If H = 0.5, the cumulative behavior is a random walk and theprocess produces uncorrelated white noise. Values of H b 0.5 representnonpersistent behavior whereas values of H N 0.5 represent fractionalBrownian motion with increasing persistence strength as H approaches1. The rescaled range analysis (R/S) implies the ratio of the rescaledrange (R) to the standard deviation (S) and can be used to estimatethe Hurst exponent (Mandelbrot and Wallis, 1969) as follows. An or-dered data sequence is divided into d contiguous sub-series of lengthn, such that d × n = N is the total number of samples. For each of thesub-seriesm, wherem = 1,…, d, the following analyses are performed.

(i) Determine the mean, Em, and standard deviation, Sm, of the datain each sub-series.

(ii) Normalize each data point (Zi, m) in each sub-series by subtracting

Table 13D interpolation block models of three orebodies in Tongshan deposit.

Orebody I Orebody II Orebody III

Grade Volume Accumulated volume Grade Volume Accumulated volume Grade Volume Accumulated volume

≤0.0795 162,848 162,848 ≤0.0635 855,232 855,232 ≤0.0625 1,643,920 1,643,9200.159 108,072 270,920 0.127 1,454,256 2,309,488 0.125 1,281,216 2,925,1360.2385 185,128 456,048 0.1905 2,160,448 4,469,936 0.1875 2,841,424 5,766,5600.318 376,328 832,376 0.254 1,941,040 6,410,976 0.25 4,771,368 10,537,9280.3975 398,224 1,230,600 0.3175 2,101,152 8,512,128 0.3125 7,143,920 17,681,8480.477 361,944 1,592,544 0.381 2,199,208 10,711,336 0.375 9,972,752 27,654,6000.5565 310,640 1,903,184 0.4445 2,060,336 12,771,672 0.4375 10,149,696 37,804,2960.636 270,344 2,173,528 0.508 1,643,752 14,415,424 0.5 6,223,960 44,028,2560.7155 265,976 2,439,504 0.5715 1,839,640 16,255,064 0.5625 4,281,888 48,310,1440.795 140,776 2,580,280 0.635 1,404,736 17,659,800 0.625 2,731,632 51,041,7760.8745 109,944 2,690,224 0.6985 895,968 18,555,768 0.6875 1,616,096 52,657,8720.954 137,384 2,827,608 0.762 803,888 19,359,656 0.75 915,072 53,572,9441.0335 91,032 2,918,640 0.8255 349,256 19,708,912 0.8125 493,176 54,066,1201.113 57,432 2,976,072 0.889 386,616 20,095,528 0.875 220,552 54,286,6721.1925 37,224 3,013,296 0.9525 78,496 20,174,024 0.9375 105,816 54,392,4881.272 14,848 3,028,144 1.016 55,640 20,229,664 1 35,392 54,427,8801.3515 3512 3,031,656 1.0795 7712 20,237,376 1.0625 16,056 54,443,9361.431 10,776 3,042,432 1.143 2320 20,239,696 1.125 9016 54,452,9521.5105 15,760 3,058,192 1.2065 96 20,239,792 1.1875 5592 54,458,5441.59 14,712 3,072,904 1.27 16 20,239,808 1.25 12,040 54,470,584

88 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

Em:

Xi;m ¼ Zi;m−Em;m ¼ 1;2;…;n ð3Þ

(iii) Create a cumulative series by consecutively summing the normal-ized data points:

Yi;m ¼Xni¼1

Xi;m ð4Þ

(iv) Use cumulative series to find the range:

Rm ¼ max Yi:m;…; Yn;m

� �−min Yi:m;…;Yn;m

� �ð5Þ

(v) Rescale the range by dividing the range by the standard deviation(i.e., Rm / Sm).

(vi) Calculate themean of the rescaled range for all sub-series of lengthn:

R=Sð Þn ¼ 1d

Xdm¼1

Rm=Sm ð6Þ

(vii) The length of nmust be increased to the next higher value, whered × n = N, and d is an integer value. Repeat steps (i) to (vi) untiln = N/2.

(viii) Finally, estimate the value of H as the slope of the regression linefor log (N) versus log (R/S).

2.3.2. C–V fractal modelThe fractal concentration–area model in 2D space can be used to

separate geochemical anomalies from background (Cheng et al., 1994)and identify various mineralization zones in potential targets (Wanget al., 2011a,b). Afzal et al. (2011) proposed the C–V fractal model fordelineating of supergene enrichment and hypogene zones from oxida-tion zones and barren host rocks in the Chah-Firouzeh and Sungunporphyry Cu deposits, northwestern Iran, which are situated in SE andNW parts of Iran, respectively.

The C–V fractal model can be expressed as

V ρ≤νð Þ∞ρ−a1 ;V ρ≥νð Þ∞ρ−a2 ; ð7Þ

where V(ρ ≤ ν) and V(ρ ≥ ν) denote two volumes with concentrationvalues (ρ) less thanor equal to and greater than or equal to, respectively,the contour value (ν), which represents the cutoff/threshold value of azone (or volume); and a1 and a2 are characteristic exponents.

The C–V fractalmethodwas used to identifymineralization, primaryand secondary orebodies (based on Cu concentrations at the center oredge) in 3D space based on the 3D geological model and borehole logsin study area. The terms “high,” “medium” and “low” in 3D space havebeen used to classify mineralized zones based on C–V fractal modelingin 3D space in the Tongshan deposit. To calculate V(ρ ≤ ν) andV(ρ ≥ ν) in the 3D model, 23,800 geochemical samples were collectedfrom the 94 boreholes at 1-m intervals. The deposit was modeledusing 50 m × 50 m × 25 m voxels based on the geometric propertiesof the deposit and grid drilling dimensions established as a Cu depositexploration standard in China (2002). The Cu grade distribution blockmodels of the study area were generated by the ordinary kriging meth-od using Micromine software. Log–log plots of the corresponding vol-umes (V(ρ ≤ ν) and V(ρ ≥ ν)) follow a power–law relationship, andthebreaks between strait-line segments in those log–log plots representthreshold values separating populations of geochemical concentrationvalues representing mineralogical zones (Afzal et al., 2011; Yasrebiet al., 2013). The C–V fractal method can be implemented with the aidof Matlab software: (1) first, a text file of the 3D interpolation blockmodel data is imported and read using Micromine software, (2) next,grades are sorted form high to low, (3) the block model data are classi-fied, (4) the number of voxels for each class are counted and theaccumulated value of these in orebodies I, II, and III, respectively, is com-puted (Table 1), (5) and finally, the logarithm of all Cu grade data andaccumulated frequency values are calculated and a C–V log–log plot isdrawn.

3. Geological setting of case study

The Tongshan porphyry Cu deposit is located in the Da HingganMountain fold system of Inner Mongolia and is located 4 km from thewell-known Duobaoshan porphyry Cu deposit. The 3D study area issituated within the coordinates 4,248,400–4,249,000 N and 3,764,000–3,767,000 E. Elevations, including the subsurface portions of the model,range from 620 m to −1000 m relative to sea level (Figs. 2 and 3).

The study area consists of up to 6000 m of Ordovician marinevolcano-sedimentary rocks (of basaltic, andesitic or rhyolitic composi-tions) formed in an active continental margin, island arc environment

Fig. 2. Geological map of the Tongshan copper deposit and cross section along the 1080 exploration line (AB) delineating three orebodies (Wang and Huang, 2012).

89G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

(Du et al., 1988). The Tongshan Cu deposit is located on the southwest-ern limb of an inverted anticline. The core of the inverted anticline con-sists ofMiddleOrdovician rocks of the TongshanFormation,whereas thelimbs consist of andesite and andesitic tuff of the Middle OrdovicianDuobaoshan Formation. Volcanic rocks of the Duobaoshan Formation,with a thickness of approximately 3000 m, host the primary stratum

of Cu mineralization (with 106–132 ppm Cu) (Du et al., 1988). EarlyOrdovician granodiorite and other intrusive rocks are considered to bethe Cu-ore source rock. SHRIMPU–Pb dating of zircon from the granodi-orite yielded an age of 479.15 Ma, and Re–Os isotopic isochron agesobtained from molybdenites are 506 ± 14 Ma (Cui et al., 2008; Wuet al., 2009). The granodiorite is associatedwith tonalite with amarginal

Fig. 3. (A) 3D model of orebody and alteration zoning, and (B) 94 boreholes, Tongshancopper deposit.

Fig. 5. 3Dmodel of orebody Cugrade, Duobaoshan Formation, Luohe Formation, Tongshanfault, and intrusive rock with 500 m buffer, Tongshan copper deposit. Orebodies areclassified by different Cu grade classification using irregular hexahedrons.

90 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

facies of quartz diorite porphyry developed along the footwall of theTongshan fault. The mineralized Duobaoshan Formation exhibits stronghydrothermal alteration, similar to typical porphyry-type alterationzoningwith intense potassic, silica, chlorite, andpropylite (locally devel-oped illite-carbonate) zonation from the center outward. The average

Fig. 4. Cu histogram of 23,800 sample surveys from 94 boreholes in the Tongshan copperdeposit.

amount of Cu in the alteration rock is more than 0.1%. The orebody ishosted mainly in potassic, silica and phyllic alteration zones within thequartz diorite porphyry; however, coppermineralization is closely asso-ciated with silicification and sericitization. The Tongshan deposit is atypical magmatic-hydrothermal deposit and has a geological setting, al-teration sequence, and mineralization characteristics similar to those ofthe Duobaoshan porphyry Cu deposit. These two deposits are bothskarn-type orebodies created whenmagma of basaltic, andesitic or rhy-olitic compositions was emplaced next to volcano-sedimentary wallrocks (Du et al., 1988). Orebody II is the longest orebody (2.2 km) inthe Tongshan deposit; its width is 25–713 m. Orebody I is present atthe highest elevation (530 m), whereas orebody III is concealed and incontact with granodiorite at a depth of 862.5 m. The Tongshan fault isa 30–40° dipping reverse fault that strikes primarily E–W for morethan 10 km and is more than 10 m wide (Fig. 3). The fault transectsand offsets orebodies II and III in the study area and thus postdates theformation of the Tongshan deposit. Therefore, there are two key geolog-ical questions that needed to be addressed: (1) Did the Tongshan faultdestroy orebody II? and (2) where is the deep potential target?

4. Discussion

4.1. 3D geological model of Tongshan deposit

4.1.1. Multiple geoscience information datasetsThe 3D geological models of the study area were constructed using

geoscience datasets collected from geological objects and metallogenicfeatures, including a 1:2000 geologicalmap, 21 1:2000 geological explo-ration cross-sections, a 1:2000 digital elevation model, 44,420 m logsfrom 94 boreholes (the maximum depth was 1342 m; the logs de-scribed the collar, deviation from vertical, depths, geology, mineralizedintersections, faults, alteration indexes, magnetic susceptibility, density,minerals, and Cu assay), 23,800 Cu-grade surveys from the 94 boreholeswith a L distribution (Fig. 4), and 5880 geophysical survey points (mag-netic and topographic). The Cu grade mean from the 23,800 assay datais 0.32%, which is larger than the value of industrial grade of Cu depositin China (0.30%), and it shows generally low grade characteristics ofporphyry-type deposit in the world. However, in Tongshan Cu deposit,the Orebody I is oxidation-type zone, the value of Cu grade is larger

(A) Omni- direction variogram of Tongshan copper deposit (B) Vertical variogram of Tongshan copper deposit

(C) variogram of III orebody in Tongshan copper deposit (D) Vertical variogram of III orebody in Tongshan copper deposit

Fig. 6.Variograms for the Tongshan copper deposit. (A) Omnidirectional variogram of the Tongshan copper deposit. (B) Vertical variogram of the Tongshan copper deposit. (C) Variogramof orebody III in the Tongshan copper deposit. (D) Vertical variogram of orebody III in the Tongshan copper deposit.

91G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

than 0.30%, and the high value of Cu grade is from 1.50% to 2.80% from1190 assay data; the Orebody II is skarn-type zone, and the value ofCu grade is less than 1.20% from 7150 assay data; the Orebody III isporphyry-type zone, and the value of Cu grade is less than 0.90% from15,460 assay data. The high-precision magnetic survey was carried outusing a WCZ-1 proton magnetometer with ±0.1 nT resolution and areading accuracy of ±0.5 nT. The magnetic anomaly contour map ofthe study area has a 40 m × 40 m grid size and a contour interval of50 nT and was developed using the 5880 geophysical data points. Themagnetic declination is 9° west in the study area.

Based on the concept of a magmatic-hydrothermal polymetallicmineralization and porphyry Cu depositmodel, a spatial relational data-base of multiple types of geoscience information pertaining to mineral-ization in the study area (geology, geophysics, geochemistry, borehole,and cross-section data) was developed. Geological, geophysical, topo-graphical and geochemical data were digitized and managed as point,line or polygon objects and were quantified and standardized in thedatabases using a 3D coordinate system.

4.1.2. 3D geological objects modelingThe 3D stratum and intrusive rock models of the Tongshan deposit

are constructed from 21 cross-sections and 1:2000 geological and

topographic maps. Three-dimensional models of the Tongshan fault,altered rocks, and orebodies I, II and III are constructed using the bore-hole dataset and the geological map in Micromine software (Figs. 3and 4). The alteration zones are assigned to classes based on typicalporphyry-type concentric zones of intense potassic, silica, chlorite, andpropylite (locally developed illite-carbonate) alteration (Fig. 3A). Faultinformation (e.g., thickness and dip) is derived from the boreholedataset, including alteration and brecciation information, from whichthe fault thickness can be calculated. The boundaries/wireframes offault, orebody and alteration zones are interpreted/inferred by combingthe hard/survey data from the borehole logs and soft/interpretationdata of geological information (stratum thickness, fault dip, and intru-sive rock shape) and magnetic inversion information in 3D spacepresented in the Specifications for copper, lead, zinc, silver, nickel andmolybdenum mineral exploration in China (DZ/T0214-2002):

(1) The orebody wireframe construction is the basis for the stratum,fault, and intrusive rock models in 3D space, and natural curvesconnect the borehole markers (Cu survey data) belonging to agiven mineralization zone.

(2) The inferred boundaries/edges of an orebody are based on theborehole or exploration cross-section distance, and several

Fig. 7. Cu grade plots based on borehole data from the Tongshan copper deposit.

92 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

methods can be selected to delineate the edges of an orebody: (a)point inferring based on 1/2 of the exploration net distance; (b)parallel inferring based on 1/4 of the exploration net distance;(c) natural inferring based on geological constraints; (d) no in-ferring based on the m·g/t rule in vein-type orebodies; (e) thelower boundary of an orebody is generally undefined becausethe borehole data typically do not delineate the maximumdepth extent of the orebody, but themaximum inferring distanceis never more than 1/2 of the exploration net distance.

The 3D geometric/wireframe orebody model (Fig. 3B) includesmineralization zones (Cu grade greater than 0.1%) and industrialore zones (Cu grade greater than 0.3%). Therefore, the 3D geometricorebodymodel can be further processed using the 23,800 samples inthe borehole dataset and using the kriging interpolation method in3D space. A comparison between the locations of strata, intrusions,faults and orebodies in Figs. 2, 3, and 5, those of the 3D geologicalmodel shows that the model of the Tongshan deposit is accurate.The study area is characterized by typical porphyry alteration

Fig. 8. Hurst exponent plots of borehole data from the Tongshan copper deposit.

93G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

zonation (Fig. 3A): orebodies I and II are in the phyllitic zone abovethe Tongshan fault. Orebody III is in the potassic, silica (biotite-K-feldspar) alteration zone below the Tongshan fault. On the basis ofore-forming intrusive rock buffer analysis using 500 m as buffer dis-tance (determined from geochemical data of alteration zoning of theintrusive rock (Du et al., 1988) in the 3D model of the study area),orebody III constitutes the host mineralization of the Tongshan deposit.Orebody II was formed by magmatic-hydrothermal metallogenesis, andorebody I forms the upper part of orebody III. Orebody III was destroyed

by the Tongshan fault in the Jurassic Period (Wang and Huang, 2012).Since the intrusive rock of orebody III connects with the batholith ofthe Duobaoshan region at depth, it was not destroyed by the Tongshanfault.

4.2. Variogram analysis

Using the Stanford Geostatistical Modeling Software (Remy et al.,2009), we implemented an ordinary kriging algorithm on a geological

Fig. 9. 3D model of orebody III and boreholes in the Tongshan copper deposit.

Fig. 10. The trending model produced using KT3D.exe (GSLIB software) (cell:25 m × 25 m × 25 m).

94 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

model discretized into blocks measuring 50 m × 50 m in plain view by25 m tall in accordancewith the Specifications for copper, lead, zinc, sil-ver, nickel, and molybdenum mineral exploration in China (DZ/T0214-2002). The data were formatted using GSLIB (Deutsch and Journel,1998). Fig. 6 presents the omnidirectional and vertical semi-variograms for the Tongshan deposit. Azimuths 90° and 135° in thesemi-variogram display characteristics similar to each other, and theomnidirectional and vertical semi-variograms of orebody III are similarto that developed for all the data from the Tongshan deposit. The pat-tern of the grade estimates appears to be consistent with concentrationtrends controlled by the positions and orientation of the observed faultand shape of the intrusive mineralization rock.

4.3. Fractal analysis

Figs. 7 and 8 show 6 sets of borehole data pertinent to orebody III.Fig. 8 shows that all the Hurst exponents of the boreholes (the depthis more than 1000 m) are larger than 0.5, and the borehole values ofthe Hurst exponents in the center of orebody III (e.g., all theHurst expo-nents from ZK760, ZK775 and ZK831 are larger than 0.85) are higherthan those along the edge of orebody III (e.g., all the values of Hurstexponents of ZK761, ZK777, and ZK833 are less than 0.84) (Fig. 9).Therefore, the Hurst exponent value (N0.5) can delineate the verticalpersistence and continuity of themineralization and themineralizationzones in the intrusive complex.

To calculate the 3Dmodels of the grades in the three orebodies of theTongshan deposit, a C–V fractalmodelwas used to delineate the Cu con-centration rule. A C–V fractal calculation program was developed inMatlab software to implement the C–V fractal method. The C–V fractalcalculation results are shown in Table 2 and Fig. 12. The threshold C–Vvalues were used to calculate the Cu grade distribution in the 3D block

Table 2C–V fractal parameters and mineral resources calculation of Tongshan deposit.

Orebody C–V fractal calculation

Cutoff of lowgrade of orebody

Cutoff of mediumgrade of orebody

Cutoffgrade o

I b0.4214 0.4214–1.0787 N1.078II b0.2542 0.2542–0.6367 N0.636III b0.2943 0.2943–0.5497 N0.549

model, which can show the delineations of copper grade in 3D in theTongshan deposit (Figs. 9 and 13).

Fig. 9 shows that the high-concentration volumes/voxels in orebodyIII (the lower cutoff value of the C–V fractal model is 0.5497) (Table 2,Figs. 3 and 12) are located in the center, the medium-concentrationvolumes/voxels (the cutoff values of C–V fractal model are 0.2943 and

Mineral resources calculation

of highf orebody

Accumulativeore value (t)

Averagegrade (%)

Cu resourcevalue (t)

7 8,590,713 0.5638 48434.447 56,671,462 0.3628 205604.077 149,794,106 0.3720 557234.07

Fig. 11. Comparison of 3D orebody II model and its 3D reconstruction model.

Fig. 12. C–V fractal plots of Tongshan orebodies.

95G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

Fig. 13. 3D model of grades in the Tongshan copper deposit.

96 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

0.5497) are located at depth, and the low-concentration volumes/voxels in orebody III (the high cutoff value of the C–V fractal model is0.2943) are located along the edges of the 3D orebody model. The re-sults of C–V fractal calculations may be correlated with those of theHurst exponent: (a) high values of the borehole Hurst exponent wereobserved in the center of orebody III, and (b) low values of the boreholeHurst exponent were observed along the edges of orebody III.

4.4. 3D estimation model using KT3D.exe

Judging from the 3D geological model of the Tongshan deposit(Figs. 3 and 5), the III orebody is associated with porphyry mineraliza-tion, which is correlated with orebodies I and II. To identify and delin-eate the high-concentration center of orebody III, six trend models(the elevation zones were from the surface to 400 m, 400–300 m,300–200 m, 200–0 m, 0 to−200 m, and−200 to−400 m) of orebodyIII were developed using kt3D.exe and using the appropriate boreholedatasets and semi-variogram parameters (Figs. 6, 9 and 10). The blockcells in all the trend models measure 25 m × 25 m × 1 m. Table 3presents the second block (the vertical range is from 350 m to 150 m)parameters used in KT3D.exe. The result shows that orebody III hasone continuous mineralization center from depth to the surface, andthis mineralization zone is associated with the intrusion complex.

The results presented above can be summarized as follows:

(1) Comparing the reconstructed 3D model of orebody II withthe orebody III trend model from KT3D.exe indicates that theconcealed orebody II is located in the northwestern zone of theorebody III; the depth is from −200 m to −500 m and thewidth is 220 m.

(2) The 3D intrusion buffer range (it is less than 500 m) (Fig. 5) is astatistical result of the alteration rocks survey and geochemicaldata analysis, and the KT3D.exe calculation range is 25–350 min the horizontal direction and the depth is no more than1350 m.

5. Conclusions

We combined outcrop observations, cross-sections, magneticand borehole datasets, Hurst exponent and C–V fractal modeling,geostatistical analysis, and grade estimation to present correlations be-tween orebodies and geological features (strata, faults, and intrusions)in a 3D space.

The Hurst exponent can be used to recognize the continuity ofmineralization with depth in the Tongshan copper district in zonespenetrated by boreholes in the intrusive rocks (Figs. 5 and 8), whichindicated that the intrusive rock has higher continuous mineralizationat depth. The higher Hurst exponent value can be used to validate thecenter of orebody III, which can be modeled using the 3D orebodymodel and can be estimated using KT3D.exe.

The KT3D.exe can be used to extract and delineate the trend ofmineralization in horizontal and vertical directions in 3D space.Comparing the six different elevation blocks in Fig. 10 reveals thatthe surface block (400 m) is not similar to the other five blocks,which have stronger mineralization continuity and mineral concen-tration center(s), and this comparison indicates that the Tongshanfault has affected the mineral distribution in the subsurface(between elevations 500 m and 300 m). The results can be used toidentify the mineralized zone that belongs to orebody II and wasdestroyed by the Tongshan fault. The location of the mineralizationzone is in the southwestern part of orebody II at depth(X: 42,487,800 to 42,488,000, Y: 5,565,600 to 5,565,900,Elevation: −500 m to −800 m). The mineralization zone belongsto the zone of hypogene enrichment, and the mineralization is ofthe magmatic-hydrothermal type, similar to the skarn-type poten-tial Cu exploration targets (Figs. 10 and 11). Combining the 3D geo-logical model and the sixth trend model analysis result fromKT3D.exe indicates that the deep part of orebody III has a low min-eralization zone that is of the magmatic/porphyry type of potentialCu exploration target, and the depth is from −800 m to −1000 m(Figs. 3 and 10).

On basis of these results, both the Hurst exponent analysis resultsand 3D grade models of the Tongshan deposit can be used to delineatemineralization continuity at depth. In the 3D geological model of theTongshan copper deposit, the alteration zones indicate that the intru-sive rock is associatedwith themineralization center (Fig. 3). The calcu-lated results demonstrate that the three orebodies of the Tongshancopper deposit are associated with the intrusive rock, and the Tongshanfault is a thrust fault that destroyed orebodies I and II. The displacementalong the Tongshan fault is less than 400 m in the north–south directionand less than 200 m in the northwest direction. This quantitative anal-ysis can assist in deep exploration for orebody II in the foot wall ofTongshan fault. Thus, we reconstructed orebody II using the aboveparameters (Fig. 11). Fig. 9 is a 3D intrusion buffer model in the 3Denvironment (the buffer distance is 500 m), and Figs. 9 and 13 show amodel of the orebody grades using the C–V cutoff values. This modelshows that the mineralization center coincides with the intrusion, butmany higher grade values surrounding it are due to the Tongshanfault. Therefore, the fractal method and 3D geological modeling canbe integrated to identify potential mineral targets quantitatively. Themethods presented in this paper are well-suited and most useful fordistrict-scale mineral resource assessment and prediction in other re-gions of the world.

Acknowledgments

The authors would like to thank Drs. Clayton V. Deutsch (Universityof Alberta, Canada), John Carranza (James Cook University, Australia),Renguang Zuo (China University of Geosciences, Wuhan), ChengyinTan (Heilong Mineral Resources Co., LTD, Harbin, China), and two re-viewers for their clear and full comments. The research was supportedby the National Science and Technology Support Project of the 12th“Five-Year Plan” (Grant No. 2011BAB04B06), the Ministry of Land andResources Public Service Sectors Fund (Grant No. 201111007), the Fun-damental Research Funds for the Central Universities, China Universityof Geosciences (Beijing: Grant No. 2-9-2012-143), and the State KeyLaboratory of Geological Processes and Mineral Resources (Grant No.GPMR2011).

Table 3The second block (400–300 m) parameters for KT3D.exe.

START OF PARAMETERS:

checkmodr350.out - file with data

1 2 3 4 1 0 0

-10.0

0

xvk.dat

2

0

kt3dtsr350.dbg

kt3dtsr350.out

60 42486800 25.0

40

300

3 3

4

40

250.0

0.0 0.0

1 0.0

0 0 0 0 0 0 0 0 0

0

extdrift.dat

4

1 0.2

1 0.8 0.0

250.0

- columns for DH,X,Y, Z,var,sec var

- trimming limits

- option: 0=grid, 1=cross, 2=jackknife

- file with jackknife data

- columns for X,Y,Z,vr and sec var

- debugging level: 0,1,2,3

- file for debugging output

- file for kriged output

- nx,xmn,xsiz

- ny,ymn,ysiz

- nz,zmn,zsiz

- x, y and z block discretization

- min, max data for kriging

- max per octant (0-> not used)

- maximum search radii

- angles for search ellipsoid

- 0=SK,1=OK,2=non-st SK, 3=exdrift

- drift: x,y,z,xx,yy,zz,xy,xz,zy

- 0, variable; 1, estimate trend

- gridded file with drif/mean

- column number in gridded file

- nst nugget

- it,cc,ang1,ang2,ang3

- a_hmax, a_hmin, a_vert250.0 200.0

0.0 0.0

0.0

250.0 200.0

150

3

200 1.0

5565400 25.0

3 4 10 0

10.0

97G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

References

Afzal, P., Khakzad, A., Moarefvand, P., Rashidnejad, O.N., Esfandiari, B., Fadakar, A.Y., 2010.Geochemical anomaly separation bymultifractal modeling in Kahang (Gor) porphyrysystem, Central Iran. Journal of Geochemical Exploration 104, 34–46.

Afzal, P., Fadakar, A.Y., Khakzad, A., Moarefvand, P., Rashidnejad, O.N., 2011. Delineation ofmineralization zones in porphyry Cu deposits by fractal concentration–volumemodelling. Journal of Geochemical Exploration 18, 220–232.

Afzal, P., Zia Zarifi, A., Yasrebi, A.B., 2012. Identification of uranium targets based onairborne radiometric data analysis by using multifractal modeling, Tark and Avanligh1:50 000 sheets, NW Iran. Nonlinear Processes in Geophysics 19, 283–289.

Agterberg, F.P., 2012. Multifractals and geostatistics. Journal of Geochemical Exploration122, 113–122.

Bansal, A.R., Gabriel, G., DimriV, P., Krawczyk, C.M., 2011. Estimation of the depth to thebottom of magnetic sources by a modified centroid method for fractal distributionof sources: an application to aeromagnetic data in Germany. Geophysics 76, L11–L22.

Calcagno, P., Chiles, J., Courrioux, G., Guillen, A., 2008. Geological modeling from field dataand geological knowledge: part I. Modelling method coupling 3D potential-field in-terpolation and geological rules. Physics of the Earth and Planetary Interiors 171(1–4), 147–157.

Carlson, C.A., 1991. Spatial distribution of ore deposits. Geology 19, 111–114.Carranza, E.J.M., 2008. Geochemical anomaly and mineral prospectivity mapping in

GIS. Handbook of Exploration and Environmental Geochemistry, vol. 11. Elsevier,Amsterdam.

Carranza, E.J.M., 2010a. Mapping of anomalies in continuous and discrete fields of streamsediment geochemical landscapes. Geochemistry: Exploration, Environment, Analy-sis 10, 171–187.

Carranza, E.J.M., 2010b. Catchment basin modelling of stream sediment anomaliesrevisited: incorporation of EDA and fractal analysis. Geochemistry: Exploration, Envi-ronment, Analysis 10, 365–381.

Carranza, E.J.M., Sadeghi, M., 2010. Predictive mapping of prospectivity and quantitativeestimation of undiscovered VMS deposits in Skellefte district, Sweden. Ore GeologyReviews 38, 219–241.

Carranza, E.J.M., Owusu, E.A., Hale, M., 2009. Mapping of prospectivity and estimation ofnumber of undiscovered prospects for lode gold, southwestern Ashanti Belt, Ghana.Mineralium Deposita 44, 915–938.

Cheng, Q., 1995. The perimeter–area fractal model and its application to geology. Mathe-matical Geology 27, 69–82.

Cheng, Q., 2004. A newmodel for quantifying anisotropic scale invariance and for decom-position of mixing patterns. Mathematical Geology 36, 345–360.

Cheng, Q., Agterberg, F.P., Ballantyne, S.B., 1994. The separation of geochemical anomaliesfrom background by fractal methods. Journal of Geochemical Exploration 54,109–130.

Cui, G., Wang, J., Zhang, J., Cui, G., 2008. U–Pb SHRIMP dating of zircons from Duobaoshangranodiorite in Heilongjiang and its geological significance. Global Geology 27 (4),387–394.

Daneshvar Saein, L., Rasa, I., Rashidnejad, O.N., Moarefvand, P., Afzal, P., 2012. Appli-cation of concentration–volume fractal method in induced polarization and resis-tivity data interpretation for Cu–Mo porphyry deposits exploration, case study:Nowchun Cu–Mo deposit, SE Iran. Nonlinear Processes in Geophysics 19,431–438.

David, M., 1977. Geostatistical ore Reserve Estimation: Developments in Geomathematics2. Elsevier Scientific Publishing Company, Netherlands.

De Kemp, E.A., Monecke, T., Sheshpart, M., 2011. 3D GIS as a support for mineral discov-ery. Geochemistry: Exploration, Environment, Analysis 11, 117–128.

Delavar, S.T., Afzal, P., Borg, G., Rasa, I., Lotfi, M., Rashidnejad, O.N., 2012. Delineation ofmineralization zones using concentration–volume fractal method in Pb–Zn Carbon-ate hosted deposits. Journal of Geochemical Exploration 118, 98–110.

Deutsch, C.V., 2002. Geostatistical Reservoir Modeling. Oxford University Press, New York(376 pp.).

Deutsch, C.V., Journel, A., 1998. GSLIB: Geostatistical Software Library and User's Guide.Oxford University Press, New York (369 pp.).

Du, Q., Zhao, Y.M., Lu, B.G., 1988. Duobaoshan Porphyry Copper Deposit. GeologicalPublishing House, Beijing 368 (in Chinese).

Fallara, F., Legualt, M., Rabeau, O., 2006. 3-D Integrated geological modeling in the Abitibisubprovince (Québec, Canada): techniques and applications. Exploration and MiningGeology 15, 27–41.

Heidari, M., Ghaderi, M., Afzal, P., 2013. Delineating mineralized phases based onlithogeochemical data using multifractal model in Touzlar epithermal Au–Ag (Cu)deposit, NW Iran. Applied Geochemistry 31, 119–132.

Houlding, S.W., 1994. 3D Geoscience Modeling-computer Techniques for GeologicalCharacterization. Springer Verlag, Berlin, Germany (320 pp.).

Houlding, S.W., 2000. Practical Geostatistics: Modeling and Spatial Analysis. Springer,Berlin, Germany.

Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Transactions of the AmericanSociety of Civil Engineers 116, 770–808.

Journel, A., Huijbregts, C.J., 1978. Mining Geostatistics. Academic Press, New York.Kaufman, O., Martin, T., 2008. 3D geological modelling from boreholes, cross- sections and

geological maps, application over former natural gas storages in coal mines. Com-puters & Geosciences 34 (3), 278–290.

Lemon, A.M., Jones, N.L., 2003. Building solid models from boreholes and user- definedcross-sections. Computers & Geosciences 29, 547–555.

Leuangthong, O., Deutsch, C.V., 2004. Transformation of residuals to avoid artifacts ingeostatistical modelling with a trend. Mathematical Geology 36 (3), 287–305.

Mallet, J.L., 2002. Geomodeling. Applied Geostatistics. Oxford University Press, New York,pp. 1–10.

Mandelbrot, B., 1983. The Fractal Geometry of Nature, Updated and Augmented Edition.W.H. Freeman and Company, New York (468 pp.).

Mandelbrot, B., Wallis, J.R., 1969. Some long-run properties of geographical records.Water Resources Research 5, 321–340.

Raines, G.L., 2008. Are fractal dimensions of the spatial distribution of mineral depositsmeaningful? Nature Resources Research 17, 87–97.

Remy, N., Boucher, A., Wu, J., 2009. Applied Geostatistics With SGeMS: User's Guide. Cam-bridge University Press, Cambridge (288 pp.).

Sadeghi, B., Moarefvand, P., Afzal, P., Yasrebi, A.B., Daneshvar, S.L., 2012. Application offractal models to outline mineralized zones in the Zaghia iron ore deposit, CentralIran. Journal of Geochemical Exploration 122, 9–19.

Turcotte, D.L., 1997. Fractals and Chaos in Geology and Geophysics, 2nd edn. CambridgeUniversity Press, Cambridge, United Kingdom (398 pp.).

Wang, G., Huang, L., 2012. 3D geological modeling for mineral resource assessment ofthe Tongshan Cu deposit, Heilongjiang Province, China. Geoscience Frontiers 3 (4),483–491.

Wang, G., Zhang, S., Yan, C., Song, Y., Sun, Y., Li, D., Xu, F., 2011a. Mineral potentialtargeting and resource assessment based on 3D geological modeling in Luanchuanregion, China. Computers & Geosciences 37, 1976–1988.

Wang, G., Zhang, S., Yan, C., Xu, G., Ma, M., Li, K., Feng, Y., 2011b. Application of themultifractal singular value decomposition for delineating geophysical anomalies as-sociated with molybdenum occurrences in the Luanchuan ore field (China). Journalof Applied Geophysics 86, 109–119.

Wang, G., Carranza, E.J.M., Zuo, R., Hao, Y., Du, Y., Pang, Z., Sun, Y., Qu, J., 2012a. Mapping ofdistrict-scale potential targets using fractal models. Journal of Geochemical Explora-tion 122, 34–46.

Wang, G., Zhu, Y., Zhang, S., Yan, C., Song, Y., Ma, Z., Hong, D., Chen, T., 2012b. 3Dgeological modeling based on gravitational and magnetic data inversion in theLuanchuan ore region, Henan Province, China. Journal of Applied Geophysics80, 1–11.

Wilson, C.E., Aydin, A., Durlofsky, L.J., Boucher, A., Brownlow, D., 2011. Use of outcropobservations, geostatistical analysis, and flow simulation to investigate structuralcontrols on secondary hydrocarbon migration in the Anacacho Limestone, Uvalde,Texas. AAPG Bulletin 95 (7), 1181–1206.

Wu, G., Liu, J., Zhong, W., Zhu, M., Mei, M., Wan, Q., 2009. Fluid inclusion study of theTongshan porphyry copper deposit, Heilongjiang province, China. Acta PetrologicaSinica 25 (11), 2995–3006.

Yasrebi, A.B., Afzal, P., Wetherelt, A., Foster, P., Esfahanipour, R., 2013. Correlation betweengeological and concentration–volume fractal models for Cu andMomineralised zonesseparation in Kahang porphyry deposit, Central Iran. Geologica Carpathica 64 (2),153–163.

Zuo, R., 2011a. Decomposing of mixed pattern of arsenic using fractal model in Gangdesebelt, Tibet, China. Applied Geochemistry 26, S271–S273 (Suppl.).

98 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 85–98

Zuo, R., 2011b. Identifying geochemical anomalies associated with Cu and Pb–Zn skarnmin-eralization using principal component analysis and spectrum–area fractal modeling inthe Gangdese Belt, Tibet (China). Journal of Geochemical Exploration 111 (1–2), 13–22.

Zuo, R., 2012. Exploring the effects of cell size in geochemical mapping. Journal ofGeochemical Exploration 112, 357–367.

Zuo, R., Agterberg, F.P., Cheng, Q., Yao, L., 2009a. Fractal characterization of the spatialdistribution of geological point processes. International Journal of Applied EarthObservation and Geoinformation 11, 394–402.

Zuo, R., Cheng, Q., Xia, Q., 2009b. Evaluation of the uncertainty in estimation of metalresources of skarn tin in Southern China. Ore Geology Reviews 35, 415–422.

Zuo, R., Cheng, Q., Xia, Q., Agterberg, F.P., 2009c. Application of fractal models todistinguishing between different mineral phases. Mathematical Geosciences 41,71–80.

Zuo, R., Xia, Q., Zhang, D., 2013. A comparison study of the C–A and S–A models withsingularity analysis to identify geochemical anomalies in covered areas. AppliedGeochemistry. http://dx.doi.org/10.1016/j.apgeochem.2013.02.009.