Journal of Geochemical Exploration

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1 Journal of Geochemical Exploration 134 (2013) Contents lists available at ScienceDirect Journal of Geochemical Exploration journal homepage: Quantitative assessment of mineral resources by combining geostatistics and fractal methods in the Tongshan porphyry Cu deposit (China) Gongwen Wang a,, Zhenshan Pang b,, JeffB.Boisvert c,yinglonghao a,yuanxingcao a, Jianan Qu a a State Key laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Beijing , China b Technical Guidance Center for Mineral Resources Exploration, MLR, Beijing , China c Center for Computational Geostatistics, School of Mining and Petroleum Engineering, Markin/CNRL, Natural Resources Engineering Facility, University of Alberta, Edmonton, Alberta T6G 2W2, Canada article info abstract Article history: Received 3 January 2013 Accepted 5 August 2013 Available online 14 August 2013 Keywords: 3D geological modeling Geostatistics Hurst exponent C V fractal model 3D trend modeling Tongshan porphyry-cu deposit Three-dimensional (3D) geological, geostatistical, and fractal/multifractal modeling are combined for the identification of new exploration targets in the Tongshan porphyry Cu deposit (China): (1) A 3D geological model of the 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 omnidirectional and vertical semi-variogram calculations of the orebody, ordinary kriging interpolation of the orebody and 3D trend modeling using the assay data; (3) fractal models consisting of Hurst exponent estimation of the continuity of vertical mineralization and its concentration volume (C V) fractal model separation mineralized zones in a 3D block model; and (4) interpretation and validation: magnetic inversion was utilized to constrain intrusive rock shape between cross-sections and additional interpret orebody geometry model by ordinary kriging interpolation method using Tongshan borehole dataset. The results indicate that (a) the Hurst exponent is useful for identifying the vertical continuity of mineralization (with the range between 0 and 1200 m), (b) the C V fractal model is useful for identifying thresholds of Cu values in oxidation-type, skarn-type, and magmatic-type orebodies in the Tongshan deposit, and (c) the 3D geological and trend model can be combined to recognize potential subsurface targets in the Tongshan deposit. The methods can be applied to estimate mineral resources through district-scale exploration Elsevier B.V. All rights reserved. 1. Introduction Mineral exploration in a maturing mining district is challenging because it is accompanied by an increase in cost and risk of targeting deposits at increasingly great depths, which requires more detailed data and more expensive data acquisition methods (De Kemp et al., 2011; Houlding, 2000; Wang et al., 2011a,b). Combing geological knowledge and mathematical analysis aids in improving the understanding of the distribution of mineral resources at depth and the relationships among strata, intrusive bodies, faults, and orebodies, which are important parameters for mineral exploration. The various types of kriging interpolation methods, both in 2D and 3D space, are key steps in mineral resource calculation and assessment. For example, kriging-based estimation techniques are generally important for the recognition of spatial distribution patterns (Deutsch, 2002). Geostatistics has become increasingly popular for numerical modeling and uncertainty assessment in the earth sciences (De Kemp et al., 2011; Deutsch, 2002; Deutsch and Journel, 1998; Leuangthong and Deutsch, 2004). Corresponding author. Tel.: Corresponding author. Tel.: addresses: gwwang@cugb.edu.cn (G. Wang), pzs927@163.com (Z. Pang). Three-dimensional geological modeling is an important technology in quantitative assessment and prediction of mineral resources on a district scale, and conventional geostatistics has been developed to use 3D reverse estimation. Three-dimensional geological modeling integrates geological, geochemical, and geophysical data for delineating of metallogenesis of mineral deposits and exploration targets in a 3D block model. Moreover, the variogram as a geostatistical tool can be used to derive omnidirectional and vertical distributions of elements in 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 environment (De Kemp et al., 2011). Since the 1980s, fractal and multifractal models have been effectively 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 models are used to model geochemical or geophysical data (e.g., Afzal et al., 2010, 2012; Carranza, 2008, 2010a,b; Cheng, 2004; Daneshvar Saein et 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 /$ see front matter 2013 Elsevier B.V. All rights reserved.

2 86 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) used to map geochemical and geophysical anomalies (Carranza and Sadeghi, 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 the Tongshan porphyry Cu deposit and geostatistical and fractal methods are combined to assess the mineral resources quantitatively and to delineate potential exploration targets at substantial depths, revise certain interpretations of the Tongshan fault that were poorly correlated with borehole data, improve the understanding of the geological history of the Tongshan district, and serve as a guide during detailed exploration. The construction of the 3D geological model links sample observations to geostatistical analysis and subsurface grade estimation using a borehole dataset. 2. Methodology Results derived from the 3D geological, geostatistical, and fractal/ multifractal modeling are combined in quantitative assessment of mineral resources and delineation of potential targets in the Tongshan porphyry Cu deposit, China. The 3D geological model (the geological objects include faults, alteration zones, orebodies, geophysical inversions, and intrusive rocks) of the Tongshan deposit was constructed using 94 boreholes, 21 cross-sections, and 23,800 samples from the borehole dataset. The geostatistical analysis involved semi-variogram modeling of metal distribution in orebodies, ordinary kriging interpolation of metals in the orebodies and 3D trend modeling using KT3D.exe in GSLIB software (Deutsch and Journel, 1998). The fractal models which were used include (a) estimation of the Hurst exponent from the borehole dataset to model the continuity of mineralization and (b) application of the concentration volume (C V) fractal model to define an ore element threshold value to constrain the mineralization fluid center or a path in a 3D block model (Afzal et al., 2011). These methods were applied to identifying potential copper targets, which is the aim of this paper. For example, the Hurst exponent can be used to constrain segments classified in KT3D.exe calculation for trend modeling, parameters from omnidirectional and vertical semi-variograms of metal data are used in ordinary kriging interpolation analysis, and the ordinary kriging interpolation results are subjected to C V fractal analysis for recognition of a Cu concentration center and the edges of an orebody D geological modeling The use of 3D models to better understand surface and subsurface geology 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 geological modeling of the Tongshan porphyry Cu deposit involved the following four steps (Fig. 1): (1) Step 1, geoscience data handling: acquiring, compiling, digitizing and 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 digital elevation model into the Micromine software (ASCII format) to model the topographic surface; importation of the borehole dataset (23,800 samples) including coordinates (x, y, z), dips, azimuths, depths, survey, geology, minerals, and alteration indexes into Micromine software; and integration of geological contacts combining a 1:2000 scale geological map and 21 cross sections at a scale of 1: 2000 in AutoCAD. (3) Step 3, 3D geological modeling: construction wireframe/geometry models of geological objects (Duobaoshan Formation, Luohe Formation, Tongshan fault, intrusive rocks, altered rocks, three orebodies) using integration of the 2D geological data. Geological surface models were built by contact curves and dip vectors derived from the surface geological maps, cross-sections, and digital elevation models. Geological subsurface objects were validated and interpreted by geophysical inversions and sparse Fig. 1. Schematic flow-chart for 3D modeling by integration of multiple types of geoscience data.

3 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) borehole data at depth. The contact relationship between two objects can be identified combing geological knowledge and wireframe Boolean operation model in Micromine software. When the 3D orebody wireframe/geometry model is completed, the 3D orebody model can be created using the borehole dataset and interpolation method. When the interpolation results of grade model between inverse distance weight (Wang and Huang, 2012) was compared to the ordinary kriging methods, we observed that the latter method created a better model of the geometry of mineralization associated with the zone of alteration in 3D space. (4) Step 4, interpretation and validation: geological maps, the borehole dataset and magnetic inversion were used as additional control elements between the interpreted cross-sections; magnetic inversion was utilized to constrain intrusive rock shape between cross-sections and additional interpret Cu geometry model by ordinary kriging interpolation method using Tongshan borehole dataset; geological knowledge was used to analyze the potential mineral targets (e.g., 3D buffer analysis was used to construct a 3D intrusive rock model for delineating the likely porphyry Cu mineralization zones, and 3D models of the porphyry alteration rocks were used to identify the edges or center of the orebody) Geostatistics analyses Semi-variogram analysis A semi-variogram model is a mathematical expression that relates semi-variance (γ) to distance and represents the measured variability oftheavailablesamples(journel and Huijbregts, 1978). Semi-variogram analysis provides a powerful technique for analyzing the adequacy of the available samples, specifically their spatial distribution and density for purposes of characterization (Houlding, 2000). One of the advantages of the analytical semi-variogram is that it provides a logical basis for deciding which of the available samples of a regional variable are relevant for estimation of a point in the subsurface (Houlding, 2000). Semi-variograms serve a number of functions with respect to assessing characterization quality. These functions include providing a measure of the adequacy of sampling, a measure of the spatial variability of the samples, and the degree of correlation between the semivariogram models employed for estimation and the measured spatial variability. The variations in mineral grade may not be the same in all directions (David, 1977). Therefore, omnidirectional and vertical analysis of semivariograms is important for 3D orebody modeling and 3D mineralization trend modeling. The former is associated with interpolation, and the latter is associated with selecting a search radius in a 3D space. In this study, both the Stanford Geostatistical Modeling Software (Remy et al., 2009) and the GSLIB (Deutsch and Journel, 1998) gamv.exe variogram program were used to analyze irregularly distributed borehole data in the 3D space. The vertical variogram is a combination of all borehole data. The experimental variogram may show a trend in any one or more of the principal directions, and the trend can be easily identified as the experimental variogram continues to increase above random variance as the lag distance D trend modeling Trends are deterministic or predictable patterns of the spatial distribution of grade or petrophysical properties. Certain trends can be inferred from geological knowledge, and certain trends can be detected by applying geostatistics tools (e.g., kriging) to well/borehole data (Deutsch and Journel, 1998). In certain cases where the mineralization environment is well understood, trends can be detected using geological knowledge of the site of interest. In most cases, however, the data are the sources of information for trend detection. Large-scale spatial features can be detected during several stages of data analysis and modeling. The most common and straightforward approach is to the separate residual value (RV) into two components, the trend and the residual: Zu ð Þ ¼ mu ð ÞþRu ð Þ; where Z is the original RV, m is the trend or mean component, R is the RV, and u denotes the location, commonly in the form of Cartesian coordinates (x, y, z). The mean component is defined from all locations via a 3D trend model, while residual values are defined only for data locations. Geostatistical modeling is then only performed on residuals considered to be stationary. Multiple realizations of residuals are generated and added back to the single trend model to produce multiple realizations of the original RV. There is no unique way to integrate these two trends into a consistent 3D trend model (Deutsch, 2002). However, one approach can be used to scale the areal trend by the proportion of the vertical trend to the global mean:!! mz ðþ mx; ð yþ mðx; y; zþ ¼ m global : ð2þ m global m global This approach is straightforward and well-adapted to practice in cases where limited data may make it difficult to develop a full 3D trend model. Inherent in Eq. (2) is an assumption of conditional independence of the vertical trend component within the horizontal plane and the horizontal trend component in the vertical direction (Leuangthong and Deutsch, 2004). The GSLIB program KT3D.exe is a particularly powerful modeling tool (Deutsch and Journel, 1998; Leuangthong and Deutsch, 2004). The program KT3D.exe provides a fairly advanced 3D kriging program for blocks by simple kriging, ordinary kriging, or kriging with a polynomial trend model with up to nine monomial terms Fractal modeling The fractal models are utilized to analyze spatial features in the Tongshan deposit: (1) a Hurst exponent model is used to characterize the continuity of mineralization along boreholes and identify the center of the mineralization or the edge of orebody III; and (2) the C V fractal model is used to distinguish supergene enrichment and hypogene zones from oxidation-type zones and to separate skarn-type orebodies and porphyry-type orebodies based on the distribution of Cu grades in the 3D block model Hurst exponent model The Hurst exponent proposed by Hurst (1951) is directly related to the fractal dimension of a process and provides a measure of process roughness. The Hurst exponent is associated with a self-affine record, which measures the long-range dependence in a time series and provides a measure of long-term nonlinearity. The values of H lie between 0 and 1. If H = 0.5, the cumulative behavior is a random walk and the process produces uncorrelated white noise. Values of H b 0.5 represent nonpersistent behavior whereas values of H N 0.5 represent fractional Brownian motion with increasing persistence strength as H approaches 1. The rescaled range analysis (R/S) implies the ratio of the rescaled range (R) to the standard deviation (S) and can be used to estimate the Hurst exponent (Mandelbrot and Wallis, 1969) as follows. An ordered data sequence is divided into d contiguous sub-series of length n, suchthatd n = N is the total number of samples. For each of the sub-series m, where m = 1,, d, the following analyses are performed. (i) Determine the mean, E m, and standard deviation, S m,ofthedata in each sub-series. (ii) Normalize each data point (Z i, m ) in each sub-series by subtracting ð1þ

4 88 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Table 1 3D 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 , , , , ,643,920 1,643, , , ,454,256 2,309, ,281,216 2,925, , , ,160,448 4,469, ,841,424 5,766, , , ,941,040 6,410, ,771,368 10,537, ,224 1,230, ,101,152 8,512, ,143,920 17,681, ,944 1,592, ,199,208 10,711, ,972,752 27,654, ,640 1,903, ,060,336 12,771, ,149,696 37,804, ,344 2,173, ,643,752 14,415, ,223,960 44,028, ,976 2,439, ,839,640 16,255, ,281,888 48,310, ,776 2,580, ,404,736 17,659, ,731,632 51,041, ,944 2,690, ,968 18,555, ,616,096 52,657, ,384 2,827, ,888 19,359, ,072 53,572, ,032 2,918, ,256 19,708, ,176 54,066, ,432 2,976, ,616 20,095, ,552 54,286, ,224 3,013, ,496 20,174, ,816 54,392, ,848 3,028, ,640 20,229, ,392 54,427, ,031, ,237, ,056 54,443, ,776 3,042, ,239, ,452, ,760 3,058, ,239, ,458, ,712 3,072, ,239, ,040 54,470,584 E m : X i;m ¼ Z i;m E m ; m ¼ 1; 2; ; n (iii) Create a cumulative series by consecutively summing the normalized data points: Y i;m ¼ Xn i¼1 X i;m (iv) Usecumulativeseriestofind the range: R m ¼ max Y i:m ; ; Y n;m min Y i:m ; ; Y n;m (v) Rescale the range by dividing the range by the standard deviation (i.e., R m / S m ). (vi) Calculate the mean of the rescaled range for all sub-series of length n: ðr=sþ n ¼ 1 d X d m¼1 R m =S m (vii) The length of n must be increased to the next higher value, where d n = N,andd is an integer value. Repeat steps (i) to (vi) until n = N/2. (viii) Finally, estimate the value of H as the slope of the regression line for log (N)versuslog(R/S) C V fractalmodel The 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 (Wang et al., 2011a,b). Afzal et al. (2011) proposed the C V fractal model for delineating of supergene enrichment and hypogene zones from oxidation zones and barren host rocks in the Chah-Firouzeh and Sungun porphyry Cu deposits, northwestern Iran, which are situated in SE and NW parts of Iran, respectively. The C V fractal model can be expressed as Vðρ νþ ρ a 1 ; Vðρ νþ ρ a 2 ; ð7þ ð3þ ð4þ ð5þ ð6þ where V(ρ ν) and V(ρ ν) denote two volumes with concentration values (ρ) less than or equal to and greater than or equal to, respectively, the contour value (ν), which represents the cutoff/threshold value of a zone (or volume); and a 1 and a 2 are characteristic exponents. The C V fractal method was used to identify mineralization, primary and secondary orebodies (based on Cu concentrations at the center or edge) in 3D space based on the 3D geological model and borehole logs in study area. The terms high, medium and low in 3D space have been used to classify mineralized zones based on C V fractal modeling in 3D space in the Tongshan deposit. To calculate V(ρ ν) and V(ρ ν) in the 3D model, 23,800 geochemical samples were collected from the 94 boreholes at 1-m intervals. The deposit was modeled using 50 m 50 m 25 m voxels based on the geometric properties of the deposit and grid drilling dimensions established as a Cu deposit exploration standard in China (2002). The Cu grade distribution block models of the study area were generated by the ordinary kriging method using Micromine software. Log log plots of the corresponding volumes (V(ρ ν) andv(ρ ν)) follow a power law relationship, and the breaks between strait-line segments in those log log plots represent threshold values separating populations of geochemical concentration values representing mineralogical zones (Afzal et al., 2011; Yasrebi et al., 2013). The C V fractal method can be implemented with the aid of Matlab software: (1) first, a text file of the 3D interpolation block model data is imported and read using Micromine software, (2) next, grades are sorted form high to low, (3) the block model data are classified, (4) the number of voxels for each class are counted and the accumulated value of these in orebodies I, II, and III, respectively, is computed (Table 1), (5) and finally, the logarithm of all Cu grade data and accumulated frequency values are calculated and a C V log log plot is drawn. 3. Geological setting of case study The Tongshan porphyry Cu deposit is located in the Da Hinggan Mountain fold system of Inner Mongolia and is located 4 km from the well-known Duobaoshan porphyry Cu deposit. The 3D study area is situated 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, rangefrom620mto 1000 m relative to sea level (Figs. 2 and 3). The study area consists of up to 6000 m of Ordovician marine volcano-sedimentary rocks (of basaltic, andesitic or rhyolitic compositions) formed in an active continental margin, island arc environment

5 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) 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). (Du et al., 1988). The Tongshan Cu deposit is located on the southwestern limb of an inverted anticline. The core of the inverted anticline consists of Middle Ordovician rocks of the Tongshan Formation, whereas the limbs consist of andesite and andesitic tuff of the Middle Ordovician Duobaoshan Formation. Volcanic rocks of the Duobaoshan Formation, with a thickness of approximately 3000 m, host the primary stratum of Cu mineralization (with ppm Cu) (Du et al., 1988). Early Ordovician granodiorite and other intrusive rocks are considered to be the Cu-ore source rock. SHRIMP U Pb dating of zircon from the granodiorite yielded an age of Ma, and Re Os isotopic isochron ages obtained from molybdenites are 506 ± 14 Ma (Cui et al., 2008; Wu et al., 2009). The granodiorite is associated with tonalite with a marginal

6 90 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Fig. 5. 3D model of orebody Cu grade, Duobaoshan Formation, Luohe Formation, Tongshan fault, and intrusive rock with 500 m buffer, Tongshan copper deposit. Orebodies are classified by different Cu grade classification using irregular hexahedrons. Fig. 3. (A) 3D model of orebody and alteration zoning, and (B) 94 boreholes, Tongshan copper deposit. facies of quartz diorite porphyry developed along the footwall of the Tongshan fault. The mineralized Duobaoshan Formation exhibits strong hydrothermal alteration, similar to typical porphyry-type alteration zoning with intense potassic, silica, chlorite, and propylite (locally developed illite-carbonate) zonation from the center outward. The average amount of Cu in the alteration rock is more than 0.1%. The orebody is hosted mainly in potassic, silica and phyllic alteration zones within the quartz diorite porphyry; however, copper mineralization is closely associated with silicification and sericitization. The Tongshan deposit is a typical magmatic-hydrothermal deposit and has a geological setting, alteration sequence, and mineralization characteristics similar to those of the Duobaoshan porphyry Cu deposit. These two deposits are both skarn-type orebodies created when magma of basaltic, andesitic or rhyolitic compositions was emplaced next to volcano-sedimentary wall rocks (Du et al., 1988). Orebody II is the longest orebody (2.2 km) in the Tongshan deposit; its width is m. Orebody I is present at the highest elevation (530 m), whereas orebody III is concealed and in contact with granodiorite at a depth of m. The Tongshan fault is a dipping reverse fault that strikes primarily E W for more than 10 km and is more than 10 m wide (Fig. 3). The fault transects and offsets orebodies II and III in the study area and thus postdates the formation of the Tongshan deposit. Therefore, there are two key geological questions that needed to be addressed: (1) Did the Tongshan fault destroy orebody II? and (2) where is the deep potential target? 4. Discussion D geological model of Tongshan deposit Fig. 4. Cu histogram of 23,800 sample surveys from 94 boreholes in the Tongshan copper deposit Multiple geoscience information datasets The 3D geological models of the study area were constructed using geoscience datasets collected from geological objects and metallogenic features, including a 1:2000 geological map, 21 1:2000 geological exploration cross-sections, a 1:2000 digital elevation model, 44,420 m logs from 94 boreholes (the maximum depth was 1342 m; the logs described the collar, deviation from vertical, depths, geology, mineralized intersections, faults, alteration indexes, magnetic susceptibility, density, minerals, and Cu assay), 23,800 Cu-grade surveys from the 94 boreholes with a L distribution (Fig. 4), and 5880 geophysical survey points (magnetic and topographic). The Cu grade mean from the 23,800 assay data is 0.32%, which is larger than the value of industrial grade of Cu deposit in China (0.30%), and it shows generally low grade characteristics of porphyry-type deposit in the world. However, in Tongshan Cu deposit, the Orebody I is oxidation-type zone, the value of Cu grade is larger

7 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) (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) Variogram of orebody III in the Tongshan copper deposit. (D) Vertical variogram of orebody III in the Tongshan copper deposit. than 0.30%, and the high value of Cu grade is from 1.50% to 2.80% from 1190 assay data; the Orebody II is skarn-type zone, and the value of Cu grade is less than 1.20% from 7150 assay data; the Orebody III is porphyry-type zone, and the value of Cu grade is less than 0.90% from 15,460 assay data. The high-precision magnetic survey was carried out using a WCZ-1 proton magnetometer with ±0.1 nt resolution and a reading accuracy of ±0.5 nt. The magnetic anomaly contour map of the study area has a 40 m 40 m grid size and a contour interval of 50 nt and was developed using the 5880 geophysical data points. The magnetic declination is 9 west in the study area. Based on the concept of a magmatic-hydrothermal polymetallic mineralization and porphyry Cu deposit model, a spatial relational database of multiple types of geoscience information pertaining to mineralization in the study area (geology, geophysics, geochemistry, borehole, and cross-section data) was developed. Geological, geophysical, topographical and geochemical data were digitized and managed as point, line or polygon objects and were quantified and standardized in the databases using a 3D coordinate system D geological objects modeling The 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 borehole dataset and the geological map in Micromine software (Figs. 3 and 4). The alteration zones are assigned to classes based on typical porphyry-type concentric zones of intense potassic, silica, chlorite, and propylite (locally developed illite-carbonate) alteration (Fig. 3A). Fault information (e.g., thickness and dip) is derived from the borehole dataset, including alteration and brecciation information, from which the fault thickness can be calculated. The boundaries/wireframes of fault, orebody and alteration zones are interpreted/inferred by combing the hard/survey data from the borehole logs and soft/interpretation data of geological information (stratum thickness, fault dip, and intrusive rock shape) and magnetic inversion information in 3D space presented in the Specifications for copper, lead, zinc, silver, nickel and molybdenum mineral exploration in China (DZ/T ): (1) The orebody wireframe construction is the basis for the stratum, fault, and intrusive rock models in 3D space, and natural curves connect the borehole markers (Cu survey data) belonging to a given mineralization zone. (2) The inferred boundaries/edges of an orebody are based on the borehole or exploration cross-section distance, and several

8 92 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Fig. 7. Cu grade plots based on borehole data from the Tongshan copper deposit. 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 inferring based on the m g/t rule in vein-type orebodies; (e) the lower boundary of an orebody is generally undefined because the borehole data typically do not delineate the maximum depth extent of the orebody, but the maximum inferring distance is never more than 1/2 of the exploration net distance. The 3D geometric/wireframe orebody model (Fig. 3B) includes mineralization zones (Cu grade greater than 0.1%) and industrial ore zones (Cu grade greater than 0.3%). Therefore, the 3D geometric orebody model can be further processed using the 23,800 samples in the borehole dataset and using the kriging interpolation method in 3D space. A comparison between the locations of strata, intrusions, faults and orebodies in Figs.2,3,and5,thoseofthe3Dgeological model shows that the model of the Tongshan deposit is accurate. The study area is characterized by typical porphyry alteration

9 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Fig. 8. Hurst exponent plots of borehole data from the Tongshan copper deposit. zonation (Fig. 3A): orebodies I and II are in the phyllitic zone above the Tongshan fault. Orebody III is in the potassic, silica (biotite-kfeldspar) alteration zone below the Tongshan fault. On the basis of ore-forming intrusive rock buffer analysis using 500 m as buffer distance (determined from geochemical data of alteration zoning of the intrusive 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, and orebody 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 of the Duobaoshan region at depth, it was not destroyed by the Tongshan fault Variogram analysis Using the Stanford Geostatistical Modeling Software (Remy et al., 2009), we implemented an ordinary kriging algorithm on a geological

10 94 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Fig. 9. 3D model of orebody III and boreholes in the Tongshan copper deposit. model discretized into blocks measuring 50 m 50 m in plain view by 25 m tall in accordance with the Specifications for copper, lead, zinc, silver, nickel, and molybdenum mineral exploration in China (DZ/T ). The data were formatted using GSLIB (Deutsch and Journel, 1998). Fig. 6 presents the omnidirectional and vertical semivariograms for the Tongshan deposit. Azimuths 90 and 135 in the semi-variogram display characteristics similar to each other, and the omnidirectional and vertical semi-variograms of orebody III are similar to that developed for all the data from the Tongshan deposit. The pattern of the grade estimates appears to be consistent with concentration trends controlled by the positions and orientation of the observed fault and shape of the intrusive mineralization rock 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 depth is more than 1000 m) are larger than 0.5, and the borehole values of the Hurst exponents in the center of orebody III (e.g., all the Hurst exponents from ZK760, ZK775 and ZK831 are larger than 0.85) are higher than those along the edge of orebody III (e.g., all the values of Hurst exponents of ZK761, ZK777, and ZK833 are less than 0.84) (Fig. 9). Therefore, the Hurst exponent value (N0.5) can delineate the vertical persistence and continuity of the mineralization and the mineralization zones in the intrusive complex. To calculate the 3D models of the grades in the three orebodies of the Tongshan deposit, a C V fractal model was used to delineate the Cu concentration rule. A C V fractal calculation program was developed in Matlab software to implement the C V fractal method. The C V fractal calculation results are shown in Table 2 and Fig. 12. The threshold C V values were used to calculate the Cu grade distribution in the 3D block Fig. 10. The trending model produced using KT3D.exe (GSLIB software) (cell: 25 m 25 m 25 m). model, which can show the delineations of copper grade in 3D in the Tongshan deposit (Figs. 9 and 13). Fig. 9 shows that the high-concentration volumes/voxels in orebody III (the lower cutoff value of the C V fractal model is ) (Table 2, Figs. 3 and 12) are located in the center, the medium-concentration volumes/voxels (the cutoff values of C V fractal model are and Table 2 C V fractal parameters and mineral resources calculation of Tongshan deposit. Orebody C V fractal calculation Mineral resources calculation Cutoff of low grade of orebody Cutoff of medium grade of orebody Cutoff of high grade of orebody Accumulative ore value (t) Average grade (%) Cu resource value (t) I b N ,590, II b N ,671, III b N ,794,

11 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Fig. 11. Comparison of 3D orebody II model and its 3D reconstruction model. Fig. 12. C V fractal plots of Tongshan orebodies.

12 96 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) ) are located at depth, and the low-concentration volumes/ voxels in orebody III (the high cutoff value of the C V fractal model is ) are located along the edges of the 3D orebody model. The results of C V fractal calculations may be correlated with those of the Hurst exponent: (a) high values of the borehole Hurst exponent were observed in the center of orebody III, and (b) low values of the borehole Hurst exponent were observed along the edges of orebody III D 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 mineralization, which is correlated with orebodies I and II. To identify and delineate the high-concentration center of orebody III, six trend models (the elevation zones were from the surface to 400 m, m, m, m,0to 200 m, and 200 to 400 m) of orebody III were developed using kt3d.exe and using the appropriate borehole datasets and semi-variogram parameters (Figs. 6, 9 and 10). The block cells in all the trend models measure 25 m 25 m 1 m. Table 3 presents the second block (the vertical range is from 350 m to 150 m) parameters used in KT3D.exe. The result shows that orebody III has one continuous mineralization center from depth to the surface, and this 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 with the orebody III trend model from KT3D.exe indicates that the concealed orebody II is located in the northwestern zone of the orebody III; the depth is from 200 m to 500 m and the width is 220 m. (2) The 3D intrusion buffer range (it is less than 500 m) (Fig. 5) isa statistical result of the alteration rocks survey and geochemical data analysis, and the KT3D.exe calculation range is m in the horizontal direction and the depth is no more than 1350 m. 5. Conclusions Fig D model of grades in the Tongshan copper deposit. We combined outcrop observations, cross-sections, magnetic and borehole datasets, Hurst exponent and C V fractal modeling, geostatistical analysis, and grade estimation to present correlations between orebodies and geological features (strata, faults, and intrusions) in a 3D space. The Hurst exponent can be used to recognize the continuity of mineralization with depth in the Tongshan copper district in zones penetrated by boreholes in the intrusive rocks (Figs. 5 and 8), which indicated that the intrusive rock has higher continuous mineralization at depth. The higher Hurst exponent value can be used to validate the center of orebody III, which can be modeled using the 3D orebody model and can be estimated using KT3D.exe. The KT3D.exe can be used to extract and delineate the trend of mineralization in horizontal and vertical directions in 3D space. Comparing the six different elevation blocks in Fig. 10 reveals that the surface block (400 m) is not similar to the other five blocks, which have stronger mineralization continuity and mineral concentration center(s), and this comparison indicates that the Tongshan fault has affected the mineral distribution in the subsurface (between elevations 500 m and 300 m). The results can be used to identify the mineralized zone that belongs to orebody II and was destroyed by the Tongshan fault. The location of the mineralization zone 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 belongs to the zone of hypogene enrichment, and the mineralization is of the magmatic-hydrothermal type, similar to the skarn-type potential Cu exploration targets (Figs. 10 and 11). Combining the 3D geological model and the sixth trend model analysis result from KT3D.exe indicates that the deep part of orebody III has a low mineralization zone that is of the magmatic/porphyry type of potential Cu 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 results and 3D grade models of the Tongshan deposit can be used to delineate mineralization continuity at depth. In the 3D geological model of the Tongshan copper deposit, the alteration zones indicate that the intrusive rock is associated with the mineralization center (Fig. 3). The calculated results demonstrate that the three orebodies of the Tongshan copper deposit are associated with the intrusive rock, and the Tongshan fault is a thrust fault that destroyed orebodies I and II. The displacement along the Tongshan fault is less than 400 m in the north south direction and less than 200 m in the northwest direction. This quantitative analysis can assist in deep exploration for orebody II in the foot wall of Tongshan fault. Thus, we reconstructed orebody II using the above parameters (Fig. 11). Fig. 9 is a 3D intrusion buffer model in the 3D environment (the buffer distance is 500 m), and Figs. 9 and 13 show a model of the orebody grades using the C V cutoff values. This model shows that the mineralization center coincides with the intrusion, but many higher grade values surrounding it are due to the Tongshan fault. Therefore, the fractal method and 3D geological modeling can be integrated to identify potential mineral targets quantitatively. The methods presented in this paper are well-suited and most useful for district-scale mineral resource assessment and prediction in other regions of the world. Acknowledgments The authors would like to thank Drs. Clayton V. Deutsch (University of Alberta, Canada), John Carranza (James Cook University, Australia), Renguang Zuo (China University of Geosciences, Wuhan), Chengyin Tan (Heilong Mineral Resources Co., LTD, Harbin, China), and two reviewers for their clear and full comments. The research was supported by the National Science and Technology Support Project of the 12th Five-Year Plan (Grant No. 2011BAB04B06), the Ministry of Land and Resources Public Service Sectors Fund (Grant No ), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Beijing: Grant No ), and the State Key Laboratory of Geological Processes and Mineral Resources (Grant No. GPMR2011).

13 G. Wang et al. / Journal of Geochemical Exploration 134 (2013) Table 3 The second block ( m) parameters for KT3D.exe. START OF PARAMETERS: checkmodr350.out xvk.dat kt3dtsr350.dbg kt3dtsr350.out extdrift.dat References - file with data - 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_vert Afzal, P., Khakzad, A., Moarefvand, P., Rashidnejad, O.N., Esfandiari, B., Fadakar, A.Y., Geochemical anomaly separation by multifractal modeling in Kahang (Gor) porphyry system, Central Iran. 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