Application of a Maximum Entropy Model for Mineral Prospectivity Maps
Abstract
:1. Introduction
2. Study Area and Data
2.1. Study Area
2.2. Data
2.2.1. Stratigraphic Combination Entropy
2.2.2. Structural Iso-Density
2.2.3. Structural Buffer
2.2.4. Aeromagnetic Data
2.2.5. Geochemical Data
3. Construction of the Maximum Entropy Model
- (1)
- Enter the selected β value in the MaxEnt software and set the remaining parameters (a maximum of 500 iterations, a maximum convergence threshold of 0.00001, a maximum of 10,000 background points and the replicated run type set to bootstrap) to the default values;
- (2)
- Create a MaxEnt model containing all variables, eliminate the variable with a contribution rate <1%, and eliminate the variable with the Pearson’s correlation coefficient of the highest contribution variable >0.7 to get model 1;
- (3)
- Establish a new MaxEnt model with the remaining variables, eliminate the variables with a contribution rate <1%, and remove the variables with a correlation coefficient of >0.7 with the second highest contribution variable to get model 2;
- (4)
- Repeat the above process until there is no variable with a contribution rate <1%, and get model M;
- (5)
- Change the β value in the MaxEnt software, and set the remaining parameters to the default values; repeat steps 2–4 to obtain a series of MaxEnt models for the distribution of mineral resources;
- (6)
4. Results
4.1. Model Performance Evaluation
4.2. Predictive Variable Contribution
4.3. Response Curves of the Ore-Controlling Factors
4.4. Perspective Map of Copper
5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Factors | β = 2 | β = 2.5 | β = 3 | β = 3.5 | β = 4 | |||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | con | cor | |
Model | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 9 | 9 | 10 | 10 | 11 | 11 | 12 | 12 | 13 | 13 | 14 | 14 | 15 | 15 |
Cu | 45.80 | 1.00 | 46.20 | 0.04 | 51.80 | 0.01 | 47.60 | 1.00 | 54.00 | 0.04 | 51.50 | 0.01 | 45.50 | 1.00 | 48.00 | 0.04 | 42.20 | 1.00 | 42.80 | 0.04 | 41.20 | 0.11 | 44.10 | 1.00 | 43.80 | 0.04 | 44.90 | 0.11 | 44.10 | 0.11 |
Na2O | 16.20 | 0.04 | 17.80 | 1.00 | 18.20 | −0.01 | 16.40 | 0.04 | 16.40 | 1.00 | 18.80 | 0.32 | 20.70 | 0.04 | 20.50 | 1.00 | 26.20 | 0.04 | 27.60 | 1.00 | 27.30 | 0.40 | 28.60 | 0.04 | 29.00 | 1.00 | 30.00 | 0.40 | 29.70 | 0.10 |
Li | 3.70 | 0.11 | 4.80 | 0.40 | 4.70 | 0.30 | 6.20 | 0.11 | 7.60 | 0.40 | 9.30 | 0.30 | 10.60 | 0.11 | 11.90 | 0.40 | 7.00 | 0.11 | 8.70 | 0.40 | 12.80 | 1.00 | 7.40 | 0.11 | 10.40 | 0.40 | 10.40 | 1.00 | 10.10 | 0.15 |
W | 1.10 | 0.11 | 0.40 | - | - | - | 0.90 | - | - | - | - | - | 3.30 | 0.11 | 3.70 | 0.10 | 3.50 | 0.11 | 4.90 | 0.10 | 4.30 | 0.15 | 5.60 | 0.11 | 5.60 | 0.10 | 5.80 | 0.15 | 5.70 | 1.00 |
Structural Iso-density | 1.60 | 0.02 | 3.80 | −0.01 | 2.80 | −0.06 | 3.50 | 0.02 | 3.50 | −0.05 | 2.90 | −0.07 | 2.50 | 0.02 | 2.60 | −0.05 | 4.20 | 0.02 | 4.30 | −0.05 | 4.10 | 0.15 | 4.10 | 0.02 | 4.20 | −0.05 | 4.50 | 0.15 | 4.50 | −0.02 |
SiO2 | 2.40 | 0.08 | 0.20 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 3.20 | 0.08 | 1.20 | 0.73 | - | - | 2.50 | 0.08 | 0.00 | - | - | - | - | - |
U | 10.30 | 0.01 | 10.40 | 0.32 | 8.90 | 1.00 | 10.10 | 0.01 | 9.00 | 0.32 | 8.70 | 1.00 | 7.00 | 0.01 | 5.90 | 0.32 | 5.60 | 0.01 | 5.20 | 0.32 | 5.30 | 0.30 | 2.40 | 0.01 | 2.80 | 0.32 | 1.20 | 0.30 | 1.40 | 0.15 |
Hg | 3.20 | 0.09 | 3.90 | 0.06 | 3.50 | 0.09 | 4.00 | 0.09 | 5.00 | 0.06 | 4.60 | 0.09 | 3.80 | 0.09 | 3.70 | 0.06 | 3.70 | 0.09 | 2.20 | 0.06 | 2.30 | 0.42 | 1.40 | 0.09 | 2.10 | 0.06 | 2.30 | 0.42 | 4.50 | 0.09 |
La | 1.70 | 0.14 | 1.50 | 0.50 | 1.80 | 0.37 | 2.00 | 0.14 | 1.80 | 0.50 | 1.90 | 0.37 | 1.70 | 0.14 | 1.50 | 0.50 | 1.50 | 0.14 | 1.30 | 0.50 | 1.20 | 0.62 | 1.00 | 0.14 | 0.90 | - | - | - | - | - |
Combinatorial Entropy | 1.70 | −0.02 | 2.00 | 0.01 | 2.20 | −0.02 | 2.50 | −0.02 | 2.60 | 0.01 | 2.30 | −0.02 | 2.10 | −0.02 | 2.30 | 0.01 | 1.80 | −0.02 | 1.90 | 0.01 | 1.60 | 0.04 | 1.00 | −0.02 | 1.20 | 0.01 | 0.90 | - | - | - |
Mo | 1.10 | 0.27 | 1.50 | 0.09 | 3.50 | 0.22 | 0.60 | - | - | - | - | - | 0.20 | - | - | - | 0.00 | - | - | - | - | - | 0.90 | - | - | - | - | - | - | - |
Cr | 0.00 | - | - | - | - | - | 0.20 | - | - | - | - | - | 0.50 | - | - | - | 0.00 | - | - | - | - | - | 0.70 | - | - | - | - | - | - | - |
Aeromagnetic Data | 0.90 | - | - | - | - | - | 0.80 | - | - | - | - | - | 0.60 | - | - | - | 0.50 | - | - | - | - | - | 0.30 | - | - | - | - | - | - | - |
Sb | 1.70 | 0.13 | 0.30 | - | - | - | 0.70 | - | - | - | - | - | 0.10 | - | - | - | 0.00 | - | - | - | - | - | 0.10 | - | - | - | - | - | - | - |
Ag | 0.10 | - | - | - | - | - | 0.10 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Al2O3 | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
As | 0.10 | - | - | - | - | - | 0.10 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Au | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
B | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Ba | 0.10 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Be | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Bi | 0.10 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
CaO | 1.10 | 0.05 | 0.20 | - | - | - | 0.80 | - | - | - | - | - | 0.30 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Cd | 0.20 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Co | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Structural Buffer | 1.00 | 0.05 | 0.70 | - | - | - | 0.20 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
F | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Fe2O3 | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
K2O | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
MgO | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Mn | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Nb | 0.60 | - | - | - | - | - | 0.50 | - | - | - | - | - | 0.30 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Ni | 0.80 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
pb | 0.00 | - | - | - | - | - | 0.80 | - | - | - | - | - | 0.50 | - | - | - | 0.20 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Pb | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Sn | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Sr | 0.10 | - | - | - | - | - | 0.10 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Th | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Ti | 0.20 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
V | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Y | 0.50 | - | - | - | - | - | 0.60 | - | - | - | - | - | 0.30 | - | - | - | 0.20 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Zn | 2.40 | 0.26 | 6.30 | 0.17 | 2.60 | 0.16 | 1.40 | 0.26 | 0.20 | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
Zr | 0.50 | - | - | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | 0.00 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - |
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Model | Variables | Parameters | AICc |
---|---|---|---|
1 | 43 | 53 | - |
2 | 15 | 40 | 1401.67 |
3 | 10 | 23 | 1155.42 |
4 | 43 | 36 | 1301.03 |
5 | 9 | 16 | 1125.14 |
6 | 8 | 15 | 1120.41 |
7 | 43 | 25 | 1175.31 |
8 | 9 | 16 | 1128.42 |
9 | 43 | 20 | 1149.36 |
10 | 10 | 13 | 1121.09 |
11 | 9 | 13 | 1123.42 |
12 | 43 | 21 | 1159.16 |
13 | 10 | 15 | 1131.45 |
14 | 8 | 13 | 1125.7 |
15 | 7 | 12 | 1122.91 |
No. | Training Samples | Training AUC | Test Samples | Test AUC |
---|---|---|---|---|
1 | 32 | 0.8467 | 11 | 0.8927 |
2 | 32 | 0.8468 | 11 | 0.7908 |
3 | 32 | 0.8490 | 11 | 0.7277 |
4 | 32 | 0.8259 | 11 | 0.7775 |
5 | 32 | 0.8033 | 11 | 0.7621 |
6 | 32 | 0.8492 | 11 | 0.8027 |
7 | 32 | 0.8239 | 11 | 0.8903 |
8 | 32 | 0.8733 | 11 | 0.8167 |
9 | 32 | 0.8834 | 11 | 0.8258 |
10 | 32 | 0.8841 | 11 | 0.6842 |
11 | 32 | 0.8664 | 11 | 0.7236 |
12 | 32 | 0.8615 | 11 | 0.8225 |
13 | 32 | 0.7723 | 11 | 0.7209 |
14 | 32 | 0.7938 | 11 | 0.8112 |
15 | 32 | 0.8636 | 11 | 0.7549 |
16 | 32 | 0.8167 | 11 | 0.8187 |
17 | 32 | 0.8369 | 11 | 0.8886 |
18 | 32 | 0.8516 | 11 | 0.8952 |
19 | 32 | 0.8296 | 11 | 0.7443 |
20 | 32 | 0.8497 | 11 | 0.8427 |
Average | 32 | 0.8414 | 11 | 0.7997 |
Variable | Percent Contribution | Variable | Percent Contribution |
---|---|---|---|
Cu | 38.1% | U | 8.3% |
Na2O | 15.5% | Combinatorial Entropy | 8% |
Li | 10.3% | Structural Isopycnity | 7.8% |
Hg | 10.1% | La | 2.1% |
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Li, B.; Liu, B.; Guo, K.; Li, C.; Wang, B. Application of a Maximum Entropy Model for Mineral Prospectivity Maps. Minerals 2019, 9, 556. https://doi.org/10.3390/min9090556
Li B, Liu B, Guo K, Li C, Wang B. Application of a Maximum Entropy Model for Mineral Prospectivity Maps. Minerals. 2019; 9(9):556. https://doi.org/10.3390/min9090556
Chicago/Turabian StyleLi, Binbin, Bingli Liu, Ke Guo, Cheng Li, and Bin Wang. 2019. "Application of a Maximum Entropy Model for Mineral Prospectivity Maps" Minerals 9, no. 9: 556. https://doi.org/10.3390/min9090556
APA StyleLi, B., Liu, B., Guo, K., Li, C., & Wang, B. (2019). Application of a Maximum Entropy Model for Mineral Prospectivity Maps. Minerals, 9(9), 556. https://doi.org/10.3390/min9090556