Abstract
The Luanchuan polymetallic mining district (LPMD) covers many major deposits of the East Qinling metallogenic belt in Henan Province, central China. It has attracted much attention because of its various types of minerals, abundant mineral reserves and huge metallogenic potential. Systematic research on the geology of LPMD has been carried out previously, and it is concluded that the formation of the ore deposits is dominantly controlled by fault structure. However, there are few reports on the quantitative characterization of fault structure and spatial distribution of deposits and the coupling relationship between them. This study applies fractal theory to the illustration of the characteristics of inter-relationship between fault structure and spatial distribution of the ore deposits in LPMD, which then may serve as a basis for further ore exploration. Our results indicate that the capacity dimension (CPDs) of integrated fault structure, NW-trend fault and NE-trend fault for the area investigated are 1.7206, 1.6539 and 1.2145, respectively; while the information dimension (IND) of which is 1.7143, 1.6559 and 1.2222, respectively. The studied area has superior geological environment for potential ore deposits, with major contribution from the NW-trend fault. Spatial distribution dimension value of metallic ore is 0.8873. Quantity fractal dimension and Density fractal dimension values of the metallic deposits are 1.1154 and 1.115, respectively. Quantitatively, the main ore deposits discovered in this area mainly fall on either CPD ≥ 1.49, IND ≥ 1.38 or 1.49 > CPD ≥ 1.00, 1.38 > IND ≥ 1.00. Qualitatively, conditions that facilitate ore deposits require higher fractal dimension values. Among the areas studied, we found that Rank I area is the most ideal region that fulfilled the quantitative and qualitative conditions, which is consistent with the actual location of the ore deposits discovered.
1 Introduction
The Luanchuan polymetallic mining district (LPMD) is located in Luanchuan County, Henan Province, China, where northern Qinling orogenic belt adjuncts southern Huabei continental craton [1,2]. With superior geological background, the LPMD hosts large to super-large metallic deposits including Sandaozhuang, Nannihu and Shangfanggou, which make it one of the many major components in East Qinling metallogenic belt [1,3]. With the production of many types of abundant mineral deposits and potential reserves, the LPMD has drawn much attention of numerous researchers in the past. Much progress was achieved on topics such as genetic and metallogenic age [4,5,6,7,8,9], fluid characteristics [3,10] and ore genesis [1,2,5,11,12]. Formation of the LPMD was dominantly controlled and affected by fracture systems [13,14]. They are also intimately associated with the location of intermediate-felsic intrusion in spatial distribution. Therefore, it is meaningful for the exploration of mineral resource to proceed research work on structure-controlled ore-forming processes. Being able to carry out precise description of complex structure as well as provide quantified unrevealed rules, fractal theory has been widely applied to the investigation of quantitative characterization of fracture [15,16,17], spatial distribution of ore deposits [18,19,20,21], principle of ore formation and ore exploration [21,22,23,24,25,26,27,28,29]. However, the fractal dimension value and the quantitative coupling relationship between the geological structure and spatial distribution of ore deposits are seldom reported. This study applies fractal theory to the investigation of the relationship between fault structure and spatial distribution of LPMD, which can then serve as a basis for potential ore exploration.
2 Geological background
LPMD distributes among Luanchuan fracture system and Machaoying fracture system, in which both Huabei cratonic and intra-continent orogenic structure characters are present [1,2]. LPMD shows typical binary structure [14]. The crystalline basement, Taihua Group, middle- to high-grade metamorphic complex of Archaean age, is overlain by mid-Protozoic xiong’ershan Group, Guandaokou Group, upper Protozoic Luanchuan Group and Kuanping Rock Group [2,30]. LPMD can be mainly divided into two ore fields: one is Nannihu ore field and the other is Yuku ore field [3,5,8]. Polymetallic ores of Mo, W, Pb and Zn are mainly strata-bounded in the rock formations of Guandaokou Group and Luanchuan Group. Research on these deposits shows that there are many different genetic types in LPMD, including porphyry-skarn-type molybdenum-tungsten deposit, skarn-type polymetallic deposit and hydrothermal filling metasomatic lead–zinc–silver deposit [1,2,3,5,6,7,8]. LPMD is well developed with fractures, mainly controlled by thrust nappe of southern margin of Huabei Craton and extensional stretching movement during the Yanshan stage. These are represented by NW- (including NWW-) trend and NE- (including NNE-) trend faults (Figure 1). Among them, the NW- (including NWW-) trend faults are mainly composed of a series of thrust faults napped from north to south, with great extension and scale, which is an important ore-controlling fault in this area [1,3]. The NE- (including NNE-) trend faults are superimposed on the NW trending fault zone in the later stage, with a much smaller scale and mainly in intermittent extension or echelon arrangement [1,3]. Both of them control not only the spatial intrusion of the magma but also the distribution of W, Mo, Pb and Zn ores [1,13,14,31]. Heavy magmatic activities were revealed, with multi-cycle, multi-stage signatures [32,33], among which granitic porphyry is related most intimately to metallic ores [3,34,35].
![Figure 1
(a) Tectonic division of China with the location of the East Qinling Orogen (from ref. [9]); (b) the tectonic subdivision of the Qinling Orogen, showing the location of the LPMD; and (c) geological map of the LPMD (from ref. [34]).](/document/doi/10.1515/geo-2022-0420/asset/graphic/j_geo-2022-0420_fig_001.jpg)
3 Methods
Fractal theory provides important messages including parameters of capacity dimension (CPD) and information dimension (IND) values of fracture systems as well as ore deposits, which are essential for the inference of whether there exists any coupling relationship between structure and ore bodies and thus assists the exploration of new ore deposits. Detailed procedure is described as follows.
3.1 Fractal calculation of fault structure
Among the many methods available for the calculation of linear structural CPD values, the counting-box dimension method is proven the best method, which has the benefits of being direct understandable, offering precise statistics and easy to operate. Therefore, we adopt in this study, the counting-box dimension method for the calculation of the various fractal dimension values based on the fault structure and ore-deposit distribution map. CPD and IND values are calculated.
3.1.1 CPD, D 0 calculation
The algorithm of fractal calculation by means of counting-box method is as follows: first, arbitrarily select a finite area with peripheral length of L (r = L/2n, where n = 1, 2, 3, …; for instance, L/1, L/2, L/4, L/8) as the studied area. The whole area is arbitrarily covered by square grids of various lengths, r/n, and then calculate the number of the grid that registers various fault types, N(r). The object under investigation can be regarded as fractal body which satisfies the following equation:
where C is a constant and D 0 is the CPD value that attempted to acquire. Taking the logarithm of equation (1) yields equation (2) from which the fractal dimension value, D 0, is obtained by taking the absolute value of the slope of the straight line.
In practical, the CPD values are obtained by procedures as follows: (1) choose six square grids with different r values, namely, 15.6747, 7.8373, 3.9187, 1.9593, 0.9797 and 0.4898 km to cover the 2D map in this area (31.3494 km × 15.6747 km) and thus formed six sets of grid-nets. One of the examples is shown in Figure 2, where a 2D orthogonal grid-net is established to cover the studied area by taking r = 3.9187 km and each grid is numbered; (2) once a r-valued grid-net is set, calculate the number of the grid that records if any fracture in each of the three categories, i.e., all faults, NE-trend fault and NW-trend fault found, separately to obtain N(r); (3) repeat the above procedure for different r values and plot on the X–Y plane six sets of data, using ln r as horizontal axis and ln N(r) as vertical axis to acquire linear regression on each of the three fault types and hence obtain their fractal dimension values, D 0 following equation (2). The D 0 thus obtained represent the integrated fracture CPD values for all faults, NE-trend fault and NW-trend fault, separately.
Taking r = 3.9187 km and establishing a 2-D orthogonal grid-net to cover the studied area with each grid numbered.
Another sets of D 0 values called subdivided CPD values are required to more specifically quantify the spatial distribution of fracture system. This is achieved by dividing the studied area into 32 grids as shown in Figure 2. In each grid, sub-grid-nets are established by taking r = 3.9187, 1.9593, 0.9797 and 0.4898 km as unit length to cover the grid, respectively, and thus form four sets of grid-net in each grid. In each sub-grid-net (division) with r as unit length, count total number of faults that show up in each sub-grid area, N(r). Plot on the X–Y plane four r-valued sets of data, using ln r as horizontal axis and ln N(r) as vertical axis to acquire linear regression and hence obtain fractal dimension values, D 0 following equation (2). The D 0 thus obtained represent the subdivided fracture CPD values for all faults.
3.1.2 IND, D 1 calculation
Fracture IND, D 1 contains not only messages of whether there are faults transecting the 2-D grids but also considers the number of faults (or the probability) that are distributed in the grids. For a 2-D orthogonal grid-net with the number of the grid that contains the fault N(r), the probability that fault structure shows up in the ith grid, P i (r) can be expressed as equation (3), the total information message I(r) is defined as equation (4):
By changing the grid length r in the 2-D orthogonal net, providing that a linear relationship exists between I(r) and ln r, the IND D 1 can be obtained by the following equation:
In this case, the grid lengths adopted are 15.6747, 7.8373, 3.9187, 1.9593, 0.9797 and 0.4898 km. The IND value, D 1, of various fault types can be obtained through equations (3)–(5). The IND value, D 1, of division integral structure is calculated by taking r = 1.9593, 0.9797 and 0.4898 km as grid lengths and yields separately their parameters, N(r), P i (r), I(r), for D 1 follow equation (5).
3.2 Calculation of fractal dimension values of ore deposits
Consider ore deposits as point set, the fraction dimension values of ore deposits can be calculated by the counting-box method similar to that applied to the treatment of fractal dimension values for fracture systems described in the previous sections. To quantitatively determine the distribution character of ore deposits within a circular area of radius r, we normally adopt probability density function, which is defined as:
where d(r) is the probability density function, denoting the number of ore deposits per unit area within radius r, take a known ore deposit as the center of the circle. K is a constant and D is the fractal dimension value. In a non-scale section, the higher the D value is, the more number of ore deposits can be located [19]. The fractal distribution function is proposed to represent quantitatively the number of possible ore deposits N(r) that is likely to be explored within a definite radius from the center:
In practical calculation, we take three well-known ore deposits, i.e., Laowanggou Fe deposit, Nannihu W–Mo deposit and Niandaogou Pb–Zn deposit as the center of the circle. The number and density of the ore deposits covered by areas of various radii, rs, are calculated and take the averaged values of the three deposit centers.
4 Results
4.1 Fractal characteristics of fault structures
4.1.1 CPD values
The CPD values of fault structure in this area are listed in Table 1 and accordingly the ln r versus ln N(r) plots for integrated faults, NW faults and NE faults with their linear regression parameters are shown in Figure 3. Within r scale between 0.4898 and 15.6747 km, there exists a high statistical self-similarity. The absolute value of the slopes of the three straight lines, i.e., D 0 of integrated faults, NW faults and NE faults, are 1.7206, 1.6539 and 1.2145, respectively, with excellent R 2 of ∼0.99, signifying very good linear fits among the data. D 0 of integrated faults is close to that of NW-trend faults, which is greater than that of NE-trend faults, indicating that the fault structure in the studied area is dominated by the NW-trend faults. This is in consistent with the structure characteristics of geological observation.
Statistics of the parameters of CPD values in the studied area
| Fault types | CPD values | |||
|---|---|---|---|---|
| r (km) | N(r) | ln r | ln N(r) | |
| Integrated faults | 15.6747 | 2 | 2.7520 | 0.6931 |
| 7.8374 | 8 | 2.0589 | 2.0794 | |
| 3.9187 | 32 | 1.3658 | 3.4657 | |
| 1.9593 | 108 | 0.6726 | 4.6821 | |
| 0.9797 | 310 | −0.0205 | 5.7366 | |
| 0.4898 | 738 | −0.7138 | 6.6039 | |
| NW-trend faults | 15.6747 | 2 | 2.7520 | 0.6931 |
| 7.8374 | 8 | 2.0589 | 2.0794 | |
| 3.9187 | 30 | 1.3658 | 3.4012 | |
| 1.9593 | 95 | 0.6726 | 4.5539 | |
| 0.9797 | 260 | −0.0205 | 5.5607 | |
| 0.4898 | 601 | −0.7138 | 6.3986 | |
| NE-trend faults | 15.6747 | 2 | 2.7520 | 0.6931 |
| 7.8374 | 7 | 2.0589 | 1.9459 | |
| 3.9187 | 15 | 1.3658 | 2.7081 | |
| 1.9593 | 34 | 0.6726 | 3.5264 | |
| 0.9797 | 77 | −0.0205 | 4.3438 | |
| 0.4898 | 146 | −0.7138 | 4.9836 | |
The ln r versus ln N(r) plots of CPD data for (a) integrated faults; (b) NW faults; and (c) NE faults, showing their linear regression parameters.
The statistics of the parameters of divided CPD values in the studied area are listed in Table 2. From Table 2, the 32-division-based CPD values are obtained from linear regression of observed data with nearly perfect R 2 of 0.9608–1.0000, depicting that good statistic self-similarity is reached for fault structure when sub-grid unit length r ranges between 0.4898 and 3.9189 km, with D 0 falls between 0.8340 and 1.8475, mean value 1.4504, median level 1.4832 and standard deviation 0.2585.
Statistics of the parameters of divided CPD values in the studied area
| Scale, r (km) | CPD D 0 | Coefficient of determination (R 2) | |||||
|---|---|---|---|---|---|---|---|
| Location of sub-grid | 3.9187 | 1.9593 | 0.9797 | 0.4898 | |||
| N(r) | 1 | 1 | 4 | 12 | 27 | 1.5849 | 0.9865 |
| 2 | 1 | 3 | 8 | 20 | 1.4380 | 0.9983 | |
| 3 | 1 | 2 | 5 | 13 | 1.2423 | 0.9949 | |
| 4 | 1 | 2 | 5 | 10 | 1.1287 | 0.9968 | |
| 5 | 1 | 4 | 14 | 40 | 1.7773 | 0.9962 | |
| 6 | 1 | 4 | 16 | 45 | 1.8475 | 0.9955 | |
| 7 | 1 | 3 | 9 | 29 | 1.6158 | 0.9998 | |
| 8 | 1 | 2 | 5 | 9 | 1.0831 | 0.9937 | |
| 9 | 1 | 4 | 10 | 21 | 1.4498 | 0.9790 | |
| 10 | 1 | 4 | 15 | 39 | 1.7763 | 0.9933 | |
| 11 | 1 | 4 | 13 | 38 | 1.7444 | 0.9966 | |
| 12 | 1 | 3 | 10 | 23 | 1.5307 | 0.9949 | |
| 13 | 1 | 2 | 4 | 10 | 1.0966 | 0.9949 | |
| 14 | 1 | 2 | 3 | 6 | 0.8340 | 0.9902 | |
| 15 | 1 | 4 | 9 | 16 | 1.3170 | 0.9608 | |
| 16 | 1 | 4 | 9 | 20 | 1.4135 | 0.9791 | |
| 17 | 1 | 4 | 11 | 20 | 1.4425 | 0.9698 | |
| 18 | 1 | 4 | 13 | 29 | 1.6274 | 0.9866 | |
| 19 | 1 | 4 | 12 | 28 | 1.6007 | 0.9883 | |
| 20 | 1 | 4 | 15 | 36 | 1.7416 | 0.9901 | |
| 21 | 1 | 4 | 15 | 39 | 1.7763 | 0.9933 | |
| 22 | 1 | 4 | 13 | 32 | 1.6700 | 0.9912 | |
| 23 | 1 | 3 | 10 | 22 | 1.5115 | 0.9932 | |
| 24 | 1 | 2 | 4 | 8 | 1.0000 | 1.0000 | |
| 25 | 1 | 3 | 8 | 16 | 1.3415 | 0.9902 | |
| 26 | 1 | 4 | 9 | 16 | 1.3170 | 0.9608 | |
| 27 | 1 | 3 | 9 | 22 | 1.4963 | 0.9977 | |
| 28 | 1 | 4 | 10 | 22 | 1.4700 | 0.9820 | |
| 29 | 1 | 4 | 10 | 28 | 1.5744 | 0.9919 | |
| 30 | 1 | 4 | 13 | 30 | 1.6421 | 0.9883 | |
| 31 | 1 | 3 | 6 | 13 | 1.2101 | 0.9892 | |
| 32 | 1 | 3 | 5 | 11 | 1.1115 | 0.9797 | |
4.1.2 IND value, D 1
The calculated parameters of IND of fault structure in this area are listed in Table 3, and accordingly the ln r versus I(r) plots for integrated faults, NW faults and NE faults with their linear regression parameters are shown in Figure 4. Within r scale between 0.4898 and 15.6747 km, there exists a high statistical self-similarity. The absolute value of the slopes of the three straight lines, i.e., D 1 of integrated faults, NW faults and NE faults, are 1.7143, 1.6559 and 1.2222, respectively, with excellent R 2 >0.99, signifying very good linear fits among the data. D 1 of integrated faults is close to that of NW faults, which is greater than that of NE faults, similar to that of CPD, indicating that the fault structure in the studied area is dominated by the NW-trend faults. This is also in consistent with the structure characteristics of geological observation.
Statistics of the parameters of IND values in the studied area
| Fault type | IND | ||
|---|---|---|---|
| r (km) | ln r | I(r) | |
| Integrated faults | 15.6747 | 2.7520 | 0.6730 |
| 7.8374 | 2.0589 | 1.9813 | |
| 3.9187 | 1.3658 | 3.3147 | |
| 1.9593 | 0.6726 | 4.5332 | |
| 0.9797 | −0.0205 | 5.6370 | |
| 0.4898 | −0.7138 | 6.5538 | |
| NW-trend faults | 15.6747 | 2.7520 | 0.6682 |
| 7.8374 | 2.0589 | 1.9676 | |
| 3.9187 | 1.3658 | 3.2361 | |
| 1.9593 | 0.6726 | 4.3983 | |
| 0.9797 | −0.0205 | 5.4724 | |
| 0.4898 | −0.7138 | 6.3675 | |
| NE-trend faults | 15.6747 | 2.7520 | 0.6897 |
| 7.8374 | 2.0589 | 1.8459 | |
| 3.9187 | 1.3658 | 2.5796 | |
| 1.9593 | 0.6726 | 3.4556 | |
| 0.9797 | −0.0205 | 4.3122 | |
| 0.4898 | −0.7138 | 4.9649 | |
The ln r versus I(r) plots of IND data for (a) integrated faults; (b) NW faults; and (c) NE faults, showing their linear regression parameters.
As listed in Table 4, the 32-division-based CPD values are obtained from linear fit with nearly perfect R 2 of 0.9777–1.0000, depicting that good statistic self-similarity is reached for fault structure when sub-grid unit length r ranges among 0.4898–1.9593 km, with divided D1 falls between 0.7925 and 1.7510, mean value 1.3366, median level 1.3601 and standard deviation 0.2501.
Statistics of the parameters of divided IND values in the studied area
| Scale, r (km) | IND | Coefficient of determination (R 2) | ||||
|---|---|---|---|---|---|---|
| Location of sub-grid | 1.9593 | 0.9797 | 0.4898 | |||
| I(r) | 1 | 1.3108 | 2.4255 | 3.2958 | 1.4319 | 0.9950 |
| 2 | 1.0986 | 2.0228 | 2.9470 | 1.3333 | 1.0000 | |
| 3 | 0.6730 | 1.5596 | 2.5232 | 1.3346 | 0.9994 | |
| 4 | 0.6931 | 1.6094 | 2.3026 | 1.1609 | 0.9936 | |
| 5 | 1.3813 | 2.5123 | 3.5861 | 1.5904 | 0.9998 | |
| 6 | 1.3335 | 2.6845 | 3.7610 | 1.7510 | 0.9957 | |
| 7 | 0.9433 | 2.1286 | 3.3093 | 1.7066 | 1.0000 | |
| 8 | 0.6931 | 1.6094 | 2.1972 | 1.0849 | 0.9843 | |
| 9 | 1.1685 | 2.1661 | 2.9669 | 1.2972 | 0.9960 | |
| 10 | 1.3761 | 2.6515 | 3.7909 | 1.7419 | 0.9989 | |
| 11 | 1.2853 | 2.5116 | 3.5951 | 1.6661 | 0.9987 | |
| 12 | 1.0609 | 2.1597 | 3.0431 | 1.4299 | 0.9961 | |
| 13 | 0.6730 | 1.2770 | 2.2539 | 1.1403 | 0.9818 | |
| 14 | 0.6931 | 1.0986 | 1.7918 | 0.7925 | 0.9777 | |
| 15 | 1.3297 | 2.1640 | 2.7726 | 1.0408 | 0.9919 | |
| 16 | 1.3297 | 2.1458 | 2.9650 | 1.1796 | 1.0000 | |
| 17 | 1.3297 | 2.3694 | 2.9785 | 1.1893 | 0.9778 | |
| 18 | 1.3108 | 2.5070 | 3.3285 | 1.4554 | 0.9886 | |
| 19 | 1.3421 | 2.3933 | 3.2631 | 1.3857 | 0.9970 | |
| 20 | 1.3337 | 2.5896 | 3.5027 | 1.5645 | 0.9917 | |
| 21 | 1.3337 | 2.5824 | 3.6102 | 1.6421 | 0.9969 | |
| 22 | 1.3730 | 2.4762 | 3.4365 | 1.4885 | 0.9984 | |
| 23 | 1.0790 | 2.2539 | 3.0625 | 1.4308 | 0.9888 | |
| 24 | 0.6931 | 1.3863 | 2.0794 | 1.0000 | 1.0000 | |
| 25 | 1.0549 | 2.0253 | 2.7363 | 1.2128 | 0.9921 | |
| 26 | 1.3297 | 2.1972 | 2.7726 | 1.0408 | 0.9865 | |
| 27 | 0.9003 | 2.0692 | 3.0247 | 1.5324 | 0.9966 | |
| 28 | 1.3297 | 2.2719 | 3.0910 | 1.2705 | 0.9984 | |
| 29 | 1.2799 | 2.2327 | 3.2817 | 1.4440 | 0.9992 | |
| 30 | 1.3689 | 2.5053 | 3.3633 | 1.4386 | 0.9935 | |
| 31 | 1.0986 | 1.7918 | 2.5649 | 1.0577 | 0.9990 | |
| 32 | 1.0986 | 1.6094 | 2.3979 | 0.9372 | 0.9850 | |
4.2 Fractal analysis of ore deposits
4.2.1 Spatial distribution dimension values of ore deposits
The spatial distribution dimension values of ore deposits are listed in Table 5 and accordingly the ln r versus ln N(r) plots for metallic deposits and Pb–Zn deposits are shown in Figure 4. The absolute value of the slopes of the linear fit, i.e., spatial distribution dimension values for metallic ore and Pb–Zn ore are 0.8873 and 0.6752, respectively, with R 2 of the linear regression as 0.9150 and 0.8786 (Figure 5).
Parameters for the calculation of spatial distribution dimension values of ore deposits
| Ore type | r (km) | N(r) | ln r | ln N(r) |
|---|---|---|---|---|
| Metallic ore | 15.6747 | 2 | 2.7520 | 0.6931 |
| 7.8374 | 6 | 2.0589 | 1.7918 | |
| 3.9187 | 14 | 1.3658 | 2.6391 | |
| 1.9593 | 18 | 0.6726 | 2.8904 | |
| 0.9797 | 25 | −0.0205 | 3.2189 | |
| Pb–Zn ore | 15.6747 | 2 | 2.7520 | 0.6931 |
| 7.8374 | 5 | 2.0589 | 1.6094 | |
| 3.9187 | 10 | 1.3658 | 2.3026 | |
| 1.9593 | 11 | 0.6726 | 2.3979 | |
| 0.9797 | 14 | −0.0205 | 2.6391 |
The ln r versus ln N(r) plots for the calculation of dimension values of spatial distribution of ore deposits.
4.2.2 Quantity and density fractal dimension values of ore deposits
The quantity and density distribution of ore deposits within circular areas of various radius is listed in Table 6. The quantity and density fractal dimension values of ore deposits are obtained by quantity-versus-r plot and density-versus-r plot, respectively, as shown in Figure 6. Within the radius of 2–10 km, there exists polynomial relationship between quantity-r and density-r plots, with R 2 of 0.9977 and 0.9964, respectively. The fractal dimension values, D, of the quantity and density of ore deposits are 1.1154 and 1.115 (since D-2 = −0.885), respectively (Figure 6).
The quantity and density distribution of ore deposits within circular areas of various radius
| Radius (km) | Averaged number of ore deposits | Density of ore deposits (No./km2) |
|---|---|---|
| 2 | 2.3333 | 0.5833 |
| 4 | 4.6667 | 0.2917 |
| 6 | 7.6667 | 0.2130 |
| 8 | 11.0000 | 0.1719 |
| 10 | 13.6667 | 0.1367 |
The quantity-versus-r plot and density-versus-r plot showing fractal dimension values of the quantity and density of ore deposits of 1.1154 and 1.115, respectively.
5 Discussion
5.1 Potential ore deposits of the studied area
According to self-organized criticality theory, fracture system was formed during dissipation process through which small fractures connected, evolved and organized by themselves so that the strain was focused on the main fracture belt that possessed fractal geometry [36,37]. Fracture fractal dimension values are highly related to the connectivity of the fracture system. When fracture fractal value is lower than the critical value, the deformation and penetration rate tend to be low, resulting in the isolation and poor connection among the fractures. On the other hand, when fracture fractal dimension value reaches or exceeds the critical value, then the intense deformation as well as high permeability results in good connectivity of the fracture, which in turn favors the transportation and accumulation of ore-forming fluids for the formation of ore deposits [15,38,39,40]. It is reported that the fractal characteristics (fractal dimension values) of fault structure are highly related to the distribution of ore deposits and are of important indication for ore-forming potential [15,16,17,21,22,29,41,42,43,44]. Two-axis compression tests on rocks and numerical simulation indicate that the critical value for fracture fractal dimension value is 1.22–1.38 [45]. Fracture fractal dimension value is related to the scale of the divided grid-net, which in this study is comparable to the scale of fault structure. Therefore, critical fracture fractal dimension values still have important indication regarding to the investigation of integrated ore-forming potential in this area. The CPD values of integrated fault and NW-trend fault are 1.7206 and 1.6539, respectively, which are much greater than the critical value of 1.22–1.38, demonstrating that the studied area owns great integrated ore-forming potential, with NW-trend faults contribute most of the potential host for ore deposits, which is in consistent with practical investigation results reported so far [1,3,31,35,46,47,48].
5.2 Coupling relationship between fault structure fractal dimension values and spatial distribution of ore deposits
Fractal dimension values of fracture signify the connecting ability of a geological body, and higher dimension values mean better connection among fractures. From the geological significance of fracture fractal dimension, there are two fractal dimension requirements that benefit the host of ore bodies, high fractal values in the individual region favor the transportation and accumulation while low dimension values in the adjacent region facilitate the blocking and closure of ore-forming fluids [17,21,29]. In contrast to our previous work [17,21,29], the studied area contains six polymetallic ores, including gold, iron, copper, lead and zinc, which cover much wider ore-hosting fractal dimension values. More specifically, there are two explored ore deposits in this area (Figure 7), (1) area that hosts Nannihu, Sandaozhuang, Majuan and Yuku ore deposits with CPD value ≥ 1.49 and IND value ≥ 1.38; (2) area that contains enriched ores of Lengshuigou and Sandaogou with 1.49 > CPD value ≥ 1.00 and 1.38 > IND value ≥ 1.00.
Projection of fractal dimension values that host ore deposits.
5.3 Prediction of ore deposits location in the studied area
Since the fractal dimension values are intimately associated with the ore deposits, the contour map of CPD and IND values is plotted and shown in Figure 8a and b, respectively, to further explore the area that may potentially host the ore deposits. As discussed above, the fractal dimension values for the host of the ore deposits in this area are (1) CPD value ≥ 1.49 and IND value ≥ 1.38 (Figure 8c, orange yellow area); (2) 1.49 > CPD value ≥ 1.00 and 1.38 > IND value ≥ 1.00 (Figure 8c, light purple area). The above conditions are required quantitatively for the host of ore deposits. Qualitatively, potential ore deposits are required to possess high individual fractal dimension values and low fractal dimension values in adjacent region.
Summing up the quantitative and qualitative requirements, the studied area can be classified as three ranks, i.e., Ranks I–III (Figure 8), based on their potential of hosting ore deposits. Rank I area facilitates the formation of ore deposits, and it contains three sub-regions, I-1, I-2 and I-3. Most of all deposits discovered are located in Rank I area, including large deposits such as Nannihu, Sandaozhuang, Majuan, Yuku, Lengshuigou and Sandaogou ore bodies. Among them, sub-regions I-1 and I-3 have highest fractal dimension values, which favor the transportation and accumulation of ore-forming fluids, and hence are of great potential for ore deposits. Situating between I-1 and I-3 regions, I-2 region is on the pathway of fluid transportation. Having fractal dimension value next to the highest ones, I-2 region can effectively block and enclose ore-forming fluids, which makes it a target location for ore deposits. Except for the ore deposits mentioned above, middle to large-scale lead, zinc and silver deposits such as Hetaocha, Yangshuwa and Hongdonggou are recently discovered in Rank I region. Rank II region locates along the direction of fluid migration, however, being lack of blocking and enclosure effect for fluid, the ore-forming potential is limited. Rank III area is classified as of the lowest potential for hosting ore deposits in this studied area.
Contour map of fracture fractal dimension value for (a) CPD; (b) IND; and (c) classification of ore-forming areas as Ranks I–III.
The present prediction on the ore location is based solely on the fractal analysis of fault systems that host the excavated ore deposits. Apparently, further geophysical and geochemical data are of vital importance for the justification of the present prediction on ore exploration.
6 Conclusions
Within the domains various r of 0.4898–15.6747 km, the fracture fractal dimension values of the integrated faults, NW-trend faults and NE-trend faults for CPD are 1.7206, 1.6539 and 1.2145, respectively, and for IND are 1.7143, 1.6559 and 1.2222, respectively. The studied area has superior integrated ore-forming geological conditions with NW-trend fracture contributing most for the host of ore deposits.
Within the grid-nets of 0.9797–15.6747 km, the spatial distribution fractal dimension values are 0.8873 and 0.6752, respectively. In the domains of radius ranging from 2 to 10 km, the metallic ore deposits show a quantity fractal dimension value of 1.1154 and a density fractal dimension value of 1.115.
Ore deposits in this area locate in areas containing the following fractal dimension values: CPD value ≥ 1.49 and IND value ≥1.38; 1.49 > CPD value ≥ 1.00 and 1.38 > IND value ≥ 1.00.
The studied area is classified as three ranks according to their potential for hosting ore deposits. Rank I is the most ideal location for the host of ore deposits.
Acknowledgments
This work was supported financially by the Science and Technology Project of Department of Education, Jiangxi Province (No. GJJ213014). The authors wish to thank Jianchao Song, Zhiqiang Liu, Yiyong Zhan and other colleagues of Jiangxi Institute of Applied Science and Technology, for their assistance during the process of this article.
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Author contributions: Methodology, data curation, investigation, writing – original draft: Z.C.; methodology, supervision, writing – review and editing: E.H.; investigation, formal analysis, writing – review and editing: G.L.; formal analysis, data curation: H.C.; data curation, investigation, validation: X.G. All authors have read and agreed to the published version of the article.
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Conflict of interest: Authors state no conflict of interest.
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