Data-driven based logistic function and prediction-area plot for mineral prospectivity mapping: a case study from the eastern margin of Qinling orogenic belt, central China

11 The present work combines data-driven based logistic function with prediction-area plot for delineating 12 target areas of orogenic gold deposits in eastern margin of Qinling metallogenic belt, central China. 13 Firstly, the values of geological and geochemical information layer were transformed into a series of 14 fuzzy numbers with a range of 0-1 through a data-driven based logistic function on the basis of 15 mineralization theory of the orogenic gold deposits. Secondly, the prediction-area(P-A) plot was 16 performed on the above evidence layers and their corresponding fuzzy overlay layers to pick out a proper 17 prediction scheme for mineral prospectivity mapping(MPM) based on the known gold occurrences. 18 What’s more, to further prove th e advantages of this method, we also used a knowledge-driven approach 19 for comparison purpose. Finally, with the concentration-area(C-A) fractal model, the fractal thresholds 20 were determined and a mineral prospecting map was generated. The result, five of the six known gold 21 deposits are located in high and moderate potential areas (accounts for 18.6 % of the study area), one in 22 low potential area (accounts for 38.4 % of the study area) and none in weak potential area (accounts for 23 43 % of the study area), confirmed the joint application of data-driven based logistic function and 24 prediction-area plot a simple, effective and low-cost method for mineral prospectivity mapping, which 25 can be a guidance for further work in the research area. 26


38
Mineral prospectivity mapping is a comprehensive research, during which geological engineers 39 depict metallogenic target areas with known information and data in the study area to guide further 40 exploration. It is essentially a classification technique (Yousefi and Carranza, 2015a), by which the study 41 area could be divided into areas with high, moderate and low favorability of mineralization, respectively 42 (Knox-Robinso, 2000; Abedi, 2012). Simply, its objective is to portray the smallest area where usually 43 contains the most mineral deposits in the study area. In the above process, however, two key difficulties 44 remain yet. One is to convert evidence layers with different orders of magnitude values into a same space 45 and integrate them (Yousefi and Nykänen, 2016), the other is to determine a group of reasonable 46 thresholds to demarcate the study area (Knox-Robinso, 2000).

3
Recent decades have witnessed researches on foregoing issues by many scholars. All of them could 48 be grouped into three categories (Yousefi and Nykänen, 2016;Yousefi and Carranza ,2016;Du et al., 49 2016). One is the knowledge-driven method, which mainly assess mineralization evidences based on the 50 knowledge of geological experts and assigns different weights to each mineralization factor. It is 51 generally suitable for study areas with low exploration levels (Carranza, 2010), in which a large amount 52 of mineralization data is absent. Among them, fuzzy sets and fuzzy logistic, proposed by Zadeh (1965),

67
In order to solve these problems, many geologists attempted not to use training points to assign 68 weights to evidence layers (Luo, 1990;Chung and Fabbri, 1993

72
Recently, a data-driven approach based on logistic functions proposed by Yousefi et al.(2012Yousefi et al.( , 2013 73 2014) and Yousefi and Carranza (2015a) could well overcome the defects of the above two methods. It 74 assigns weights to the evidence layers in a data-driven way without experts' bias and without using the 75 known mines. In this paper, the logistic function is applied to convert the evidence values into fuzzy 76 values with the range of 0-1. Whereafter, the P-A plot advocated by Yousefi andCarranza(2015a, 2015b, 77 2016)was applied to evaluate the prediction ability and fuzzy overlay was used to integrate these fuzzy 78 layers to generate a prospective map. Consequently, three prospective maps were obtained and assembled 79 and the best one was identified. Finally, a prospectivity map was obtained by means of concentration -    In this paper, we used the 1: 50000 regional geological map and 1: 50000 stream sediment survey 101 prepared by the second geology prospecting institute of Henan bureau of geology and mineral exploration 102 and development. A total of 4036 samples were collected, processed and analyzed with a sampling 103 density of 4-6 points per square kilometer in about 1000 square kilometers in the study area. Each of the 104 original samples weighed more than 150g with a particle size less than 60 mesh (<216μm).

105
A multi-element (Au, Ag, As, Sb, Cu, Pb, Zn, Mo, W, Cd) was obtained with Graphite Furnace        the intrusive contact was used as the indicator criterion. However, the further from the intrusive, the less 135 the possibility of mineralization , thus, the inverse square of the distance from intrusive was taken as the 136 evidence value in each cell (Fig. 2a). It is generally accepted that faults are important channels for the 137 movement of geological fluids (Pirajno, 2010). Without faults, there could be little migration and 138 enrichment of elements, as a result, impossible to generate gold deposits as well. Consequently, we take 139 proximity to fault as the evidence value, whose acquisition way is similar to that of heat source (Fig. 2b). 144 Table 1 145 Rotated factor matrix of staged factor analysisor data of samples from the study area. Loadings in bold 146 represent the selected elements based on threshold of 0.6 (the absolute threshold value) for each stage.

147
From the results of staged factor analysis (Table 1) Table   196 2 and the obtained fuzzy score layers are revealed in Fig.3.
197 Table 2 198 Parameter values calculated for each evidence layer.

200
In order to check whether the fuzzy score could be a good representation of the mineralization 201 favorability, the obtained Fuzzy score layers (Fig.3a, 3b, 3c

218
The P-A plot of evidence layer were shown in Fig.4.The intersection of the two curves represents 219 the prediction ability of the evidence layer. The higher the intersection, the stronger the prediction ability, 220 and the closer it is to mineralization.

222
As can be seen from Table 3, the prediction capability of each fuzzy evidence layers was quite 223 different. The best one is the heat source, with a value of 81, significantly exceeds other layers. In order 224 to better find out the relationship between each fuzzy evidence layer and mineralization, we conducted 225 fuzzy overlay with a γ value of 0.95 (Bonham-Carter, 1995) to integrate these layers.
226 Table 3 227 Prediction ability of each evidence layers.

228
Evidential layer % of known Au occurrences % of study area The fuzzy evidence layers with prediction ability greater than or equal to 81, 67, 65 and 61are 229 integrated separately to obtain 3 overlay maps (Fig.5), which were then estimated by P-A plot and their 230 evaluation results are shown in Table 4.

233
Though there are many similarities between the Fig.5a and 5b, the latter has slightly stronger 234 predictive value Fig.5d, 5e and Table 4). However, we also noticed that the corresponding forecasting 235 capacity from Fig. 5d to 5f possessed a trend of increasing first and then declining. Among them, Fig.5e 236 reached a maximum with a prediction rate of 84%, at this point, the evidence layers for integration were 237 Fig.3b, 3c and 3d with prediction rate of 81%, 65% and 67%, respectively. This phenomenon is weird,

238
because several layers with lower prediction ability have a better result when integrated. In spite of this,

239
it is in line with previous study (Yousefi, 2015). What is interesting is that the prediction rate of Fig.5c 240 dropped significantly when fault is added for integrating. This may be caused by the multi-phase 241 superposition of tectonic movements in this area, leading to the development of a large number of faults,

242
while there is no magmatic hydrothermal activity in some faults.
243 Table 4 244 Prediction ability of each integrated layers.

245
Fuzzy prospectivity map % of known Au occurrences % of study area

257
Subsequently, with fuzzy gamma(γ = 0.95) operation was performed, the fuzzy prospectivity score 258 and the matching P-A plot were obtained (Fig.7a, 7b). According to Fig. 7b, the intersection value is 77, 259 obviously lower than that of Fig.5b (83). The above results indicate that that the weighting of the evidence 260 layer by using the logistic function not only avoids subjective judgment but also has a higher prediction 261 rate compared with the traditional discrete linear method. This is consistent with the findings of Yousefi   (1962,1983,1985) and Carlson(1991) mentioned, in many cases, ore deposits are 267 characterized by aggregation and fractal distribution. Therefore, in order to figure out the high, moderate, 268 low and weak areas of the mineralization more accurately, we conducted the C-A method to defuzzify 269 Fig. 5b so as to obtain a prospectivity map. This method was proposed by Cheng (1994) and has been

278
In this paper, the logarithm of the fuzzy score and the logarithm of the cumulative area were taken 279 as the X-axis and Y-axis, respectively (Fig.8a). Three inflection points were obtained (-1.41, -1.11, -0.19) 280 and the corresponding fuzzy prediction values (0.039, 0.078, 0.643) were acquired, which then were used 281 20 to divide the study area into four parts (Fig.8b). The result, high potential area accounts for 2.5% of the 282 study area with 2 known Au occurences contained, moderate potential area accounts for 16.1% of the 283 study area with 3, low potential area accounts for 38.4% of the study area with 1 and low potential area 284 accounts for 43% of the study area with none, would be an ideal metallogenic prediction map.

285
Although there was a known Au occurrence located in the low potential area, we noticed it was so 286 close to the moderate potential area. This may be attribute to the substitution of point position for area 287 projection. This Au occurrence was, acturally, an alteration zone about 0.76km in length with a trend near 288 east-west, while projected only its center on the horizontal. Therefore, it can be seen from the 289 prospectivity map that the gold occurrence is away from the favorable metallogenic area less than 2 cells 290 (400). In reality, the gold occurrence was partially contained by the moderate areas.

300
Obtaining s and i by solving equations, as a data-driven method, is able to factually reflect the relative 301 importance of evidence values.

302
In this paper, a total of 4 fuzzy layers of geology and geochemistry were evaluated by P-A plot. The 303 results demonstrate that the heat source possess the highest prediction rate, which is consistent with the 304 strong control of orogenic gold deposits by geological hydrothermal. The prediction rate of faults also 305 reaches 61%, which has obvious positive correlation of mineralization. At the same time, both the two 306 multi-element geochemistry l evidence layers have a prediction rates greater than 65%, which is in line 307 with the SFA analysis.

308
When overlying, a fuzzy gamma operation is used with a recommended value of 0.95 (Bonham-

309
Carter, 1995). The results revealed that the heat source, Au-As-Pb factor and Cu-Zn-Mo-Cd factor had a 310 relatively high prediction rate, which was then integrated to get a perspectivivity map with a maximum 311 prediction rate of 83%. This is higher than each of the evidence layers or integrating all of them. However, 312 the prediction ability from Fig.5a to 5c has a tendency of going up first and declining latter. We wonder 313 whether there would be a specific prediction rate, elevates the final prediction ability with evidence layer

321
(2) In this paper, the data-driven logistic function and the P-A evaluation were jointly applied to 322 mineralization prediction .The result, heat source P-A plot has the highest predictive ability (81%),

323
indicating the strong correlation between mineralization and the intermediate-acid intrusive rock (vein),

324
which is in line with the general characteristics of orogenic gold deposits.

325
(3) The mineralization prediction map was generated for the study area. The metallogenic target 326 spread roughly along the northwest -southeast (consistent with the regional tectonic), which shows the 327 high correlation between gold mineralization and tectonic activities, and provides guidance for further 328 large-scale exploration .