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Self-similar fractal analysis of gold mineralization of Dayingezhuang disseminated-veinlet deposit in Jiaodong gold province, China
Journal of Geochemical Exploration 102 (2009) 95–102
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Journal of Geochemical Exploration j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j g e o ex p
Self-similar fractal analysis of gold mineralization of Dayingezhuang disseminatedveinlet deposit in Jiaodong gold province, China Jun Deng a,b, Qingfei Wang a,b,⁎, Li Wan a,c, Liqiang Yang a,b, Qingjie Gong a,b, Jie Zhao a,b, Huan Liu a,b a b c
State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Beijing 100083, China Key Laboratory of Lithosphere Tectonics and Lithoprobing Technology of Ministry of Education , China University of Geosciences, Beijing 100083, China School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
a r t i c l e
i n f o
Article history: Received 15 October 2008 Accepted 24 March 2009 Available online 16 April 2009 Keywords: Fractal Gold grade Disseminated Dayingezhuang Jiaodong
a b s t r a c t The mineralization degree in drifts in the Dayingezhuang disseminated-veinlet gold deposit in Jiaodong gold Province, China, can be categorized into non-mineralized, weakly mineralized, moderately mineralized and intensely mineralized ranks based on the number of the gold grades greater than cut-off. The grades sampled equidistantly and continuously along different drifts at − 140 m, − 175 m and − 210 m levels of the deposit are systematically calculated via the self-similar fractal model. The grade distributions often show bifractal characteristics, including two or three non-scale ranges. It shows that with the increase of mineralized rank, the fractal dimension of the second non-scale range decreases and the corresponding threshold becomes greater. The dimension decrease comes from the increase of proportion of the wider microfracture in the orecontrolling structure system; and the threshold increase is a result from the magnitude elevation of the microfractures from the extension-shear zone to compression-shear zone. The smaller fractal dimension means the proportion of the higher gold grades increases, suggesting the thickness of the orebody is proportional to its mean gold grade. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fractal geometry is a theory describing the distribution of inhomogeneous or irregular objects, and fractal dimension is an important parameter for measuring the extent of irregularity (Mandelbrot, 1983; Turcotte, 1997). Many geological objects or events could be considered in fractal terms. A number of fracture features commonly show fractal distributions, such as fracture aperture (Laubach and Ward, 2006), fracture intensity (Ortega et al., 2006), fault displacements and lengths (Aviles et al., 1987; Okubo and Aki, 1987; Walsh et al., 1991; Jackson and Sanderson 1992; Manning 1994; Fossen and Rørnes 1996; Knott et al., 1996; Needham et al., 1996; Nicol et al., 1996; Watterson et al., 1996; Yielding et al., 1996; Pickering et al., 1997), earthquake magnitudes (Turcotte, 1997; Dimri, 2005), particle sizes of comminuted rock and fault gouge (Sammis and Biegel 1989; Korvin, 1992). The thickness distributions of veins have also frequently been described by power–law relationships (Monecke et al., 2001; Sanderson et al., 1994; Clark et al., 1995; McCaffrey and Johnston 1996; Roberts et al., 1998; Monecke et al., 2005). Mandelbrot (1983) first suggested that mineral distribution conforms to fractal distribution.
⁎ Corresponding author. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, No. 29, Xueyuan Road, Beijing 100083, China. E-mail address: [email protected] (Q. Wang). 0375-6742/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gexplo.2009.03.003
More comprehensive fractal analyses of ore deposit distributions are made by Carlon (1991), Turcotte (2002), Kaye (1994), Blenkinsop (1994), Agterberg (1995) and Agterberg et al. (1996). The statistical relationship among the fractal dimensions of the spatial distribution of deposits, faults and magmatic bodies, are discussed to reveal their geological relationship by Deng et al. (2001, 2006). Fractal models are also applied to the distribution of elements (Cheng et al., 1994; Cheng, 1995, 1999; Zhang et al., 2001; Li et al., 2003; Lima et al., 2003). Cheng et al. (1994) proposed the background geochemical values usually have normal or log-normal distributions, and the anomalous values may follow fractal distribution; he utilized a bifractal model to find the threshold value dividing the abnormal and the background levels. Yet, there are few detailed fractal analyses of grade distributions in the deposits. De Wijs (1951, 1953) pointed that the log-normal or binomial curve can fit the frequency distributions of mine samples. Yet Sanderson et al. (1994) showed that gold grades in the quartz vein deposit La Codosera, Spain, follow a power–law distribution, and Monecke et al. (2001) noted that base metal concentrations in drill core from the Hellyer massive sulphide deposit, Australia, also obey the power–law relationship. Monecke et al. (2005) showed that the frequency distributions of Zn, Pb, Cu, and Ag in the Waterloo massive sulphide deposit conform to truncated power–law relationships. Wang et al. (2007b) found that the grade distributions of the Au, Ag, Pb, Zn, Mn elements in the Damoqujia disseminated-veinlet deposit, Shandong province, China can be
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Fig. 1. Generalized geological map of the western part of Jiaodong gold province, China (revised from Fan et al., 2003).
Fig. 2. Geological map of − 175 m level in the Dayingezhuang ore deposit (General geologic survey report of Dayingezhuang gold ore district in Zhaoyuan county, Shandong province, 1987, the sixth geologic team of Shandong provincial bureau of resource exploration). (a) geological map, (b) sketch showing stress condition change (The displacement of the Dayingezhuang fault is recovered).
Fig. 3. Sketches of the pyrite-quartz veins in drift 73 at − 175m level in Dayingezhuang ore deposit.
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Table 1 Grades sampled along different drifts at − 140 m level. 73.5
67.5
72.5
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1.3 1.2 2.4 2.7 2.2 1 2.3 1.1 7.5 6.9 2.7 2.7 2.8 4.6 1.8 2.8 1.2 4.1 7.4 1.2
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
1.4 35.9 11.8 3.8 3.6 4.1 2.3 14.8 3.9 5.8 3.7 13.5 2.8 1.6 13.6 5.4 4.2 8 3.7 2.8
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
3.2 1.7 2.2 1.2 1.1 1.7 2.3 4 1.8 0 0.7 2 1 3.1 1.8 3.8 1.5 0.7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.2 0.2 0.3 0.2 0.6 0.55 0.7 0.6 0.2 0.2 0.2 0.3 0.3 0.6 0.3 0.5 0.3 0.4 0.3 0.2
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
0.2 0.7 0.8 1.3 0.4 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.8 0.6 0.6 0.4 1.2 1.3 0.6 1
41 42 43 44 45 46 47 48 49 50 51 52 53 54
1.5 0.5 1.1 1.8 0.5 0.25 0.25 0.4 0.2 0.2 0.2 0.2 0.2 0.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1.5 0.3 1.3 0.7 0.7 1.2 1.5 3.1 0.3 1 1.8 1.9 0.5 0 0 1.9 1.6 0.2 4.9 1.6
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
1 1.1 0.5 5.7 2 1.7 0.6 2.8 1.1 0 1.5 0 1 1.6 3 6.7 0.8 5.4 4.9 0.6
41 42 43 44 45 46 47 48 49 50
0.7 0.6 0.7 1.5 4.4 6.6 12.2 2.6 5.8 0.8
described by the bifractal model. Deng et al. (2008a) and Wang et al. (2007a, 2008) also applied the self-affine fractal and multifractal to analyze the element distributions in deposits. Since the gold deposits usually contain the irregular orebodies due to the complicated distribution of grades, the fractal characteristics of the grade distribution on different locations with various mineralization ranks are still ambiguous. Taking the Dayingezhuang disseminated-veinlet gold deposit located in the Jiaodong gold province, China as an example, this paper utilizes the self-similar fractal model to distinguish the ranks of mineralization intensity. 2. Geological settings and data acquisition The Jiaodong gold province is situated along the south-eastern margin of the North China craton, which is dominated by Archean rock units. It is bounded by the N- to NE-trending Tan-Lu fault zone to the west and the Su-Lu ultrahigh-pressure metamorphic belt to the south (Fig. 1). The gold province mainly comprises 3 ore-bearing fault zones, i.e., the Sanshandao zone, the Jiaojia zone, and the Zhaoping zone from west to east in the northwestern part. Gold deposits in the northwestern part of the Jiaodong Peninsula are divided into two types: the “Linglong-type” and the “Jiaojia-type” (Fig. 1). The “Linglong-type” quartz vein-style gold mineralization occurs as single or multiple relatively continuous quartz veins. Disseminated-veinlet “Jiaojia-type” gold mineralization is surrounded by broad alteration
halos, also called the altered-rock type (Qiu et al., 2002; Deng et al., 2008b). The “Linglong-type” deposits are controlled by secondary faults off the regional fault zones and occur where auriferous fluids filled large fractures developed in competent host rock. The “Jiaojiatype” gold deposit is typically developed at lithologic contacts along the fault zones (Fig. 1). These “Jiaojia-type” deposits occur where auriferous fluid infiltrates wallrocks along the regional fault zones, deposits quartz or sulphide veinlets and disseminated metal-bearing grains. The major orebodies in the disseminated-veinlet deposits are concentrated in dilational zones within shear zones, where the attitude of the fault has gentle change. It is considered that both styles of gold deposit formed at the same time, based on the similarity of geological features, and also that they may be transitional parts of single deposits, the difference of the types is resulted from the various magnitude of ore-controlling structures (Qiu et al., 2002; Deng et al., 2005; Yang et al., 2006, 2007; Deng et al., 2008b). The first-order fault has undergone pervasive concentration of strain in this fault zone forming wide zone of cataclastic rock with numerous microfractures, whereas strain decreases away from it, such that deformation is represented by discrete fault planes. The Dayingezhuang gold deposit is located about 18 km southwest to the Zhaoyuan city and in the middle of the Zhaoping Fault (Deng et al., 2005) (Fig. 1). The gold deposit contains reserves of greater than 100 tonnes, with an estimated annual production greater than 2.6 t. The Zhaoping fault with dips of 21°–58° towards SE is cross-cut by the
Fig. 4. Histograms of the grade distribution of the drifts in Dayingezhuang ore deposit. (a) drift 74 at − 175 m level, (b) drift 74 at − 175 m level.
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Fig. 5. Consistent flux along the strike and the dip of the grade and thickness at − 175 m level of No. II-1 orebody in Dayingezhuang ore deposit (a) flux along the strike, (b) flux along the dip (ZK represents the drill hole, CM represents the drift).
Dayingezhuang fault with dips of 43°–60° towards NE in the Dayingezhuang gold deposit (Fig. 2). The hanging wall of the Zhaoping fault zone is composed of Jiaodong group metamorphic rocks, and the footwall is Mesozoic “Linglong-type” granite (mediumgrained metaluminous to slightly peraluminous biotite granite). The dextral movement of the Zhaoping fault induces the development of brittle structures, accompanied by hydrothermal alteration and gold mineralization. Rocks at the hanging wall of the Zhaoping fault zone are characterized by carbonatization, chloritization, and by weak silicification and gold mineralization, with gold grades less than 0.10 g/t. Orebodies are confined in the footwall of the Zhaoping fault zone. The orebodies mainly comprise pyritized, sericitized and silicified granitic rocks, with different degrees of cataclasis. Generally, the degree of fracturing and alteration gradually weakens away from the main fracture plane of the Zhaoping fault. There are more than 20 alteration zones in the footwall. No. I and II alteration zones, which are located to the south and the north of the Dayingezhuang fault respectively, are the two biggest. The explored No.II-1 orebody in the No. II altered zone strikes N17°–26°E with dips 18°–51° towards NW, possessing 59% of the proven reserves of the deposit. The No. II-1 orebody extends from −26 m to −492 m within drifts 66 and 88. This paper focuses on the fractal analysis of the grades distributed in the No. II-1 orebody and the
surrounding alteration zone on −140 m, −175 m, and −210 m levels. As shown in Fig. 2, the gentle strike change of the Zhaoping fracture plane at −175 m level induces the transition of the local force conditions from extension-shear, compression-shear, to shear, corresponding to the pronounced development of orebodies in segment 1, little development in segment 2 and small development in segment 3 respectively. In the extension-shear place with thicker orebody, there develop with thicker pyrite-quartz veins with smaller ones branching from these (Fig. 3). Sulphide minerals in ores include mainly pyrite, sphalerite, galena, chalcopyrite and arsenopyrite. Among them, pyrite is the most abundant and the main gold-bearing mineral. Gangue minerals dominantly comprise quartz, sericite, feldspar, calcite, barite and chlorite. Gold minerals are dominantly electrum with trace amounts of native gold. The original grades involved in the reserve calculation and the following fractal analysis are obtained from channel sampling, with length of 1 m, distributed continuously, except that the interlying dikes are skipped, in the intense alteration zone with obvious minable grade along different drifts on several levels below the fault plane. And the samples are cut, reduced in bulk, and assayed (Table 1). The histograms of the grade distribution along the drifts in the deposit can't be effectively fitted by the exponential and log-normal trend lines (Fig. 4), the grade distribution should be described by the fractal models. Based on the grades, taking cut-off grade as 2 g/t, block cut-off as 2.8 g/t and minimum true thickness as 1.2 m, the geometry of orebodies are defined. It shows that the thickness of the orebody shows positive relationship with its mean value in the deposit, e.g., the grade and the thickness of No. II-1 orebody show the consistent flux along the strike and dip (Fig. 5). The drifts on all three levels can be categorized into various mineralization ranks according to development of the orebodies as follows: (1) non-mineralized areas, where the grades are less than the cutoff grade 2 g/t; (2) weakly mineralized areas, where the grades are rarely greater than 2 g/t, the orebodies are barely developed; (3) moderately mineralized areas with discontinuous orebodies; and (4) intensely mineralized areas, where more than half of the grades are greater than the cut-off and the orebodies are huge or continuous in the sample range (Table 2). 3. Fractal model and calculation process The number-size model is described by: Nðzr Þ = cr
−D
ð1Þ
where r is the scale, and means the grade in g/t in this paper r; N (≥r) is the cumulative number of grade with values greater than or equal to r; c is the constant and D is the fractal dimension of the grade distribution. In a diagram displaying the cumulative number plotted against the corresponding scale in ln–ln coordinates, i.e. lnN (≥ r) versus lnr plot, Eq. (1) results in a straight line with the slope − D within a scale interval named as non-scale range. Other common distributions such as normal (Gaussian), log-normal or negative exponential yield distinctly curved graphs with lnN (≥ r) versus nlr plot. Fractal dimension can indicate the irregularity in which the data is spread in the data space. The intervals of the selected scales change congruously with the differences of the grades ordered from large to small. The scales are often selected as 0.1 g/t when the scale is smaller than 1 g/t, as
Table 2 Description of mineralization rank in the Dayingezhuang gold ore deposit. Mineralization rank
Name
Gold grade distribution
Orebody distribution
Example
I II III IV
Non-mineralized area Weakly mineralized area Moderately mineralized area Intensely mineralized area
Less than the cut-off grade 2 g/t Rarely greater than 2 g/t A few grades are greater than the cut-off Half of the grades are greater than the cut-off
No The orebody is very thin The orebodies are discontinuous The orebody is huge or continuous
Drift 67.5 at − 140 m level Drift 72 at − 140 m level Drift 72.5 at − 140 m level Drift 73.5 at − 140 m level
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Table 3 Fractal dimensions in different drifts at − 140 m, − 175 m, − 210 m level in the Dayingezhuang ore deposit. Level (m)
Drift
Rank
Threshold
D
R2
Drift
Rank
Threshold
D
R2
− 140
67.5 68 68.5 69 69.5 70 60.5 61.5 62 71.5 72 72.5 73 73.5 74 74.5 67.5 68 68.5 69 69.5 70 70.5 71 71.5 72 72.5 73 73.5 74
I III III III III II III III II I II III III IV IV III I III II II III III I II II III II III III III
1.0 1.0 0.9 1.0 1.0 0.8 1.0 1.1 1.1 0.5 0.7 0.9 1.2 1.6 4.0 0.6 0.5 1.0 1.0 1.2 0.5 0.5 0.5 0.3 0.4 0.6 1.0 1.2 1.0 0.8
4.26 1.60 1.30 1.03 1.13 2.09 1.37 1.33 1.90 2.68 1.75 1.10 1.42 1.62 2.53 1.00 1.81 1.21 2.19 2.65 1.18 1.23 1.76 1.17 1.29 1.08 3.15 1.86 1.54 1.21
0.95 0.96 0.99 0.98 0.99 0.99 0.99 0.98 0.98 0.98 0.99 0.98 0.99 1.00 0.97 0.99 0.99 0.99 0.97 0.98 0.95 0.97 0.98 0.98 0.97 0.97 0.95 0.98 0.99 0.98
72 72.5 73 73.5 74 74.5 75 75.5 76 76.5 77 77.5 78 78.5 79 79.5 74.5 75 75.5 76 77 78 78.5 79 79.5 80 81 81.5 82 83
II III IV IV III III III III III III IV IV III IV III III III IV IV III I III IV III III III II III I III
0.8 1.0 1.8 2.0 1.0 1.0 1.0 1.0 1.2 1.0 0.8 0.9 1.0 1.2 1.0 1.0 1.0 1.6 1.8 0.9 0.8 1.2 2.0 1.0 1.6 1.0 0.8 1.2 0.2 1.2
2.03 1.00 2.15 1.37 1.14 1.23 0.98 1.22 1.34 1.72 0.63 0.76 1.37 0.83 0.95 1.61 1.08 1.41 1.40 1.84 3.17 1.18 1.77 1.03 1.82 1.24 2.20 1.78 1.56 1.72
0.97 0.98 0.98 0.98 0.99 0.97 0.96 0.99 0.97 0.98 0.99 1.00 0.99 1.00 0.96 0.98 0.97 0.98 0.99 0.98 0.97 0.99 0.98 0.99 0.97 0.96 0.96 0.99 0.99 0.99
− 175
− 210
Mineralization Rank I: non-mineralization drift; Rank II: weakly mineralization drift; Rank III: moderately mineralization drift; IV: intensely mineralization drift. R2 is the regression coefficient.
0.1 g/t or 0.2 g/t when the grade is beyond 1 g/t, and much greater as the grade is beyond 2 g/t for each drift. After systematic calculations, it is demonstrated that the grade distributions in the drifts have the bifractal characteristics. The lnN–lnr plots can be fitted by two straight lines for most drifts and by three lines for few drifts. The threshold and fractal dimension of the second line is selected for study. The threshold is determined via adjusting it to achieve the highest regression coefficient of the second fitted line. The regression coefficients for all drifts are beyond 0.95, the thresholds mostly fall into the range from 0.5 g/t to 1.2 g/t (Table 3). 4. Fractal analysis of grade distribution The fractal analysis for drift 67.5 to drift 74.5 on −140 m level is carried out (Fig. 6). The grades on drifts 73.5 and 73 are mostly greater than 2 g/t and these two drifts are grouped into intensely mineralized area. The thresholds on drifts 73 and 73.5 are 1.8 g/t and 2.0 g/t respectively, which are the greatest two on the −140 m level; and their fractal dimensions are 2.15 and 1.37 respectively. The thresholds of the drifts in moderately mineralized rank are much smaller and
equal to 0.9 g/t or 1 g/t, the fractal dimensions range from 1.00 to 1.60. Only a few grades on the drifts 70 and 72 are greater than the cut-off grade, and the drifts are categorized into weakly mineralized areas; the fractal dimensions of drifts 70 and 72 are 2.09 and 2.03 respectively, which are greater than those in the moderately mineralized drifts, the thresholds are both 0.8 g/t. The fractal dimension on the non-mineralized drift 67.5 is 4.25, which is the maximum at this level; the threshold here is 1 g/t. It is shown that the fractal dimensions of the non-mineralized, weakly mineralized and moderately mineralized areas on the − 140 m level are distinguished when the thresholds range from 0.8 g/t to 1 g/t. Moreover, the intensely mineralized area is characterised by the high threshold. It is shown that the mineralization rank can be identified by the combination of fractal dimension and threshold. The characteristics of the fractal distribution in the drifts from 71.5 to 79.5 on the − 175 m level are similar to those on the − 140 m (Fig. 7). The intensely mineralized area includes drifts 73.5, 74, 77, 77.5 and 78.5. The thresholds on the drifts 77, 77.5 and 78.5 are smaller than 1 g/t and their dimensions are 0.63, 0.76 and 0.83 respectively, which are the smallest on this level; the thresholds on drifts 73.5 and 74 are greater than or equal to 1.6 g/t. In addition, the fractal models in
Fig. 6. Calculation diagrams of fractal dimensions in different drifts at − 140 m level in Dayingezhuang ore deposit. (a) drift 67.5; (b) drift 70; (c) drift 73.5.
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Fig. 7. Calculation diagrams of fractal dimensions in different drifts at − 175 m level in Dayingezhuang ore deposit. (a) drift 71.5; (b) drift 74.5; (c) drift 77.5.
Fig. 8. Calculation diagrams of fractal dimensions in different drifts at − 210 m level in Dayingezhuang ore deposit. (a) drift 69; (b) drift 72; (c) drift 75.
the drifts 77.5 and 78.8 comprise three non-scale ranges, and the dimensions increase from the first non-scale range to the third. The thresholds of the moderately mineralized drifts range from 0.6 g/t to 1.2 g/t and the fractal dimensions from 0.98 to 1.61. The drift 71.5 is grouped into the non-mineralized area, and its fractal dimension is 2.68 and threshold 0.5 g/t. The dimension of the weakly mineralized drift 72 is 1.75, which is smaller than the dimensions of the nonmineralized drifts and greater than those of the moderately mineralized drifts. The thresholds of intensely mineralized drifts 78.5, 75.5 and 75 on − 210 m level are 2 g/t, 1.8 g/t and 1.6 g/t, and dimensions are 1.77, 1.4 and 1.41 respectively. The threshold of the moderately mineralized drift 79.5 is smaller and equal to 1.6 g/t and dimension is 1.82, which is comparatively greater than that of the intensely mineralized drifts. The other drifts categorized into moderately mineralized rank are with the dimension ranging from 1.03 to 1.86 and threshold from 0.5 g/t to 1.2 g/t. The weakly mineralized drifts 68.5, 69, 72.5 and 81 are with thresholds from 0.8 g/t to 1.2 g/t and their dimensions vary from 2.19 to 3.15; the thresholds of drifts 71 and 71.5 in weakly mineralized rank are 0.3 g/t and 0.4 g/t, their dimensions are 1.17 and 1.29 respectively. The thresholds of the nonmineralized drifts 82, 70.5 and 67.5 are less than or equal to 0.5 g/t, and the dimensions for these drifts are greater than 1.5, which is greater than those in the weakly mineralized drifts with the similar threshold. In addition, the fractal dimension of the non-mineralized drift 77 is 3.17 and the threshold 0.8 g/t (Fig. 8).
Fig. 9. Change of the fractal models with the increasing metallogenic intensity. I: nonmineralized rank; II: weakly mineralized rank; III: moderately mineralized rank; IV: intensely mineralized rank.
5. Discussions From systematic fractal calculations of grades distributed along different drifts on the −140 m, − 175 m and −210 m levels, results show that the fractal characteristics can denote the various development degrees of the orebodies, i.e. the mineralized rank, across all levels. With the elevation of mineralized rank, the threshold increases, yet the dimension declines (Fig. 9). The plots of thresholds vs. fractal dimensions in all the drifts involved in this paper show that the drifts with various metallogenic intensity fall into different areas in Fig. 10. The fractal dimension shows approximately negative correlation with
Fig. 10. Plots of thresholds vs. fractal dimensions of the fractal models of the grade distribution in different drifts in Dayingezhuang ore deposit.
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Fig. 11. The fractal models for the thickness distribution of the veins indicating various mineralization rank. (a) models of intensely mineralized veins and barren veins in the Cambrian Hellyer volcanic-hosted massive sulphide deposit, Australia; (b) models of the veins in mineralized sites and those in non-mineralized sites from Central Iberia.
the mineralization rank, that is, the smaller fractal dimension represents a greater thickness of the orebodies. In addition, the smaller fractal dimension or the higher threshold still means a greater proportion of the relatively higher values in the data, suggesting a higher mean value. So the fractal analysis proved that the thickness of the orebody is proportional to its mean value in the disseminatedveinlet gold deposit, which can be verified by the positive relationship of the grade and the thickness of No.II-1 orebody shown in Fig. 4. The fractal characteristics of the vein thickness in the vein-type deposits show similar change from non-mineralization to mineraliza-
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tion, although the fractal dimension is mainly discussed in previous literature. In the study of the Cambrian Hellyer volcanic-hosted massive sulphide deposit in Australia, it is revealed the vein thickness distributions show bifractal distribution; the intensely mineralized veins tend to have relatively low fractal dimensions and great thresholds, whereas weakly mineralized or barren veins are characterised by elevated fractal dimension and declined threshold (Fig. 11a) (Monecke et al., 2001). It is also demonstrated that the thickness fractal distribution of the veins in variably mineralized sites in Central Iberia differs from those in the un-mineralized sites, by showing lower fractal dimension and higher threshold (Fig. 11b) (Roberts et al., 1998). The fractal dimension change mentioned above is explained by the different characteristics of underlying fracture system which controls the metallogenic fluid movement. The lower dimension represents the fracture system is dominated by the wider fractures. The gold minerals in disseminated or veinlet deposit are more enriched in the extensional fractures. The grade for the channel sample can represent the aperture of the total microfractures per sample length in the cataclastic rock. So the fractal models of the grade distribution reflect those of the distribution of overall microfracture apertures per meter along drifts. In the intensely mineralized area, the ore-controlling structure system is dominated by the extensional and wider microfractures formed in the dilational condition, resulting in a lower fractal dimension of grade distribution; while the structure system produced in the compression-shear condition is developed with more narrow microfractures, corresponding to the less mineralized rank and greater fractal dimension (Fig. 12). Thus this study reveals the fracture distributions in the vein-type deposit and in disseminated-veinlet deposit share similar fractal characteristics, suggesting that the fracture system has consistent power–law distribution over approximately several orders of magnitude as demonstrated by other studies (Laubach and Ward, 2006; Ortega et al., 2006). Although the magnitude difference of the ore-controlling structures in the Jiaodong gold province causes the type variation, it induces the similar features between the two types. Since the fracture system also shows bifractal features (Laubach and Ward, 2006), the magnitude increase of the microfracture can produce the threshold increase in the fractal models for grade distribution from barely mineralized zone to intensely mineralized zone. 6. Conclusions According to the orebody thickness along drifts in the Dayingezhuang disseminated-veinlet gold deposit, the drifts at three levels are categorized into the non-mineralized, weakly mineralized, moderately mineralized and intensely mineralized areas. The orebody thickness can only reflect the number of the grades beyond the cut-off, while can not reveal the scatter pattern of the grades. The grade distribution can be described by the bifractal model, in which the threshold and fractal dimension of the second non-scale range are
Fig. 12. Sketch showing the various development of the microfracture in the shear, compression-shear, and extension-shear zone in a shear fault.
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analyzed. With the increase of mineralized rank, the threshold becomes greater and the dimension tends to be smaller, indicating the orebody thickness is proportional to its mean gold grade. The selfsimilar fractal models of the grade reflect the characteristics of the mineral-bearing micofractures. The transition from extension-shear to compression-shear zone induces the decrease of dimensions, the elevation of thresholds, and the raise of mineralization rank. It is suggested the ore-controlling structure system in disseminated or veinlet deposit shares consistent fractal characteristics with that in vein-type deposit. Acknowledgements Thanks to Professor Qiuming Cheng for his help. This research is jointly supported by the National Natural Science Foundation of China (Grant nos. 40572063, 40672064, 40872194, and 40872068), the 111 project (No. B07011) and the Program for Changjiang scholars and Innovative Research Team in University (PCSIRT). References Agterberg, F.P., 1995. Multifractal modeling of the sizes and grades of giant and supergiant deposits. International Geology Review 37, 1–8. Agterberg, F.P., Cheng, Q.M., Wright, D.F., 1996. Fractal modelling of mineral deposits. In: Elbrond, J., Tang, X. (Eds.), Proceedings of the International Symposium on the Application of Computers and Operations Research in the Minerals Industries, pp. 43–53. Montreal. Aviles, C.A., Scholz, C.H., Boatwright, J., 1987. Fractal analysis applied to characteristic segments of the San Andreas Fault. Journal of Geophysical Research 92 (B1), 341–344. Blenkinsop, T., 1994. The fractal distribution of gold deposits: two examples from the Zimbabwe Archaean Craton. In: Kruhl, J.H. (Ed.), Fractals and Dynamic Systems in Geoscience, pp. 247–258. Springer-Verlag Berlin Heidelberg. Carlon, C.A., 1991. Spatial distribution of ore deposits. Geology 19, 111–114. Cheng, Q.M., 1995. The perimeter-area fractal model and its application to geology. Mathematical Geology 27, 69–82. Cheng, Q.M., 1999. Spatial and scaling modeling for geochemical anomaly separation. Journal of Geochemical Exploration 65 (3), 175–194. Cheng, Q.M., Agterberg, F.P., Ballantyne, S.B., 1994. The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration 51 (2), 109–130. Clark, M.B., Brantley, S.L., Fisher, D.M., 1995. Power–law vein-thickness distributions and positive feedback in vein growth. Geology 23, 975–978. De Wijs, H.J., 1951. Statistics of ore distribution: (1) Frequency distribution of grades. Journal of the Royal Netherlands Geological and Mining Society 13, 365–375. De Wijs, H.J., 1953. Statistics of ore distribution: (2) Theory of binomial distribution applied to sampling and engineering problems. Journal of the Royal Netherlands Geological and Mining Society 15, 12–24. Deng, J., Fang, Y., Yang, L.Q., Yang, J.C., Sun, Z.S., Wang, J.P., Ding, S.J., Wang, Q.F., 2001. Numerical modelling of ore-forming dynamics of fractal dispersive fluid systems. Acta Geologica Sinica 75 (2), 220–232. Deng, J., Wang, Q.F., Yang, L.Q., Gao, B.F., 2005. An analysis of the interior structure of the gold hydrothermal metallogenic system of the northwestern Jiaodong Peninsula, Shandong Province (in Chinese). Earth science-Journal of China University of Geosciences 30 (1), 102–108 (in Chinese with English abstract). Deng, J., Wang, Q.F., Huang, D.H., Wan, L., Yang, L.Q., Gao, B.F., 2006. Transport network and flow mechanism of shallow ore-bearing magma in Tongling ore cluster area. Science in China (Series D) 49 (4), 397–407. Deng, J., Wang, Q.F., Wan, L., Yang, L.Q., Zhou, L., Zhao, J., 2008a. The random difference of the trace element distribution in skarn and marbles from Shizishan orefield, Anhui Province, China. Journal of China University of Geosciences 19 (4), 123–137. Deng, J., Wang, Q.F., Yang, L.Q., Zhou, L., Gong, Q.J., Yuan, W.M., Xu, H., Guo, C.Y., Liu, X.W., 2008b. The structure of ore-controlling strain and stress fields in the Shangzhuang gold deposit in Shandong Province, China. Acta Geological Sinica 83 (5), 769–780. Dimri, V.P., 2005. Fractals in geophysics and seismology: an introduction. In: Dimri, V.P. (Ed.), Fractal Behaviour of the Earth System, pp. 1–22. Springer-Verlag Berlin Heidelberg. Fan, H.R., Zhai, M.G., Xie, Y.H., Yang, J.H., 2003. Ore-forming fluids associated with granite-hosted gold mineralization at the Sanshandao deposit, Jiaodong gold province, China. Mineralium Deposita 38, 739–750. Fossen, H., Rørnes, A., 1996. Properties of fault populations in the Gullfaks field, northern North Sea. Journal of Structural Geology 18, 179–190. Jackson, P., Sanderson, D.J., 1992. Scaling of fault displacements from the Badajoz–Córdoba shear zone, SW Spain. Tectonophysics 210 (3–4), 179–190.
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Multifractal IDW interpolation and fractal filtering method in environmental studies: an application on regional stream sediments of Campania Region (Italy). Applied Geochemistry 18 (12), 1853–1865. Mandelbrot, B.B., 1983. The Fractal Geometry of Nature. Freeman, San Francisco. 468 pp. Manning, C.E., 1994. Fractal clustering of metamorphic veins. Geology 22, 335–338. McCaffrey, K.J.W., Johnston, J.D., 1996. Fractal analysis of a mineralized vein deposit: Curraghinalt gold deposit, County Tyrone. Mineralium Deposita 31, 52–58. Monecke, T., Gemmell, J.B., Monecke, J., 2001. Fractal distributions of veins in drill core from the Hellyer VHMS deposit, Australia: constraints on the origin and evolution of the mineralizing system. Mineralium Deposita 36 (5), 406–415. Monecke, T., Monecke, J., Herzig, P.M., Gemmell, J.B., Mönch, W., 2005. Truncated fractal frequency distribution of element abundance data: a dynamic model for the metasomatic enrichment of base and precious metals. Earth and Planetary Science Letters 232 (3–4), 363–378. Needham, T., Yielding, G., Fox, R., 1996. Fault population description and prediction using examples from the offshore U.K. Journal of Structural Geology 18 (2–3), 155–167. Nicol, A., Walsh, J.J., Watterson, J., Gillespie, P.A., 1996. Fault size distributions – are they really power-law? Journal of Structural Geology 18 (2–3), 191–197. Okubo, P.G., Aki, K., 1987. Fractal geometry in the San Andreas Fault system. Journal of Geophysical Research 92 (B1), 345–355. Ortega, O.J., Marrett, R.A., Laubach, S.E., 2006. A scale-independent approach to fracture intensity and average spacing measurement. AAPG Bulletin 90 (2), 193–208. Pickering, G., Peacock, D.C.P., Sanderson, D.J., Bull, J.M., 1997. Modeling tip zones to predict the throw and length characteristics of faults. AAPG Bulletin 81, 82–99. Qiu, Y.M., Groves, D.I., McNaughton, N.J., Wang, L.G., Zhou, T.H., 2002. Nature, age and tectonic setting of granitoid-hosted, orogenic gold deposits of the Jiaodong Peninsula, eastern North China craton, China. Mineralium Deposita 37 (3–4), 283–305. Roberts, S., Sanderson, D.J., Gumiel, P., 1998. Fractal analysis of Sn-W mineralization from central Iberia: insights into the role of fracture connectivity in the formation of an ore deposit. Economic Geology 93, 360–365. Sammis, C.G., Biegel, R.L., 1989. Fractals, fault-gouge and friction. Pure and Applied Geophysics 131 (1–2), 255–271. Sanderson, D.J., Roberts, S., Gumiel, P., 1994. A fractal relationship between vein thickness and gold grade in drill core from La Codosera, Spain. Economic Geology 89, 168–173. Turcotte, D.L., 1997. Fractals and Chaos in Geology and Geophysics. Cambridge University Press. 398 pp. Turcotte, D.L., 2002. Fractals in petrology. Lithos 65 (3–4), 261–271. Walsh, J., Watterson, J., Yielding, G., 1991. The importance of small-scale faulting in regional extension. 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Contents lists available at ScienceDirect
Journal of Geochemical Exploration j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j g e o ex p
Self-similar fractal analysis of gold mineralization of Dayingezhuang disseminatedveinlet deposit in Jiaodong gold province, China Jun Deng a,b, Qingfei Wang a,b,⁎, Li Wan a,c, Liqiang Yang a,b, Qingjie Gong a,b, Jie Zhao a,b, Huan Liu a,b a b c
State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Beijing 100083, China Key Laboratory of Lithosphere Tectonics and Lithoprobing Technology of Ministry of Education , China University of Geosciences, Beijing 100083, China School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
a r t i c l e
i n f o
Article history: Received 15 October 2008 Accepted 24 March 2009 Available online 16 April 2009 Keywords: Fractal Gold grade Disseminated Dayingezhuang Jiaodong
a b s t r a c t The mineralization degree in drifts in the Dayingezhuang disseminated-veinlet gold deposit in Jiaodong gold Province, China, can be categorized into non-mineralized, weakly mineralized, moderately mineralized and intensely mineralized ranks based on the number of the gold grades greater than cut-off. The grades sampled equidistantly and continuously along different drifts at − 140 m, − 175 m and − 210 m levels of the deposit are systematically calculated via the self-similar fractal model. The grade distributions often show bifractal characteristics, including two or three non-scale ranges. It shows that with the increase of mineralized rank, the fractal dimension of the second non-scale range decreases and the corresponding threshold becomes greater. The dimension decrease comes from the increase of proportion of the wider microfracture in the orecontrolling structure system; and the threshold increase is a result from the magnitude elevation of the microfractures from the extension-shear zone to compression-shear zone. The smaller fractal dimension means the proportion of the higher gold grades increases, suggesting the thickness of the orebody is proportional to its mean gold grade. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Fractal geometry is a theory describing the distribution of inhomogeneous or irregular objects, and fractal dimension is an important parameter for measuring the extent of irregularity (Mandelbrot, 1983; Turcotte, 1997). Many geological objects or events could be considered in fractal terms. A number of fracture features commonly show fractal distributions, such as fracture aperture (Laubach and Ward, 2006), fracture intensity (Ortega et al., 2006), fault displacements and lengths (Aviles et al., 1987; Okubo and Aki, 1987; Walsh et al., 1991; Jackson and Sanderson 1992; Manning 1994; Fossen and Rørnes 1996; Knott et al., 1996; Needham et al., 1996; Nicol et al., 1996; Watterson et al., 1996; Yielding et al., 1996; Pickering et al., 1997), earthquake magnitudes (Turcotte, 1997; Dimri, 2005), particle sizes of comminuted rock and fault gouge (Sammis and Biegel 1989; Korvin, 1992). The thickness distributions of veins have also frequently been described by power–law relationships (Monecke et al., 2001; Sanderson et al., 1994; Clark et al., 1995; McCaffrey and Johnston 1996; Roberts et al., 1998; Monecke et al., 2005). Mandelbrot (1983) first suggested that mineral distribution conforms to fractal distribution.
⁎ Corresponding author. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, No. 29, Xueyuan Road, Beijing 100083, China. E-mail address: [email protected] (Q. Wang). 0375-6742/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gexplo.2009.03.003
More comprehensive fractal analyses of ore deposit distributions are made by Carlon (1991), Turcotte (2002), Kaye (1994), Blenkinsop (1994), Agterberg (1995) and Agterberg et al. (1996). The statistical relationship among the fractal dimensions of the spatial distribution of deposits, faults and magmatic bodies, are discussed to reveal their geological relationship by Deng et al. (2001, 2006). Fractal models are also applied to the distribution of elements (Cheng et al., 1994; Cheng, 1995, 1999; Zhang et al., 2001; Li et al., 2003; Lima et al., 2003). Cheng et al. (1994) proposed the background geochemical values usually have normal or log-normal distributions, and the anomalous values may follow fractal distribution; he utilized a bifractal model to find the threshold value dividing the abnormal and the background levels. Yet, there are few detailed fractal analyses of grade distributions in the deposits. De Wijs (1951, 1953) pointed that the log-normal or binomial curve can fit the frequency distributions of mine samples. Yet Sanderson et al. (1994) showed that gold grades in the quartz vein deposit La Codosera, Spain, follow a power–law distribution, and Monecke et al. (2001) noted that base metal concentrations in drill core from the Hellyer massive sulphide deposit, Australia, also obey the power–law relationship. Monecke et al. (2005) showed that the frequency distributions of Zn, Pb, Cu, and Ag in the Waterloo massive sulphide deposit conform to truncated power–law relationships. Wang et al. (2007b) found that the grade distributions of the Au, Ag, Pb, Zn, Mn elements in the Damoqujia disseminated-veinlet deposit, Shandong province, China can be
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Fig. 1. Generalized geological map of the western part of Jiaodong gold province, China (revised from Fan et al., 2003).
Fig. 2. Geological map of − 175 m level in the Dayingezhuang ore deposit (General geologic survey report of Dayingezhuang gold ore district in Zhaoyuan county, Shandong province, 1987, the sixth geologic team of Shandong provincial bureau of resource exploration). (a) geological map, (b) sketch showing stress condition change (The displacement of the Dayingezhuang fault is recovered).
Fig. 3. Sketches of the pyrite-quartz veins in drift 73 at − 175m level in Dayingezhuang ore deposit.
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Table 1 Grades sampled along different drifts at − 140 m level. 73.5
67.5
72.5
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
No.
Value
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1.3 1.2 2.4 2.7 2.2 1 2.3 1.1 7.5 6.9 2.7 2.7 2.8 4.6 1.8 2.8 1.2 4.1 7.4 1.2
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
1.4 35.9 11.8 3.8 3.6 4.1 2.3 14.8 3.9 5.8 3.7 13.5 2.8 1.6 13.6 5.4 4.2 8 3.7 2.8
41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
3.2 1.7 2.2 1.2 1.1 1.7 2.3 4 1.8 0 0.7 2 1 3.1 1.8 3.8 1.5 0.7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.2 0.2 0.3 0.2 0.6 0.55 0.7 0.6 0.2 0.2 0.2 0.3 0.3 0.6 0.3 0.5 0.3 0.4 0.3 0.2
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
0.2 0.7 0.8 1.3 0.4 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.8 0.6 0.6 0.4 1.2 1.3 0.6 1
41 42 43 44 45 46 47 48 49 50 51 52 53 54
1.5 0.5 1.1 1.8 0.5 0.25 0.25 0.4 0.2 0.2 0.2 0.2 0.2 0.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1.5 0.3 1.3 0.7 0.7 1.2 1.5 3.1 0.3 1 1.8 1.9 0.5 0 0 1.9 1.6 0.2 4.9 1.6
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
1 1.1 0.5 5.7 2 1.7 0.6 2.8 1.1 0 1.5 0 1 1.6 3 6.7 0.8 5.4 4.9 0.6
41 42 43 44 45 46 47 48 49 50
0.7 0.6 0.7 1.5 4.4 6.6 12.2 2.6 5.8 0.8
described by the bifractal model. Deng et al. (2008a) and Wang et al. (2007a, 2008) also applied the self-affine fractal and multifractal to analyze the element distributions in deposits. Since the gold deposits usually contain the irregular orebodies due to the complicated distribution of grades, the fractal characteristics of the grade distribution on different locations with various mineralization ranks are still ambiguous. Taking the Dayingezhuang disseminated-veinlet gold deposit located in the Jiaodong gold province, China as an example, this paper utilizes the self-similar fractal model to distinguish the ranks of mineralization intensity. 2. Geological settings and data acquisition The Jiaodong gold province is situated along the south-eastern margin of the North China craton, which is dominated by Archean rock units. It is bounded by the N- to NE-trending Tan-Lu fault zone to the west and the Su-Lu ultrahigh-pressure metamorphic belt to the south (Fig. 1). The gold province mainly comprises 3 ore-bearing fault zones, i.e., the Sanshandao zone, the Jiaojia zone, and the Zhaoping zone from west to east in the northwestern part. Gold deposits in the northwestern part of the Jiaodong Peninsula are divided into two types: the “Linglong-type” and the “Jiaojia-type” (Fig. 1). The “Linglong-type” quartz vein-style gold mineralization occurs as single or multiple relatively continuous quartz veins. Disseminated-veinlet “Jiaojia-type” gold mineralization is surrounded by broad alteration
halos, also called the altered-rock type (Qiu et al., 2002; Deng et al., 2008b). The “Linglong-type” deposits are controlled by secondary faults off the regional fault zones and occur where auriferous fluids filled large fractures developed in competent host rock. The “Jiaojiatype” gold deposit is typically developed at lithologic contacts along the fault zones (Fig. 1). These “Jiaojia-type” deposits occur where auriferous fluid infiltrates wallrocks along the regional fault zones, deposits quartz or sulphide veinlets and disseminated metal-bearing grains. The major orebodies in the disseminated-veinlet deposits are concentrated in dilational zones within shear zones, where the attitude of the fault has gentle change. It is considered that both styles of gold deposit formed at the same time, based on the similarity of geological features, and also that they may be transitional parts of single deposits, the difference of the types is resulted from the various magnitude of ore-controlling structures (Qiu et al., 2002; Deng et al., 2005; Yang et al., 2006, 2007; Deng et al., 2008b). The first-order fault has undergone pervasive concentration of strain in this fault zone forming wide zone of cataclastic rock with numerous microfractures, whereas strain decreases away from it, such that deformation is represented by discrete fault planes. The Dayingezhuang gold deposit is located about 18 km southwest to the Zhaoyuan city and in the middle of the Zhaoping Fault (Deng et al., 2005) (Fig. 1). The gold deposit contains reserves of greater than 100 tonnes, with an estimated annual production greater than 2.6 t. The Zhaoping fault with dips of 21°–58° towards SE is cross-cut by the
Fig. 4. Histograms of the grade distribution of the drifts in Dayingezhuang ore deposit. (a) drift 74 at − 175 m level, (b) drift 74 at − 175 m level.
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Fig. 5. Consistent flux along the strike and the dip of the grade and thickness at − 175 m level of No. II-1 orebody in Dayingezhuang ore deposit (a) flux along the strike, (b) flux along the dip (ZK represents the drill hole, CM represents the drift).
Dayingezhuang fault with dips of 43°–60° towards NE in the Dayingezhuang gold deposit (Fig. 2). The hanging wall of the Zhaoping fault zone is composed of Jiaodong group metamorphic rocks, and the footwall is Mesozoic “Linglong-type” granite (mediumgrained metaluminous to slightly peraluminous biotite granite). The dextral movement of the Zhaoping fault induces the development of brittle structures, accompanied by hydrothermal alteration and gold mineralization. Rocks at the hanging wall of the Zhaoping fault zone are characterized by carbonatization, chloritization, and by weak silicification and gold mineralization, with gold grades less than 0.10 g/t. Orebodies are confined in the footwall of the Zhaoping fault zone. The orebodies mainly comprise pyritized, sericitized and silicified granitic rocks, with different degrees of cataclasis. Generally, the degree of fracturing and alteration gradually weakens away from the main fracture plane of the Zhaoping fault. There are more than 20 alteration zones in the footwall. No. I and II alteration zones, which are located to the south and the north of the Dayingezhuang fault respectively, are the two biggest. The explored No.II-1 orebody in the No. II altered zone strikes N17°–26°E with dips 18°–51° towards NW, possessing 59% of the proven reserves of the deposit. The No. II-1 orebody extends from −26 m to −492 m within drifts 66 and 88. This paper focuses on the fractal analysis of the grades distributed in the No. II-1 orebody and the
surrounding alteration zone on −140 m, −175 m, and −210 m levels. As shown in Fig. 2, the gentle strike change of the Zhaoping fracture plane at −175 m level induces the transition of the local force conditions from extension-shear, compression-shear, to shear, corresponding to the pronounced development of orebodies in segment 1, little development in segment 2 and small development in segment 3 respectively. In the extension-shear place with thicker orebody, there develop with thicker pyrite-quartz veins with smaller ones branching from these (Fig. 3). Sulphide minerals in ores include mainly pyrite, sphalerite, galena, chalcopyrite and arsenopyrite. Among them, pyrite is the most abundant and the main gold-bearing mineral. Gangue minerals dominantly comprise quartz, sericite, feldspar, calcite, barite and chlorite. Gold minerals are dominantly electrum with trace amounts of native gold. The original grades involved in the reserve calculation and the following fractal analysis are obtained from channel sampling, with length of 1 m, distributed continuously, except that the interlying dikes are skipped, in the intense alteration zone with obvious minable grade along different drifts on several levels below the fault plane. And the samples are cut, reduced in bulk, and assayed (Table 1). The histograms of the grade distribution along the drifts in the deposit can't be effectively fitted by the exponential and log-normal trend lines (Fig. 4), the grade distribution should be described by the fractal models. Based on the grades, taking cut-off grade as 2 g/t, block cut-off as 2.8 g/t and minimum true thickness as 1.2 m, the geometry of orebodies are defined. It shows that the thickness of the orebody shows positive relationship with its mean value in the deposit, e.g., the grade and the thickness of No. II-1 orebody show the consistent flux along the strike and dip (Fig. 5). The drifts on all three levels can be categorized into various mineralization ranks according to development of the orebodies as follows: (1) non-mineralized areas, where the grades are less than the cutoff grade 2 g/t; (2) weakly mineralized areas, where the grades are rarely greater than 2 g/t, the orebodies are barely developed; (3) moderately mineralized areas with discontinuous orebodies; and (4) intensely mineralized areas, where more than half of the grades are greater than the cut-off and the orebodies are huge or continuous in the sample range (Table 2). 3. Fractal model and calculation process The number-size model is described by: Nðzr Þ = cr
−D
ð1Þ
where r is the scale, and means the grade in g/t in this paper r; N (≥r) is the cumulative number of grade with values greater than or equal to r; c is the constant and D is the fractal dimension of the grade distribution. In a diagram displaying the cumulative number plotted against the corresponding scale in ln–ln coordinates, i.e. lnN (≥ r) versus lnr plot, Eq. (1) results in a straight line with the slope − D within a scale interval named as non-scale range. Other common distributions such as normal (Gaussian), log-normal or negative exponential yield distinctly curved graphs with lnN (≥ r) versus nlr plot. Fractal dimension can indicate the irregularity in which the data is spread in the data space. The intervals of the selected scales change congruously with the differences of the grades ordered from large to small. The scales are often selected as 0.1 g/t when the scale is smaller than 1 g/t, as
Table 2 Description of mineralization rank in the Dayingezhuang gold ore deposit. Mineralization rank
Name
Gold grade distribution
Orebody distribution
Example
I II III IV
Non-mineralized area Weakly mineralized area Moderately mineralized area Intensely mineralized area
Less than the cut-off grade 2 g/t Rarely greater than 2 g/t A few grades are greater than the cut-off Half of the grades are greater than the cut-off
No The orebody is very thin The orebodies are discontinuous The orebody is huge or continuous
Drift 67.5 at − 140 m level Drift 72 at − 140 m level Drift 72.5 at − 140 m level Drift 73.5 at − 140 m level
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Table 3 Fractal dimensions in different drifts at − 140 m, − 175 m, − 210 m level in the Dayingezhuang ore deposit. Level (m)
Drift
Rank
Threshold
D
R2
Drift
Rank
Threshold
D
R2
− 140
67.5 68 68.5 69 69.5 70 60.5 61.5 62 71.5 72 72.5 73 73.5 74 74.5 67.5 68 68.5 69 69.5 70 70.5 71 71.5 72 72.5 73 73.5 74
I III III III III II III III II I II III III IV IV III I III II II III III I II II III II III III III
1.0 1.0 0.9 1.0 1.0 0.8 1.0 1.1 1.1 0.5 0.7 0.9 1.2 1.6 4.0 0.6 0.5 1.0 1.0 1.2 0.5 0.5 0.5 0.3 0.4 0.6 1.0 1.2 1.0 0.8
4.26 1.60 1.30 1.03 1.13 2.09 1.37 1.33 1.90 2.68 1.75 1.10 1.42 1.62 2.53 1.00 1.81 1.21 2.19 2.65 1.18 1.23 1.76 1.17 1.29 1.08 3.15 1.86 1.54 1.21
0.95 0.96 0.99 0.98 0.99 0.99 0.99 0.98 0.98 0.98 0.99 0.98 0.99 1.00 0.97 0.99 0.99 0.99 0.97 0.98 0.95 0.97 0.98 0.98 0.97 0.97 0.95 0.98 0.99 0.98
72 72.5 73 73.5 74 74.5 75 75.5 76 76.5 77 77.5 78 78.5 79 79.5 74.5 75 75.5 76 77 78 78.5 79 79.5 80 81 81.5 82 83
II III IV IV III III III III III III IV IV III IV III III III IV IV III I III IV III III III II III I III
0.8 1.0 1.8 2.0 1.0 1.0 1.0 1.0 1.2 1.0 0.8 0.9 1.0 1.2 1.0 1.0 1.0 1.6 1.8 0.9 0.8 1.2 2.0 1.0 1.6 1.0 0.8 1.2 0.2 1.2
2.03 1.00 2.15 1.37 1.14 1.23 0.98 1.22 1.34 1.72 0.63 0.76 1.37 0.83 0.95 1.61 1.08 1.41 1.40 1.84 3.17 1.18 1.77 1.03 1.82 1.24 2.20 1.78 1.56 1.72
0.97 0.98 0.98 0.98 0.99 0.97 0.96 0.99 0.97 0.98 0.99 1.00 0.99 1.00 0.96 0.98 0.97 0.98 0.99 0.98 0.97 0.99 0.98 0.99 0.97 0.96 0.96 0.99 0.99 0.99
− 175
− 210
Mineralization Rank I: non-mineralization drift; Rank II: weakly mineralization drift; Rank III: moderately mineralization drift; IV: intensely mineralization drift. R2 is the regression coefficient.
0.1 g/t or 0.2 g/t when the grade is beyond 1 g/t, and much greater as the grade is beyond 2 g/t for each drift. After systematic calculations, it is demonstrated that the grade distributions in the drifts have the bifractal characteristics. The lnN–lnr plots can be fitted by two straight lines for most drifts and by three lines for few drifts. The threshold and fractal dimension of the second line is selected for study. The threshold is determined via adjusting it to achieve the highest regression coefficient of the second fitted line. The regression coefficients for all drifts are beyond 0.95, the thresholds mostly fall into the range from 0.5 g/t to 1.2 g/t (Table 3). 4. Fractal analysis of grade distribution The fractal analysis for drift 67.5 to drift 74.5 on −140 m level is carried out (Fig. 6). The grades on drifts 73.5 and 73 are mostly greater than 2 g/t and these two drifts are grouped into intensely mineralized area. The thresholds on drifts 73 and 73.5 are 1.8 g/t and 2.0 g/t respectively, which are the greatest two on the −140 m level; and their fractal dimensions are 2.15 and 1.37 respectively. The thresholds of the drifts in moderately mineralized rank are much smaller and
equal to 0.9 g/t or 1 g/t, the fractal dimensions range from 1.00 to 1.60. Only a few grades on the drifts 70 and 72 are greater than the cut-off grade, and the drifts are categorized into weakly mineralized areas; the fractal dimensions of drifts 70 and 72 are 2.09 and 2.03 respectively, which are greater than those in the moderately mineralized drifts, the thresholds are both 0.8 g/t. The fractal dimension on the non-mineralized drift 67.5 is 4.25, which is the maximum at this level; the threshold here is 1 g/t. It is shown that the fractal dimensions of the non-mineralized, weakly mineralized and moderately mineralized areas on the − 140 m level are distinguished when the thresholds range from 0.8 g/t to 1 g/t. Moreover, the intensely mineralized area is characterised by the high threshold. It is shown that the mineralization rank can be identified by the combination of fractal dimension and threshold. The characteristics of the fractal distribution in the drifts from 71.5 to 79.5 on the − 175 m level are similar to those on the − 140 m (Fig. 7). The intensely mineralized area includes drifts 73.5, 74, 77, 77.5 and 78.5. The thresholds on the drifts 77, 77.5 and 78.5 are smaller than 1 g/t and their dimensions are 0.63, 0.76 and 0.83 respectively, which are the smallest on this level; the thresholds on drifts 73.5 and 74 are greater than or equal to 1.6 g/t. In addition, the fractal models in
Fig. 6. Calculation diagrams of fractal dimensions in different drifts at − 140 m level in Dayingezhuang ore deposit. (a) drift 67.5; (b) drift 70; (c) drift 73.5.
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Fig. 7. Calculation diagrams of fractal dimensions in different drifts at − 175 m level in Dayingezhuang ore deposit. (a) drift 71.5; (b) drift 74.5; (c) drift 77.5.
Fig. 8. Calculation diagrams of fractal dimensions in different drifts at − 210 m level in Dayingezhuang ore deposit. (a) drift 69; (b) drift 72; (c) drift 75.
the drifts 77.5 and 78.8 comprise three non-scale ranges, and the dimensions increase from the first non-scale range to the third. The thresholds of the moderately mineralized drifts range from 0.6 g/t to 1.2 g/t and the fractal dimensions from 0.98 to 1.61. The drift 71.5 is grouped into the non-mineralized area, and its fractal dimension is 2.68 and threshold 0.5 g/t. The dimension of the weakly mineralized drift 72 is 1.75, which is smaller than the dimensions of the nonmineralized drifts and greater than those of the moderately mineralized drifts. The thresholds of intensely mineralized drifts 78.5, 75.5 and 75 on − 210 m level are 2 g/t, 1.8 g/t and 1.6 g/t, and dimensions are 1.77, 1.4 and 1.41 respectively. The threshold of the moderately mineralized drift 79.5 is smaller and equal to 1.6 g/t and dimension is 1.82, which is comparatively greater than that of the intensely mineralized drifts. The other drifts categorized into moderately mineralized rank are with the dimension ranging from 1.03 to 1.86 and threshold from 0.5 g/t to 1.2 g/t. The weakly mineralized drifts 68.5, 69, 72.5 and 81 are with thresholds from 0.8 g/t to 1.2 g/t and their dimensions vary from 2.19 to 3.15; the thresholds of drifts 71 and 71.5 in weakly mineralized rank are 0.3 g/t and 0.4 g/t, their dimensions are 1.17 and 1.29 respectively. The thresholds of the nonmineralized drifts 82, 70.5 and 67.5 are less than or equal to 0.5 g/t, and the dimensions for these drifts are greater than 1.5, which is greater than those in the weakly mineralized drifts with the similar threshold. In addition, the fractal dimension of the non-mineralized drift 77 is 3.17 and the threshold 0.8 g/t (Fig. 8).
Fig. 9. Change of the fractal models with the increasing metallogenic intensity. I: nonmineralized rank; II: weakly mineralized rank; III: moderately mineralized rank; IV: intensely mineralized rank.
5. Discussions From systematic fractal calculations of grades distributed along different drifts on the −140 m, − 175 m and −210 m levels, results show that the fractal characteristics can denote the various development degrees of the orebodies, i.e. the mineralized rank, across all levels. With the elevation of mineralized rank, the threshold increases, yet the dimension declines (Fig. 9). The plots of thresholds vs. fractal dimensions in all the drifts involved in this paper show that the drifts with various metallogenic intensity fall into different areas in Fig. 10. The fractal dimension shows approximately negative correlation with
Fig. 10. Plots of thresholds vs. fractal dimensions of the fractal models of the grade distribution in different drifts in Dayingezhuang ore deposit.
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Fig. 11. The fractal models for the thickness distribution of the veins indicating various mineralization rank. (a) models of intensely mineralized veins and barren veins in the Cambrian Hellyer volcanic-hosted massive sulphide deposit, Australia; (b) models of the veins in mineralized sites and those in non-mineralized sites from Central Iberia.
the mineralization rank, that is, the smaller fractal dimension represents a greater thickness of the orebodies. In addition, the smaller fractal dimension or the higher threshold still means a greater proportion of the relatively higher values in the data, suggesting a higher mean value. So the fractal analysis proved that the thickness of the orebody is proportional to its mean value in the disseminatedveinlet gold deposit, which can be verified by the positive relationship of the grade and the thickness of No.II-1 orebody shown in Fig. 4. The fractal characteristics of the vein thickness in the vein-type deposits show similar change from non-mineralization to mineraliza-
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tion, although the fractal dimension is mainly discussed in previous literature. In the study of the Cambrian Hellyer volcanic-hosted massive sulphide deposit in Australia, it is revealed the vein thickness distributions show bifractal distribution; the intensely mineralized veins tend to have relatively low fractal dimensions and great thresholds, whereas weakly mineralized or barren veins are characterised by elevated fractal dimension and declined threshold (Fig. 11a) (Monecke et al., 2001). It is also demonstrated that the thickness fractal distribution of the veins in variably mineralized sites in Central Iberia differs from those in the un-mineralized sites, by showing lower fractal dimension and higher threshold (Fig. 11b) (Roberts et al., 1998). The fractal dimension change mentioned above is explained by the different characteristics of underlying fracture system which controls the metallogenic fluid movement. The lower dimension represents the fracture system is dominated by the wider fractures. The gold minerals in disseminated or veinlet deposit are more enriched in the extensional fractures. The grade for the channel sample can represent the aperture of the total microfractures per sample length in the cataclastic rock. So the fractal models of the grade distribution reflect those of the distribution of overall microfracture apertures per meter along drifts. In the intensely mineralized area, the ore-controlling structure system is dominated by the extensional and wider microfractures formed in the dilational condition, resulting in a lower fractal dimension of grade distribution; while the structure system produced in the compression-shear condition is developed with more narrow microfractures, corresponding to the less mineralized rank and greater fractal dimension (Fig. 12). Thus this study reveals the fracture distributions in the vein-type deposit and in disseminated-veinlet deposit share similar fractal characteristics, suggesting that the fracture system has consistent power–law distribution over approximately several orders of magnitude as demonstrated by other studies (Laubach and Ward, 2006; Ortega et al., 2006). Although the magnitude difference of the ore-controlling structures in the Jiaodong gold province causes the type variation, it induces the similar features between the two types. Since the fracture system also shows bifractal features (Laubach and Ward, 2006), the magnitude increase of the microfracture can produce the threshold increase in the fractal models for grade distribution from barely mineralized zone to intensely mineralized zone. 6. Conclusions According to the orebody thickness along drifts in the Dayingezhuang disseminated-veinlet gold deposit, the drifts at three levels are categorized into the non-mineralized, weakly mineralized, moderately mineralized and intensely mineralized areas. The orebody thickness can only reflect the number of the grades beyond the cut-off, while can not reveal the scatter pattern of the grades. The grade distribution can be described by the bifractal model, in which the threshold and fractal dimension of the second non-scale range are
Fig. 12. Sketch showing the various development of the microfracture in the shear, compression-shear, and extension-shear zone in a shear fault.
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