# Application of Logistic Regression and Weights of Evidence Methods for Mapping Volcanic-Type Uranium Prospectivity

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Geology Setting and Uranium Mineralization

_{2}

^{2+}) can form fluoride, carbonate, hydroxyl, sulfate, chloride, silicate and other complexes. The NE- and NW-striking faults have caused a zone of weakness to control the transportation of uranium [22].

_{2}

^{2+}was mainly reduced into UO

_{2}so as to precipitate. Brittle structures developed in an extensional tectonic setting which provided pathways for fluid flow and spaces for uranium precipitation, commonly in linear fault zones, breccia pipes, fracture zones and fault intersections. At the deposit scale, the local secondary faults actually control the precipitation of individual ore zones. For example, the Maoyangtou deposit is jointly controlled by secondary NW- and NNW-striking fault zones adjacent to the south of the volcanic conduit. In addition, geologic contact surfaces and volcanic structures are also believed to be favorable structures controlling the precipitation of uranium mineralization [21,22,23,24].

## 3. Mineral Prospectivity Mapping Methods

#### 3.1. Weights of Evidence (WofE)

_{prior}): let an area be divided into a number of N(T) cells, of which there are N(D) pixels containing prospect D. The P

_{prior}that a cell selected randomly contains a prospect can be estimated as P

_{prior}defined by N(D)/N(T).

^{+}& W

^{−}): Suppose that in the area, there are N(B) and N($\overline{B}$) cells where spatial evidence B is present and absent, respectively. The weighting coefficients W

^{+}and W

^{−}spatial association of the predictor pattern B with a target mineral deposit D. W

^{+}and W

^{−}can be expressed as:

^{+}reflects that more training points occur, and a positive W

^{−}reflects that fewer training points occur. A weight of zero for either the W

^{+}or W

^{−}coefficient indicates spatially uncorrelated training points. The contrast, C = W

^{+}− W

^{−}represents a measure of spatial association between a set of spatial evidence and a set of prospects. If the spatial association is positive, C > 0, if the spatial association is negative, C < 0, and if the spatial association is lacking, C = 0.

_{post}): weights of evidence in predictor maps are combined with loge prior odds O(D) defined by P(D)/P($\overline{D}$), which are related to the prior probability. The posterior probability is then found by combining weighting coefficients using the odds formulation of Bayes’ rule. For Kth (k = 1, 2, ……, n) layers, estimates of posterior odds are converted to posterior probabilities reflecting degrees of mineral potential, which can be expressed as:

#### 3.2. Logistic Regression (LR)

_{0}+ b

_{1}x

_{1}+ b

_{2}x

_{2}+ b

_{3}x

_{3}+ … + b

_{n}x

_{n}

_{0}is the intercept of the model, b

_{1}~b

_{n}are the partial regression coefficients, and x

_{1}~x

_{n}are the independent variables. Logistic regression makes no assumption about the probability distribution of the independent predictor variables and, being a nonlinear model does not require conditional independence of input predictor maps [26]. The possibility can be calculated as an equation:

^{−Y})

## 4. Evidential Maps

#### 4.1. Geological Controls

#### 4.2. Hydrothermal Alteration

^{2+}and Fe

^{3+}-bearing minerals reflect more strongly and peak in bands 2 and 4. Therefore, it is believed that the selected band set of bands 1, 3, 4 and 6 can extract most hydroxyl-bearing mineral information, while the band set of bands 1, 2, 3 and 4 can extract most iron-oxide-bearing mineral information. Principal component analysis (PCA) is used for mapping of alteration. Table 2 shows the results of PCA for recording iron-oxide-bearing minerals with the mentioned bands. According to the results, PC2′s image shows the presence of iron-oxide-bearing minerals in the area (Figure 6a). In addition, for recording hydroxyl-bearing minerals, PCA comprising bands 1, 3, 4 and 6 have been used. Table 3 shows the results of recording hydroxyl-bearing minerals. According to the results, an image related to PC4 shows the presence of hydroxyl-bearing minerals in the study area (Figure 6b). The results show that the spatial distribution of the altered area is consistent with that of the volcanic rocks and known uranium deposits.

#### 4.3. Airborne Radioactive Anomaly

## 5. GIS-Based Prospectivity Modeling

^{2}test and the “omnibus” test have been suggested [32], it is unrealistic to assume independence of evidence layers because of the internal spatial and genetic relationships among different geological features. The posterior probabilities can be interpreted as relative estimations for mineralization [25,33]. Table 4 shows the weighting coefficients and contrast of the WofE model, while Table 5 shows the regression coefficients and the significance level of the independent variables. The outputs of the WofE and LR models were mapped to generate continuous-scale prospectivity maps (Figure 8).

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Sectional view of the Maoyangtou deposit [20].

**Figure 6.**Alteration anomaly map of (

**a**) iron-oxide-bearing minerals and (

**b**) hydroxyl-bearing minerals.

Lithostratigraphic Unit (Code) | Lithological Description | Thickness (m) | |
---|---|---|---|

Quaternary (Q) | Eluvium, Deluvium, Alluvium. | 0~20 | |

Akaishi Group (K_{2}ch) | Gray-purple thick-layer conglomerate. | 313~2015 | |

Shaxian Formation (K_{2}s) | Purple-red thick-layer siltstone interbedded with tuffaceous sandstone. | 144~1160 | |

Shimaoshan Group (K_{1}sh) | The second member: tuff, tuffaceous sandstone interbedded with basalt. The first member: red thick-layer conglomerate. | 182~1265 | |

Bantou Formation (J_{3}b) | The second member: tuff, tuff lava, rhyolite interbedded with tuffaceous and siltstone; the first member: gray feldspar quartz sandstone, shale, conglomerate, tuffaceous sandstone. | 336~1774 | |

Nanyuan Formation (J_{3}n) | The third member: porphyroclastic lava, rhyolite; the second member: tuff, tuff lava, rhyolite interbedded with tuff and tuffaceous sandstone; The first member: siltstone, tuffaceous sandstone. | >5576 | |

Changlin Formation (J_{3}c) | Tuff and tuffaceous sandstone. | 644~1774 | |

Lishan Formation (J_{1}l) | Grey medium coarse grain siltstones, interbedded with sandstone. | 33~1524 | |

Jiaokeng Formation (T_{3}j) | Carbonaceous siltstone, coal seam; feldspar quartz sandstone. | 58~508 | |

Mamianshan Group | Longbeixi Formation (Pt_{2}l) | Marble, schist and granulite. | >2117 |

Dongyan Formation (Pt_{2}dn) | Green schist, plagioclasite amphibolite interbedded with marble lens. | >2760 | |

Mayuan Group | Nanshan Formation (Pt1n) | Granulite interbedded with schist, plagioclase amphibolite. | 1681~3498 |

Dajinshan Formation (Pt_{1}d) | Crystalline graphite-bearing granulite and schist interbedded with amphibolite, occasionally marble lens. | >3300 | |

Tianjingping Formation (Ar_{2}t) | Biotite plagioclase granulite interbedded with amphibolite schist. | >732 |

Band 1 | Band 2 | Band 3 | Band 4 | |
---|---|---|---|---|

PC1 | 0.34 | 0.38 | 0.68 | 0.52 |

PC2 | 0.41 | 0.62 | −0.65 | 0.14 |

PC3 | −0.33 | −0.30 | −0.31 | 0.84 |

PC4 | 0.78 | −0.62 | −0.08 | 0.06 |

Band 1 | Band 3 | Band 4 | Band 6 | |
---|---|---|---|---|

PC1 | −0.32 | −0.71 | −0.53 | −0.34 |

PC2 | −0.46 | 0.68 | −0.34 | −0.46 |

PC3 | 0.81 | 0.13 | −0.51 | −0.24 |

PC4 | 0.16 | 0.13 | 0.58 | −0.79 |

Targeting Criteria | Evidence Layer | W^{+} | W^{−} | C |
---|---|---|---|---|

Sources | F1: uranium-rich Nanyuan Formation | 1.24 | −1.92 | 3.16 |

F2: uranium-rich granite | 0.11 | −0.13 | 0.24 | |

Pathways | F3: NE-striking faults | 0.42 | −1.53 | 1.95 |

F4: NW-striking faults | 0.72 | −0.91 | 1.63 | |

Traps | F5: Linear structures intersection | 2.13 | −0.08 | 2.23 |

F6: Linear structures density | 0.66 | −0.56 | 1.22 | |

Deposition and preservation | F7: Airborne radioactive gamma | 0.92 | −0.66 | 1.58 |

F8: Airborne radioactive U | 0.62 | −0.22 | 0.84 | |

F9: Iron-stained alteration | 1.35 | −0.21 | 1.56 | |

F10: Hydroxyl alteration | 0.93 | −0.12 | 1.05 |

Variable | b | Standard Deviation | Wald’s Statistics | Significance Level |
---|---|---|---|---|

Nanyuan Formation | 2.401 | 0.428 | 31.414 | 0.000 |

Granite | 0.502 | 0.734 | 0.467 | 0.495 |

Radioactive U | 1.287 | 0.666 | 3.731 | 0.053 |

Radioactive gamma | 1.914 | 0.552 | 12.049 | 0.001 |

Iron alteration | 0.861 | 0.59 | 2.131 | 0.144 |

Hydroxyl alteration | −1.251 | 0.671 | 3.477 | 0.062 |

Structures density | 0.865 | 0.332 | 6.807 | 0.009 |

Structures intersection | 0.564 | 0.377 | 2.238 | 0.135 |

NE-striking fault | 2.004 | 0.45 | 19.795 | 0.002 |

NW-striking fault | 1.746 | 0.363 | 23.169 | 0.010 |

Constant | −8.49 | 0.548 | 239.803 | 0.350 |

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**MDPI and ACS Style**

Zhao, J.; Sui, Y.; Zhang, Z.; Zhou, M.
Application of Logistic Regression and Weights of Evidence Methods for Mapping Volcanic-Type Uranium Prospectivity. *Minerals* **2023**, *13*, 608.
https://doi.org/10.3390/min13050608

**AMA Style**

Zhao J, Sui Y, Zhang Z, Zhou M.
Application of Logistic Regression and Weights of Evidence Methods for Mapping Volcanic-Type Uranium Prospectivity. *Minerals*. 2023; 13(5):608.
https://doi.org/10.3390/min13050608

**Chicago/Turabian Style**

Zhao, Jiangnan, Yu Sui, Zongyao Zhang, and Mi Zhou.
2023. "Application of Logistic Regression and Weights of Evidence Methods for Mapping Volcanic-Type Uranium Prospectivity" *Minerals* 13, no. 5: 608.
https://doi.org/10.3390/min13050608