**1. Introduction**

A huge prospecting potential is in concealed and deep mines, especially in the socalled "Second depth space" (500 m–2000 m); there are very likely to be abundant mineral resources there [1,2]. At present, some domestic and foreign examples of deep mineral exploration have proved the views of experts and scholars [3,4]. Although a series of deep mine exploration results show the prospecting potential of concealed and deep mines, there are also many problems, such as difficulty in exploration and imperfect exploration methods [5–7]. Therefore, more reasonable and effective technology is needed at this stage to adapt to the prospecting work in the large-scale Quaternary strata coverage area and the lower-cost method to find hidden and deep mines.

In recent years, with the development of computer technology and the support of geophysical methods, 3D modeling technology can fully integrate multivariate and multidimensional data to accurately depict deep geological structures [8–11]. At present, the wide application of artificial intelligence, especially machine learning technology, can provide a new way to process massive geological big data. Compared with traditional

**Citation:** Meng, F.; Li, X.; Chen, Y.; Ye, R.; Yuan, F. Three-Dimensional Mineral Prospectivity Modeling for Delineation of Deep-Seated Skarn-Type Mineralization in Xuancheng–Magushan Area, China. *Minerals* **2022**, *12*, 1174. https:// doi.org/10.3390/min12091174

Academic Editor: Behnam Sadeghi

Received: 31 July 2022 Accepted: 11 September 2022 Published: 18 September 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

methods, machine learning often has higher prediction accuracy, especially for geological data with massive and high-dimensional characteristics, which can effectively explore the complex nonlinear relationship between ore-control characteristics and ore-forming mechanisms. At present, machine learning methods include the probabilistic neural network, the support vector machine, the random forest, adaptive learning, the restricted Boltzmann machine, etc.; most of them have been applied and developed in the field of 2DMPM. Oh et al. [12] analyzed the potential of hydrothermal gold–silver mineral deposits in the Taebaeksan mineralized district, Korea, and the Artificial neural network (ANN) method and selected factors related to the occurrence of gold and silver minerals as ore-control factors, including magnetic anomaly geophysical data, geological and fault structure geological data, geochemical data, etc. Good results have been achieved [12]. Xiong et al. [13] identified multiple geochemical anomalies related to Fe polymetallic mineralization in the southwestern Fujian district (China) by using the limited Boltzmann machine. The research shows that most of the known skarn-type iron deposits are located in geochemical anomaly areas, which can provide reference for further exploration [13]. In order to effectively delineate favorable exploration targets for Cu-Au mineralization in the Moalleman District, NE Iran, Ghezelbash et al. [14] integrated several effective evidence layers such as geochemistry, geology, structure, and hydrothermal alteration in the study area; used SVM with radial basis function kernel to predict mineralization; and delineated the metallogenic prospect area [14]. However, the above methods are only based on twodimensional geological data for prediction, which cannot fully characterize the multiple geological characteristics and may be difficult to make fine prediction of deep mines and hidden mines. The combination of 3D technology and artificial intelligence is beneficial to more fully excavate and integrate 3D prediction information and achieve more accurate positioning and quantitative predictions of deeply hidden ore bodies [15–18].

Compared with other mineralized areas in the Middle-Lower Yangtze River Metallogenic Belt, the Quaternary strata in the Xuancheng–Magushan area within the Middle-Lower Yangtze River Metallogenic Belt have a large coverage area and shallow geological exploration. The deep geological structure is not yet clear. It is difficult to describe the deep geological structure in this area in detail, which seriously affects the research of deep ore prospecting and prediction there [19]. Aiming at the Xuancheng–Magushan area, this paper firstly builds a 3D geological model that can accurately describe the deep geological structure with the support of geophysical methods and geological data. Based on this, two machine learning methods, the logistic regression model and the random forest model, were used to predict skarn deposits in the study area in three dimensions. Then, we divide the training set and the test set according to the data, the former trains the model, and the latter evaluates the performance of the model. The optimal results were selected to delineate the prospecting. Finally, the target area is expected to provide a new prospecting direction for further deep prospecting and exploration work in this area.

#### **2. Methods**

#### *2.1. 3D Mineral Prospectivity Modeling*

In recent years, the MPM has become an important means of prospecting and exploration. It can guide on-site prospecting work, thereby reducing the risk of prospecting. With the development of computer technology, a quantitative-based MPM method system has been put forward at home and abroad, which promotes the development of MPMfrom qualitative to quantitative and can more accurately delineate the metallogenic target area [20–24]. However, the above-mentioned quantitative MPM methods are mainly oriented towards the traditional two-dimensional prediction, which mostly uses two-dimensional geological data. However, the deep metal mineral resources have experienced multiple periods of geological evolution, resulting in weak surface indication information and complex geological structures. It is difficult to indicate prospecting work with traditional prediction methods based on two-dimensional geological data [25]. As deep ores and hidden ores have become

the focus of prospecting in recent years, the research on the quantitative prediction of mineralization has moved from "two-dimensional" to "three-dimensional" [26]. den ores have become the focus of prospecting in recent years, the research on the quantitative prediction of mineralization has moved from "two-dimensional" to "three-dimen-

complex geological structures. It is difficult to indicate prospecting work with traditional prediction methods based on two-dimensional geological data [25]. As deep ores and hid-

*Minerals* **2022**, *12*, 1174 3 of 14

The rise of artificial intelligence also provides a new way to process and mine massive geological data contained in 3D models [27]. Machine learning simulates human learning behavior through computers. It utilizes its nonlinear learning ability to characterize potential complex geological features by continuously training models and fitting parameters. In recent years, many scholars have begun to try to carry out 3DMPM research, including using the evidence weight model, the logistic regression model, the random forest model, and the artificial neural network model [28–31]. The above methods have shown good research potential in the field of 3DMPM. They can effectively process massive multi-dimensional geological data and have become an important development trend in this field. sional" [26]. The rise of artificial intelligence also provides a new way to process and mine massive geological data contained in 3D models [27]. Machine learning simulates human learning behavior through computers. It utilizes its nonlinear learning ability to characterize potential complex geological features by continuously training models and fitting parameters. In recent years, many scholars have begun to try to carry out 3DMPM research, including using the evidence weight model, the logistic regression model, the random forest model, and the artificial neural network model [28–31]. The above methods have shown good research potential in the field of 3DMPM. They can effectively process massive multi-dimensional geological data and have become an important development

In this paper, 3D geological modeling, 3D spatial analysis and 3DMPM based on machine learning are integrated. First, a 3D geological model is established based on geological data, and then a variety of 3D spatial analysis methods are used to analyze the 3D geological model and relevant metallogenic indicative characteristics, so as to obtain quantitative ore control and indicative characteristic information. Then, the prediction method based on machine learning is used to predict the mineralization of the deep edge of the mining area, and its effect is evaluated. Finally, the prediction results are used to divide the metallogenic prospective area, to realize the positioning and quantitative prediction of the hidden ore bodies at the deep edge of the known deposits. The forecast flow chart is shown in Figure 1. trend in this field. In this paper, 3D geological modeling, 3D spatial analysis and 3DMPM based on machine learning are integrated. First, a 3D geological model is established based on geological data, and then a variety of 3D spatial analysis methods are used to analyze the 3D geological model and relevant metallogenic indicative characteristics, so as to obtain quantitative ore control and indicative characteristic information. Then, the prediction method based on machine learning is used to predict the mineralization of the deep edge of the mining area, and its effect is evaluated. Finally, the prediction results are used to divide the metallogenic prospective area, to realize the positioning and quantitative prediction of the hidden ore bodies at the deep edge of the known deposits. The forecast flow chart is shown in Figure 1.

**Figure 1.** Workflow of three-dimension prospectivity mapping. **Figure 1.** Workflow of three-dimension prospectivity mapping.

#### *2.2. Logistic Regression Algorithm 2.2. Logistic Regression Algorithm*

Logistic regression is a representative algorithm in machine learning. This algorithm has been applied in many fields such as medicine, biology, and geology [32–34]. It can calculate the correlation between the independent input variable and the dependent variable through the regression principle and calculate the specific probability value of the dependent variable belonging to a certain category according to the existing state of the independent variable. As a multivariate nonlinear regression model, it can better fit the nonlinear relationship between various ore-controlling characteristics and metallogenic facts [35,36]. In this paper, metallogenic facts are used as the dependent variable, and various ore -controlling factors related to the metallogenic mechanism are used as the independent variables. The logistic regression method calculates the probability of ore bodies' existence in the corresponding blocks. Logistic regression is a representative algorithm in machine learning. This algorithm has been applied in many fields such as medicine, biology, and geology [32–34]. It can calculate the correlation between the independent input variable and the dependent variable through the regression principle and calculate the specific probability value of the dependent variable belonging to a certain category according to the existing state of the independent variable. As a multivariate nonlinear regression model, it can better fit the nonlinear relationship between various ore-controlling characteristics and metallogenic facts [35,36]. In this paper, metallogenic facts are used as the dependent variable, and various ore -controlling factors related to the metallogenic mechanism are used as the independent variables. The logistic regression method calculates the probability of ore bodies' existence in the corresponding blocks.

$$P(Z) = \frac{1}{(1 + e^{-Z})} \tag{1}$$

$$Z = \mathfrak{a} + \mathfrak{z}\_i \mathfrak{x}\_j \tag{2}$$

In the above formulas: *P*(*Z*) is the favorable degree of mineralization, *x<sup>i</sup>* is the *i*-th ore control or indicator element, (*i* = 1, 2, . . . , *n*), *α* is a constant, *β<sup>i</sup>* is a regression factor, that is, each control contribution of ore elements to the existence of ore bodies. It can be

determined by fitting with the maximum likelihood estimation method. Each parameter is optimally solved using the gradient descent method.

#### *2.3. Random Forest Algorithm*

In the ensemble learning model [37,38], first proposed by Leo Breiman, the essence of the random forest is a classifier or regression model composed of multiple unrelated decision trees: i.e., determine the category and, if it is a regression scenario, take the average of the solution parameters as the final result. The algorithm has two important randomness characteristics. The first point is to randomize the samples. By performing multiple random extractions with replacements from the total data set, multiple subsets of the same number of data samples are obtained as training sets to reduce the phenomenon of overfitting. The second point is to randomize the features. For each decision tree, a different subset of features is extracted from the feature set for learning. In this way, the robustness of the feature selection can be enhanced, so that the user does not need to deliberately filter the features. At the same time, the important indicators of all of the features of the model's results can be obtained.

Each decision tree in the random forest selects the feature that can maximize the information gained in the feature subset as the current split node. Multiple regression decision trees constitute the random forest regression algorithm. Based on the idea of ensemble learning, the mean value of the decision tree is taken as the prediction result, namely

$$\bar{h}(\mathbf{x}) = \frac{1}{T} \sum\_{t=1}^{T} h(\mathbf{x}, \theta\_t), \tag{3}$$

where − *h*(*x*) is the model prediction result; is *h*(*x*, *θt*) the output *x* based on *x* sum, is the independent *θ<sup>t</sup>* variable, *θ<sup>t</sup>* is the independent and identically distributed random vector, and *T* is the number of regression decision trees.

#### **3. Case Study Area and Data**

#### *3.1. Geological Background*

in the late Yanshan period.

and a relatively high degree of research [44].

The stratigraphic area of the study area belongs to the Changzhou–Xuancheng stratigraphic community in the Jiangnan stratigraphic subdivision of the Yangtze stratigraphic area (Figure 2). Neritic and littoral clastic rocks dominate the Silurian and Devonian strata, the Permian early and middle Triassic strata are dominated by carbonate rocks, and subsequent continental by clastic rock and pyroclastic rock series. The accumulated total thickness reaches more than 3000 m [39,40]. *Minerals* **2022**, *12*, 1174 5 of 14

**Figure 2.** The location of Xuancheng–Magushan Area, volcanic basins, and ore concentration areas (OCAs) within the middle and lower Yangtze River Metallogenic Belt as well as the location of major settlements, faults, and major tectonic features. (Modified from Chang et al. [41], Mao et al. [42], and Ye. [43]). The structure of the study area is complex, and numerous faults have developed. The **Figure 2.** The location of Xuancheng–Magushan Area, volcanic basins, and ore concentration areas (OCAs) within the middle and lower Yangtze River Metallogenic Belt as well as the location of major settlements, faults, and major tectonic features. (Modified from Chang et al. [41], Mao et al. [42], and Ye. [43]).

faults are mainly concentrated in the vicinity of Magushan and the southeastern part of the area. The magmatic rock activity in the area is strong, consisting of mid-acid intrusions

Fenghuangshan Cu-Mo have been discovered in the study area. Among them, the Magushan Cu-Mo deposit (Figure 3) is a typical skarn deposit in the area, with a large scale

The structure of the study area is complex, and numerous faults have developed. The faults are mainly concentrated in the vicinity of Magushan and the southeastern part of the area. The magmatic rock activity in the area is strong, consisting of mid-acid intrusions in the late Yanshan period. The structure of the study area is complex, and numerous faults have developed. The faults are mainly concentrated in the vicinity of Magushan and the southeastern part of the area. The magmatic rock activity in the area is strong, consisting of mid-acid intrusions in the late Yanshan period.

**Figure 2.** The location of Xuancheng–Magushan Area, volcanic basins, and ore concentration areas (OCAs) within the middle and lower Yangtze River Metallogenic Belt as well as the location of major settlements, faults, and major tectonic features. (Modified from Chang et al. [41], Mao et al. [42], and

The deposits of Magushan Cu-Mo, Xishishan Au-Pb, Beishan Cu-Mo and Fenghuangshan Cu-Mo have been discovered in the study area. Among them, the Magushan Cu-Mo deposit (Figure 3) is a typical skarn deposit in the area, with a large scale and a relatively high degree of research [44]. The deposits of Magushan Cu-Mo, Xishishan Au-Pb, Beishan Cu-Mo and Fenghuangshan Cu-Mo have been discovered in the study area. Among them, the Magushan Cu-Mo deposit (Figure 3) is a typical skarn deposit in the area, with a large scale and a relatively high degree of research [44].

*Minerals* **2022**, *12*, 1174 5 of 14

**Figure 3.** Geological map of Magushan Cu-Mo deposit. (Modified from Bian. [19], Ye. [43], and Hong et al. [44]).

#### *3.2. Database*

Ye. [43]).

In previous studies [43], 2D geological profiles covering the whole area were first established in the Magushan ore field, and these geological profiles were interpreted using the gravity and magnetic joint inversion method. Combined with prior geological constraints and based on the collected regional physical property data, the joint inversion of gravity and magnetic fields finally obtains a 2D profile that can show the thickness, depth, extension direction, hidden rock mass shape, and geological structure of each layer in the region. After the gravity and magnetic joint inversion, a set of verification methods based on the 3D visualization function of the profile is used to verify the rationality of the interpreted profile, and the unreasonable parts in the profile are modified. The whole process of gravity and magnetic inversion interpretation and profile verification and modification is shown in Figure 4. Then, based on the two-dimensional geological profile, geological map, borehole, and other geological information interpreted by gravity and magnetic joint inversion, a 3D geological model of the Magushan ore field with a depth of 3km is established. The 3D geological model can realize the 3D visualization of each geological body in the region and can better display the geological information of the study area, such as the thickness and depth of the strata, the shape of the hidden rock mass, and the geological structure in the region. After completing the 3D geological model, the study further uses the geophysical

forward modeling method to verify the rationality of the 3D geological model and modify and improve the 3D geological model. The modeling results are shown in Figure 5. The relevant modeling results will provide an important data basis for 3DMPM research. model and modify and improve the 3D geological model. The modeling results are shown in Figure 5. The relevant modeling results will provide an important data basis for 3DMPM research. model and modify and improve the 3D geological model. The modeling results are shown in Figure 5. The relevant modeling results will provide an important data basis for 3DMPM research.

**Figure 3.** Geological map of Magushan Cu-Mo deposit. (Modified from Bian. [19], Ye. [43], and

**Figure 3.** Geological map of Magushan Cu-Mo deposit. (Modified from Bian. [19], Ye. [43], and

In previous studies [43], 2D geological profiles covering the whole area were first established in the Magushan ore field, and these geological profiles were interpreted using the gravity and magnetic joint inversion method. Combined with prior geological constraints and based on the collected regional physical property data, the joint inversion of gravity and magnetic fields finally obtains a 2D profile that can show the thickness, depth, extension direction, hidden rock mass shape, and geological structure of each layer in the region. After the gravity and magnetic joint inversion, a set of verification methods based on the 3D visualization function of the profile is used to verify the rationality of the interpreted profile, and the unreasonable parts in the profile are modified. The whole process of gravity and magnetic inversion interpretation and profile verification and modification is shown in Figure 4. Then, based on the two-dimensional geological profile, geological map, borehole, and other geological information interpreted by gravity and magnetic joint inversion, a 3D geological model of the Magushan ore field with a depth of 3km is established. The 3D geological model can realize the 3D visualization of each geological body in the region and can better display the geological information of the study area, such as the thickness and depth of the strata, the shape of the hidden rock mass, and the geological structure in the region. After completing the 3D geological model, the study further uses the geophysical forward modeling method to verify the rationality of the 3D geological

In previous studies [43], 2D geological profiles covering the whole area were first established in the Magushan ore field, and these geological profiles were interpreted using the gravity and magnetic joint inversion method. Combined with prior geological constraints and based on the collected regional physical property data, the joint inversion of gravity and magnetic fields finally obtains a 2D profile that can show the thickness, depth, extension direction, hidden rock mass shape, and geological structure of each layer in the region. After the gravity and magnetic joint inversion, a set of verification methods based on the 3D visualization function of the profile is used to verify the rationality of the interpreted profile, and the unreasonable parts in the profile are modified. The whole process of gravity and magnetic inversion interpretation and profile verification and modification is shown in Figure 4. Then, based on the two-dimensional geological profile, geological map, borehole, and other geological information interpreted by gravity and magnetic joint inversion, a 3D geological model of the Magushan ore field with a depth of 3km is established. The 3D geological model can realize the 3D visualization of each geological body in the region and can better display the geological information of the study area, such as the thickness and depth of the strata, the shape of the hidden rock mass, and the geological structure in the region. After completing the 3D geological model, the study further uses the geophysical forward modeling method to verify the rationality of the 3D geological

*Minerals* **2022**, *12*, 1174 6 of 14

*Minerals* **2022**, *12*, 1174 6 of 14

Hong et al. [44]).

Hong et al. [44]).

*3.2. Database*

*3.2. Database*

**Figure 4. Figure 4.** Gr Gravity and magnetic inversion interpretation and profile-verification flow chart. avity and magnetic inversion interpretation and profile-verification flow chart. **Figure 4.** Gravity and magnetic inversion interpretation and profile-verification flow chart.

**Figure 5.** 3D model of the Xuancheng–Magushan Area. (Modified from Ye. [43] and Hu et al. [45]).
