# Joint Application of Fractal Analysis and Weights-of-Evidence Method for Revealing the Geological Controls on Regional-Scale Tungsten Mineralization in Southern Jiangxi Province, China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Input Data

^{2}(Figure 1). Yanshanian tectonic–magmatic activity is believed to be responsible for the extensive tungsten mineralization in this region [34,37,38]. The widespread outcropped Yanshanian granites mainly comprise biotite monzogranite, monzonite, and porphyritic monzogranite [35]. The widely distributed tungsten deposits in the SJP are dominated by quartz vein-type, with lesser amounts of skarn- and greisen-types [34]. Four important ore districts containing most of the tungsten occurrences in this area are highlighted in Figure 1, namely Chongyi-Dayu-Shangyou, Ganxian-Yudu, Longnan-Dingnan-Quannan, and Ningdu-Xingguo.

#### 2.2. Box-Counting Fractal Analysis

_{B}), and A is a constant. Practically, a graph of log(N(r)) versus log(r) is plotted and a best-fit regression line is drawn using the least square method, while the slope of the regression line represents the box-counting fractal dimension (Figure 3d).

#### 2.3. Weights of Evidence Method

_{i}and mineralization is estimated by a pair of weights, namely, the positive weight W

^{+}and the negative weight W

^{−}, which can be given by

_{j}is the weight of geological feature j, and the posterior probability can be given by [42]

## 3. Results and Discussion

#### 3.1. Selection of Ore-Related Faults

_{M}) and (2) non-occurrence locations (denoted by D

_{N}). D

_{N}represents a naturally random probability density distribution of a regular pattern within the buffering range of the given distance, while D

_{M}indicates a non-random probability density distribution of the mineralized pattern, characterized by unevenly clustering within the range. The difference D, which is calculated by (D

_{M}− D

_{N}), represents how much the cumulative frequency of mineral occurrences (i.e., D

_{M}) is higher or lower than that expected due to chance (i.e., D

_{N}), implying a positive or negative spatial distribution of the analyzed geological feature with mineralization.

#### 3.2. Fractal Characteristics of Geological Features

_{B}= 1.389), the Chongyi-Dayu-Shangyou (Rigion 17, D

_{B}= 1.373), and the Ningdu-Xingguo (Region 04, D

_{B}= 1.341) ore districts (Table 1), followed by Region 27 with the sixth highest fractal dimension (1.319) belonging to the Longnan-Dingnan-Quannan ore district. More specifically, a contour map was utilized to visualize the variation of fractal dimensions in the study area, which is generated by spatial interpolation after assigning calculated fractal dimensions to the centers of the corresponding subregions. As depicted in Figure 5, most of the tungsten occurrences are located in those regions where the fractal dimensions of faults are greater than 1.2. However, it is notable that Region 13, pertaining to the Ganxian-Yudu ore district, also contains nine tungsten occurrences but has a relatively low value of fractal dimension (D

_{B}= 1.148). The reason for this may be the lack of effective outcrop, as Ganzhou City, the biggest city of Southern Jiangxi Province, is situated in this area.

_{B}= 0.360) in the Chongyi-Dayu-Shangyou ore district, Region 27 (D

_{B}= 0.313) in the Longnan-Dingnan-Quannan ore district, and Regions 19 (D

_{B}= 0.273) and 20 (D

_{B}= 0.268) in the Ganxian-Yudu ore district all have high fractal dimensions, ranking as the top six of all subregions.

#### 3.3. Quantitative Measurement of Spatial Association and Implications for Further Prospectivity

#### 3.3.1. Determination of Buffer Range

#### 3.3.2. Structure

#### 3.3.3. Granites

#### 3.3.4. Geophysical Anomalies

#### 3.3.5. Geochemical Anomalies

_{4}) in the tungsten ores at Panasqueira (Portugal) is due to the iron enrichment in the host rock. Nevertheless, the buffer analyses of iron and manganese distribution in the SJP produced a different result. The spatial association of iron anomalies and tungsten mineralization is very weak, with a maximum contrast value of 0.656 that is slightly higher than the threshold value of 0.5 (Figure 9f). In contrast, manganese anomalies show a strong correlation with tungsten occurrences, delineated by a peak contrast of 2.194 and the corresponding Studentized contrast of 9.03 at the optimum distance of 3000 m (Figure 9g). This result is in good agreement with an inference from an unpublished work conducted by Wu (one of the co-authors of this paper). He found that manganese enrichment, caused by the presence of a considerable amount of pyrophanite (MnTiO

_{3}), extensively occurs in the altered host rocks around wolframite-bearing quartz veins in the SJP. Our findings support the tungsten ore-forming contribution made by iron and manganese in the host rock, and also infer that the high manganese anomalies could be considered as an important indicator for tungsten prospecting in the study area.

#### 3.4. Predictive Targets Delineated by Combined Fractal and WofE Results

- Prospectivity I: zones delineated by high posterior probabilities in combination with high fractal dimension of faults and high fractal dimension of fault intersections. Ten Level I zones are extracted and filled with cross lines in Figure 11. A total of 70 tungsten occurrences, occupying 58.47% of all the occurrences in the SJP, fall within or proximal (<3 km) to these zones. The occurrence density of level-I zones reaches a value of 0.0325/km
^{2}compared with a background value of 0.0025/km^{2}. It is inferred that Zones I-4, I-5, and I-7 containing no occurrence at present have great potential of prospectivity and can be considered as the most favorable targets in future exploration. - Prospectivity II: zones with high posterior probabilities excluding Level I zones. A total of 25 tungsten occurrences are included in these zones, reaching an occurrence density of 0.0078/km
^{2}which is three times the value of background. Level II zones have good prospective potential and are considered as favorable targets in future exploration. - Background: zones with intermediate to low posterior probability. Twenty mineral occurrences are located in zones with intermediate posterior probability, accounting for an occurrence density of 0.0016/km
^{2}. The remaining 4 occurrences are situated in zones with low posterior probability. These zones should not be considered for exploratory targeting.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Extracted geological features in 30 subregions under fractal analysis: (

**a**) location and ID of each subregion; (

**b**) regional faults, including NE–NNE-trending faults marked in red, EW-trending faults marked in blue, and NW–NNW faults marked in green; (

**c**) fault intersections, of which the intersections of NE–NNE- and EW-trending faults are marked in red; and (

**d**) Yashanian granites.

**Figure 3.**Schematic diagram of box-counting method for measuring a fractal linear pattern: (

**a**) 8 boxes containing parts of target lines with box size r = 4; (

**b**) 21 boxes counted with box size r = 2; (

**c**) 57 boxes counted with box size r = 1; and (

**d**) log–log plot revealing the power law relationship of counted box number N(r) and box size r, obtaining box-counting fractal dimension D

_{B}= 1.2653.

**Figure 4.**Graphs of cumulative frequency of distances from tungsten occurrence (D

_{M}) and non-occurrence locations (D

_{N}) to (

**a**) NE–NNE-trending faults; (

**b**) EW-trending faults; and (

**c**) NW–NNW-trending faults. D is the difference between D

_{M}and D

_{N}.

**Figure 9.**Plots of buffer analysis and Student t-test for determining the optimum controlling range of (

**a**) regional faults; (

**b**) fault intersections; (

**c**) Yanshanian granites; (

**d**) magnetic anomalies; (

**e**) tungsten anomalies; (

**f**) iron anomalies; and (

**g**) manganese anomalies. The contrast = 0.5 dotted line is regarded as the threshold above which the spatial association between two analyzed features can be considered as strong, while the Studentized contrast = 1.96 dotted line is regarded as the threshold above which the spatial correlation can be considered as statistically significant.

**Figure 10.**Geophysical and geochemical anomalies used for weights-of-evidence (WofE) analysis: (

**a**) magnetic anomalies; (

**b**) tungsten anomalies; (

**c**) iron anomalies; and (

**d**) manganese anomalies.

Region ID | Fault | Fault Intersection | Yanshanian Granites | Tungsten Occurrences | |||
---|---|---|---|---|---|---|---|

D_{B} | R^{2} | D_{B} | R^{2} | D_{B} | R^{2} | ||

01 | 1.150 | 0.9991 | Null | Null | 1.846 | 0.9993 | 0 |

02 | 1.074 | 0.9951 | Null | Null | 1.476 | 0.9915 | 0 |

03 | 1.188 | 0.9939 | Null | Null | 1.859 | 0.9999 | 2 |

04 | 1.341 | 0.9938 | 0.468 | 0.9164 | 1.799 | 0.9988 | 4 |

05 | 1.110 | 0.9940 | Null | Null | 1.521 | 0.9971 | 0 |

06 | 1.230 | 0.9989 | 0.293 | 0.9852 | 1.712 | 0.9985 | 1 |

07 | 1.002 | 0.9943 | Null | Null | 1.682 | 0.9967 | 0 |

08 | 1.338 | 0.9980 | 0.249 | 0.9683 | 1.545 | 0.9976 | 2 |

09 | 1.326 | 0.9998 | 0.190 | 0.9212 | 1.729 | 0.9976 | 1 |

10 | 1.292 | 0.9996 | 0.134 | 0.8369 | Null | Null | 0 |

11 | 1.259 | 0.9998 | Null | Null | 1.769 | 0.9994 | 6 |

12 | 1.194 | 0.9997 | 0.149 | 0.8895 | 1.553 | 0.9984 | 6 |

13 | 1.148 | 0.9996 | 0.151 | 0.8435 | 1.737 | 0.9993 | 9 |

14 | 1.221 | 0.9997 | 0.245 | 0.9560 | 1.322 | 0.9930 | 7 |

15 | 1.233 | 0.9992 | Null | Null | 1.159 | 0.9636 | 0 |

16 | 1.237 | 1.0000 | Null | Null | Null | Null | 0 |

17 | 1.373 | 0.9993 | 0.360 | 0.8976 | 1.602 | 0.9982 | 41 |

18 | 1.138 | 0.9995 | Null | Null | 1.429 | 0.9950 | 5 |

19 | 1.209 | 0.9996 | 0.273 | 0.6807 | 1.639 | 0.9981 | 8 |

20 | 1.389 | 0.9991 | 0.268 | 0.8691 | 1.240 | 0.9848 | 8 |

21 | 1.164 | 0.9996 | Null | Null | 1.364 | 0.9547 | 0 |

22 | 0.969 | 0.9915 | Null | Null | 1.847 | 0.9996 | 0 |

23 | 1.274 | 0.9983 | Null | Null | 1.786 | 0.9996 | 2 |

24 | 1.292 | 0.9987 | 0.216 | 0.8553 | 1.719 | 0.9984 | 0 |

25 | 0.938 | 0.9977 | Null | Null | 1.633 | 0.9987 | 0 |

26 | 1.031 | 0.9964 | Null | Null | 1.739 | 0.9977 | 0 |

27 | 1.319 | 0.9998 | 0.313 | 0.9063 | 1.601 | 0.9958 | 12 |

28 | 1.276 | 0.9998 | 0.225 | 0.8815 | 1.749 | 0.9994 | 2 |

29 | 1.106 | 0.9970 | 0.151 | 0.8435 | 1.814 | 0.9998 | 1 |

30 | 1.175 | 0.9990 | Null | Null | 1.668 | 0.9981 | 1 |

_{B}: box-counting fractal dimension; R

^{2}: coefficient of determination of regression line; and Null: indicating the region containing no corresponding geological features or no variation with different scales.

Geological Feature | Optimum Buffer/m | W^{+} | W^{−} | C | C_{s} |
---|---|---|---|---|---|

Faults | 3500 | 0.632 | −2.075 | 2.707 | 6.928 |

Fault intersections | 3500 | 1.135 | −0.429 | 1.564 | 8.127 |

Yanshanian granites | 3500 | 0.998 | −1.120 | 2.117 | 9.420 |

Magnetic anomalies | 3000 | 0.587 | −0.655 | 1.243 | 6.109 |

W anomalies | 1000 | 1.545 | −3.093 | 4.638 | 9.101 |

Fe anomalies | 1500 | 0.471 | −0.185 | 0.656 | 3.284 |

Manganese anomalies | 3000 | 0.919 | −1.274 | 2.194 | 9.030 |

^{+}: positive weight; W

^{−}: negative weight; C: contrast; C

_{s}: Studentized contrast.

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**MDPI and ACS Style**

Sun, T.; Wu, K.; Chen, L.; Liu, W.; Wang, Y.; Zhang, C. Joint Application of Fractal Analysis and Weights-of-Evidence Method for Revealing the Geological Controls on Regional-Scale Tungsten Mineralization in Southern Jiangxi Province, China. *Minerals* **2017**, *7*, 243.
https://doi.org/10.3390/min7120243

**AMA Style**

Sun T, Wu K, Chen L, Liu W, Wang Y, Zhang C. Joint Application of Fractal Analysis and Weights-of-Evidence Method for Revealing the Geological Controls on Regional-Scale Tungsten Mineralization in Southern Jiangxi Province, China. *Minerals*. 2017; 7(12):243.
https://doi.org/10.3390/min7120243

**Chicago/Turabian Style**

Sun, Tao, Kaixing Wu, Lingkang Chen, Weiming Liu, Yun Wang, and Cisheng Zhang. 2017. "Joint Application of Fractal Analysis and Weights-of-Evidence Method for Revealing the Geological Controls on Regional-Scale Tungsten Mineralization in Southern Jiangxi Province, China" *Minerals* 7, no. 12: 243.
https://doi.org/10.3390/min7120243