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Volume 32 Issue 2
Apr.  2021
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Shi Li, Jianping Chen, Chang Liu, Yang Wang. Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data. Journal of Earth Science, 2021, 32(2): 327-347. doi: 10.1007/s12583-020-1365-z
Citation: Shi Li, Jianping Chen, Chang Liu, Yang Wang. Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data. Journal of Earth Science, 2021, 32(2): 327-347. doi: 10.1007/s12583-020-1365-z

Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data

doi: 10.1007/s12583-020-1365-z
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  • Today's era of big data is witnessing a gradual increase in the amount of data, more correlations between data, as well as growth in their spatial dimension. Conventional linear statistical models applied to mineral prospectivity mapping (MPM) perform poorly because of the random and nonlinear nature of metallogenic processes. To overcome this performance degradation, deep learning models have been introduced in 3D MPM. In this study, taking the Huayuan sedimentary Mn deposit in Hunan Province as an example, we construct a 3D digital model of this deposit based on the prospectivity model of the study area. In this approach, 3D predictor layers are converted from the conceptual model and employed in a 3D convolutional neural network (3D CNN). The characteristics of the spatial distribution are extracted by the 3D CNN. Subsequently, we divide the 22 extracted ore-controlling variables into six groups for contrast experiments based on various combinations and further apply the 3D CNN model and weight of evidence (WofE) method on each group. The predictive model is trained on the basis of the coupling correlation between the spatial distributions of the variables and the underground occurrence space of the Mn orebodies, and the correlation between different ore-controlling factors. The analysis of 12 factors indicates that the 3D CNN model performs well in the 3D MPM, achieving a promising accuracy of up to 100% and a loss value below 0.001. A comparison shows that the 3D CNN model outperforms the WofE model in terms of predictive evaluation indexes, namely the success rate and ore-controlling rate. In particular, the 1-12 ore-controlling factors selected in experiment 5 provide a significantly better prediction effect than the other factors. Consequently, we conclude that the Mn deposit in the study area is not only related to the stratum and interlaminar anomalous bodies but also to the spatial distribution of the faults. The experimental results confirm that the proposed 3D CNN is promising for 3D MPM as it eliminates the interference factors.
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Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data

doi: 10.1007/s12583-020-1365-z

Abstract: Today's era of big data is witnessing a gradual increase in the amount of data, more correlations between data, as well as growth in their spatial dimension. Conventional linear statistical models applied to mineral prospectivity mapping (MPM) perform poorly because of the random and nonlinear nature of metallogenic processes. To overcome this performance degradation, deep learning models have been introduced in 3D MPM. In this study, taking the Huayuan sedimentary Mn deposit in Hunan Province as an example, we construct a 3D digital model of this deposit based on the prospectivity model of the study area. In this approach, 3D predictor layers are converted from the conceptual model and employed in a 3D convolutional neural network (3D CNN). The characteristics of the spatial distribution are extracted by the 3D CNN. Subsequently, we divide the 22 extracted ore-controlling variables into six groups for contrast experiments based on various combinations and further apply the 3D CNN model and weight of evidence (WofE) method on each group. The predictive model is trained on the basis of the coupling correlation between the spatial distributions of the variables and the underground occurrence space of the Mn orebodies, and the correlation between different ore-controlling factors. The analysis of 12 factors indicates that the 3D CNN model performs well in the 3D MPM, achieving a promising accuracy of up to 100% and a loss value below 0.001. A comparison shows that the 3D CNN model outperforms the WofE model in terms of predictive evaluation indexes, namely the success rate and ore-controlling rate. In particular, the 1-12 ore-controlling factors selected in experiment 5 provide a significantly better prediction effect than the other factors. Consequently, we conclude that the Mn deposit in the study area is not only related to the stratum and interlaminar anomalous bodies but also to the spatial distribution of the faults. The experimental results confirm that the proposed 3D CNN is promising for 3D MPM as it eliminates the interference factors.

Shi Li, Jianping Chen, Chang Liu, Yang Wang. Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data. Journal of Earth Science, 2021, 32(2): 327-347. doi: 10.1007/s12583-020-1365-z
Citation: Shi Li, Jianping Chen, Chang Liu, Yang Wang. Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data. Journal of Earth Science, 2021, 32(2): 327-347. doi: 10.1007/s12583-020-1365-z
  • With global informatization entering an advanced stage, we are gradually entering the era of big data (Zhao, 2015; Lohr, 2012). Among the various types of data, geological data are consistent with big data in terms of their characteristics. The future development of mineral prospectivity mapping (MPM) relies strongly on the complete integration of geological data, realization of an intelligent prediction and evaluation system for mineral resources by adopting deep mining and knowledge discovery method based on big data, and improvement in the effectiveness of MPM (Bristol et al., 2012). Importance must also be given to the combined application of new theories and new methods (Xiao et al., 2015; Yu et al., 2015; Zhao et al., 2003).

    Mineral resource prediction based on geological big data in a 3D space is not only associated with high data dimensions, but also more correlations between the data volume and the data. In recent years, with the improvements made to the metallogenic theory, big data processing technologies and various machine learning methods have been successfully used in geological information processing, metallogenic anomaly extraction, and comprehensive MPM (Chen et al., 2012c; Chen et al., 2008). As an important branch of artificial intelligence, machine learning not only provides an effective tool for processing a large number of evidence feature layers related to MPM, big data analysis, pattern recognition, and prediction, but also provides a technical support for constructing big data-based intelligent MPM. Moreover, it can describe nonlinear relationships between known deposits and evidence layers, and its advantage lies in its high predictive capability. Although the complexity of metallogenic geological conditions makes geological data nonlinear, machine learning algorithms can better characterize the complex nonlinear relationships between mineralized spots and evidence factors (Brown et al., 2000) than conventional methods in terms of adaptability (Abedi et al., 2012). Currently, the machine learning algorithms applied to mineral resource evaluation mainly include artificial neural networks (Leite and de Souza Filho, 2009), support vector machine (Li, 2014; Abedi et al., 2012; Zuo and Carranza, 2011; Chang et al., 2010), random forest (Hariharan, 2017; Rodrigue et al., 2015, 2014; Phillips and Dudík, 2008), Boltzmann machine (Chen, 2012), extreme learning (Chen and Wu, 2017), and maximum entropy model (Liu, 2018, 2017). In 2017, using a machine learning analysis method, Zuo and Xiong (2018) successfully identified and extracted the multielement geochemical anomalies of Fe polymetallic deposits in southwestern Fujian of China based on geological big data. Other scholars have successfully applied big data-based machine learning to anomalous information extraction for a quantitative prediction of mineral resources (Nie et al., 2018; Kirkwood et al., 2016; Xiong and Zuo, 2016; Zhao et al., 2016; Gonbadi et al., 2015; O'Brien et al., 2015; Chen et al., 2014; Twarakavi et al., 2006).

    Given the multi-source and multi-mode characteristics of metallogenic information, the data pattern tends to be complicated, bringing greater challenges for the classification and prediction and making it difficult for conventional machine learning algorithms to perform well (Lin, 2015; Yan et al., 2015). Therefore, introducing deep learning in the field of 3D MPM is particularly suitable and significant; as it represents a meaningful exploration of intelligent algorithms applied to big data in geological studies (Zhou et al., 2018, 2017; Zhang and Zhou, 2017). As a special machine learning method, deep learning also aims to build networks that simulate the human brain for analytical learning. However, it is characterized by multiple levels of abstracting for learning hierarchical representations of input data, including the convolutional neural network (CNN) (Sun and He, 2017; Simonyan and Zisserman, 2015; Lécun et al., 1998; Lawrence et al., 1997), recurrent neural network (RNN) (Martens and Sutskever, 2011), stacked automatic coding (Sainath et al., 2012; Bengio et al., 2007) (including stacked de-noising automatic coding and stacked sparse autocoder), deep belief network (DBN) (Hinton, 2011), multi-layer feedback recurrent neural network (RNN), and full convolutional neural network (FCN) (Ciresan et al., 2012). These methods help interpret data by imitating the human brain's mechanisms. Deep learning has made breakthroughs in logging lithology identification, seismic fault identification (Holtzman et al., 2018), seismic time prediction (Rouet-Leduc et al., 2017), and other aspects, which have had a profound influence on the geosciences. As spatial information with various forms acquired from the same ground object aggregation through different measuring approaches, the geological, geophysical, and geochemical information includes the underground mineral, mineralization, and geological evolution information. Therefore, the application of deep learning to the spatial information mining in the field of geosciences is significant for the prediction and evaluation of mineral resources. In addition, the combination of metallogenic theory and deep learning method is key to solving the problems of MPM (Zhou et al., 2018). So far, the method has been applied to the extraction of metallogenic geochemical anomalies (Zuo, 2019a, b; Xiong et al., 2018; Zuo and Xiong, 2018; Yang, 2016), extraction of metallogenic gravity and magnetic anomalies (Li et al., 2015; Liu et al., 2010; Bilgili et al., 2002; Albora et al., 2001), and comprehensive MPM (Zuo, 2020; Cai et al., 2019; Li et al., 2019). The problems of lack of training samples and the model construction of the deep learning network have been resolved, providing a reasonable basis for the MPM (Li T et al., 2021; Zuo et al., 2021; Zuo and Wang, 2020). Research on the quantitative delineation of a metallogenic system based on deep learning is conducive for a thorough understanding of the mineralization at different scales. With the assistance of novel techniques to delineate metallogenic prospects, we can achieve comprehensive information utilization, effective information mining, and quantitative description of the prospects. Moreover, the application of deep learning methods, particularly the CNN, to MPM is an inevitable trend in the quantitative research and development in geosciences.

    The conventional quantitative prediction of mineral resources is based on 2D layers. With the development of computer graphics technology and 3D spatial data processing technology, 3D modeling and visualization technologies are becoming increasingly popular (Thorleifson et al., 2010; Houlding and Renholme, 1998), and a 3D quantitative prediction of mineral resources is gradually being pursued (Xiang et al., 2016a, b; Rong et al., 2012; Chen et al., 2012a, b, 2009, 2008, 2007; Xiao et al., 2012; Yan et al., 2012; Mao et al., 2010, 2009; Wu et al., 2001; Zhao, 1992; Zhang et al., 1999; Li, 1991). Chen proposed a type of 3D modeling-based "cube prediction model" prospectivity method to synthesize multivariate prospecting information and realize the "localization", "quantitation", and "probability" prediction and evaluation of deep concealed orebodies (Chen et al., 2007). The commonly used prediction method is the 3D weight of evidence (WofE) method. The MPM is associated with the following problems: (1) It only focuses on the quantitative extraction of the anomalies, but neglects the importance of the spatial distribution characteristics as well as the correlation between different predictor layers while adopting the WofE method. (2) Previously, the utilization of positive boreholes has been extremely high, whereas that of negative boreholes has been relatively low. This brings up the following question: How can we realize the transformation of "trash" into "treasure"? (3) Previously, when using machine learning algorithms, we utilized the important ore-controlling factors, while neglecting the others. This approach is not rigorous, as the potential factors having a "butterfly effect" are likely to be ignored. Thus, a set of quantitative prediction methods is required to realize a synergy between the geological background and big data.

    Deep learning, as an effective tool for geoscientific spatial pattern recognition and multi-source data fusion, can be applied to depict complicated nonlinear geoscientific spatial patterns. The application of CNNs to image classification and recognition can be effective. However, a CNN cannot recognize the association between several images in the time dimension, resulting in the loss of association information. Therefore, it cannot classify the behaviors of the images. In contrast, a 3D CNN can extract not only the relationship between the continuous positions in the images like the 2D CNN, but also the relevant information contained in the continuous images in the time dimension (Deng, 2019). The 3D CNN has been extensively applied to medical diagnosis (Oh et al., 2019; Sato and Ishida, 2019; Torng and Altman, 2019; Derevyanko et al., 2018; Karasawa et al., 2018; Torng, 2018), sign language motion recognition (Wang et al., 2019; Zhu et al., 2019; Ma, 2018; Jiang and Chen, 2017), theft behavior recognition (Li Y L et al., 2020), facial expression recognition (Wu, 2019b; Wu et al., 2019), brain signal recognition (Luo and Li, 2019), gait behavior recognition (Xing et al., 2018), speaker behavior recognition (Liao et al., 2018), visual classification (Qi et al., 2018; Wang et al., 2018), hyperspectral imaging classification (Wang et al., 2019; Zhao and Yang, 2019), and other fields (Brown et al., 2019; Dizaji and Harris, 2019; Wang et al., 2019; Xu et al., 2019). A 2D CNN algorithm can typically extract only planar features and not the 3D spatial features of geological bodies. However, the data pertaining to underground mineral, mineralization, and geological evolution are included in the geological, geophysical, geochemical, and other spatial information. A 3D geological model can directly describe the spatial distributions of the geological units and the evolution relationship between them. Through the study of geochemistry and chronology, the "skeleton" of the 3D geological model can be endowed with a "soul" for constructing a real 4D time-space geological model. How to integrate these multivariate, massive, and heterogeneous information, and extract effective information from them for analyzing metallogenic geological conditions? Moreover, how to extract the time sequence features and spatial relevance based on 3D geological models? To answer these challenging questions, we implemented our study in the Huayuan ore district of Hunan Province.

    This work can be mainly divided into three parts. First, a prospecting geological model was established. Second, 3D geological models were built using 3D geophysical modeling techniques, and then 3D predictor layers were extracted using different variables, which were used to quantitatively characterize the ore-controlling factors. Third, we tested the MPM capabilities of the 3D CNN in the study area and compared it with the WofE method. Overall, our research can serve as a guidance for further mineral exploration in this important mining district and can aid in the application of 3D CNN prediction models to 3D MPM.

  • Since the Neoproterozoic Jinning Period II (850–820 Ma), the Yangtze and Cathaysian Landmasses have converged into the ancient South China continental plate along the Jiangnan orogenic belt, forming a part of the Rodinia Supercontinent (Wang and Pan, 2009). Subsequently, with the disintegration of the Rodinia Supercontinent, an extensive extensional rift valley environment was formed in the Yangtze Landmass under the influence of global cracking, and multiple periods of episodic cracking activities occurred in the southeastern margin of the Yangtze Landmass (Du et al., 2015), successively forming the Wuling and Xuefeng secondary rift basins (Zhou et al., 2016). The adjacent areas of Hunan, Guizhou, and Chongqing, located in the southeastern margin of the Yangtze Landmass, have a well-developed Neoproterozoic sedimentary stratigraphic record. As one of the important metallogenic belts in China, the ore-concentrated area of northwestern Hunan contains many large and medium-sized ore deposits, such as the Minle Mn deposit. Since the breakthrough in Mn deposit prospecting, because of the similar metallogenic environment of sedimentary Mn deposits in the adjacent areas of Hunan, Guizhou, and Chongqing, research on the tectonic pattern and deep manganese-forming space in the adjacent areas of northwestern Hunan and southeastern Chongqing has emerged as a hotspot. The area is potentially important for further prospecting the "Datangpo-type" sedimentary Mn deposits of Nanhua Period in China (Du et al., 2015; Zhou et al., 2013). The study area covers two 1 : 50 000 geological maps (Malichang and Heku), mainly including the Qingbaikou System, Nanhua System, Sinian System, Cambrian System, Ordovician System, and Quaternary System. Moreover, there are no magmatic rocks and deep metamorphic rocks in the area, and the geological tectonics are dominated by faults, whereas the folds are generally simple (Fig. 1).

    Figure 1.  Geological outline of the study area.

    The strata in the study area are extensively distributed and belong to a set of sedimentary rocks dominated by clastic and carbonate rocks; furthermore, the strata related to mineralization in the area are mainly Nanhua Period strata, including the Fulu Formation, Datangpo Formation, and Nantuo Formation (Fig. 2a). In particular, the Datangpo Formation mainly occurred in the central and western parts of the mapping area, namely in Datu-Motianling-Tianjia area of Huayuan County and Jiulongpo-Silongshan-Buzhen area of Songtao County, Hunan Province. Moreover, it is characterized by a conformable contact relationship with the underlying Fulu Formation. Its thickness is 221.05 m and is divided into upper and lower members based on the lithological combination features, where the lower member is an important occurrence horizon of the Mn deposit in the area. The metallogenic period of Mn deposits in the study area is dominated by the Middle Nanhua Period, consequently, our research focus on the sequence strata of the Nanhua Period. The Nanhua System can be divided into five three-level sedimentary sequences mainly bounded by type-I interface (SB1) and type-II interface (SB2) (Fig. 2b). Based on the sequence strata analysis, the "Datangpo-type" Mn deposits mainly occurred in the third sequence of the three-level sequence in the sequence strata. The lithology below and above the interface is slate and carbonaceous shale, respectively, representing a continuous rise in the sea level. The sequence belongs to a sequence of "condensed section (CS)+highstand systems tract (HST), " comprising the lower part of the Datangpo Formation.

    Figure 2.  (a) 1 : 200 000 geological and mineral map of Songtao-Huayuan area; (b) sequence strata division map of Nanhua Period (1. conglomerate; 2. gravel-bearing feldspar quartz sandstone; 3. gravel-bearing quartz sandstone; 4. gravel-bearing siltstone; 5. argillaceous feldspar quartz sandstone; 6. quartz sandstone; 7. siltstone; 8. manganiferous limestone; 9. limestone; 10. gravel-bearing silty slate; 11. banded sandy slate; 12. silty slate; 13. clay-bearing silty slate; 14. slate; 15. banded sericite-bearing slate; 16. sericite slate; 17. banded slate; 18. clay-bearing slate; 19. calcareous slate; 20. siliceous slate; 21. carbonaceous slate; 22. carbonaceous shale; Fm. Formation).

  • The formation of Mn deposits in the adjacent areas of Hunan, Guizhou, and Chongqing is closely related to the lithofacies paleogeographic environment of the time (Yang et al., 2002; Xu et al., 1991). Bounded by the Malichang fault, the Datangpo Formation of the Middle Nanhua Period (Datangpo Period) that occurred in the two sedimentary areas in the east and west areas exhibits the following different sedimentary characteristics (Fig. 3): The average thickness of the Mn ore (mineralized) layers in the west area is 1.5 m. Especially in the Minle territory, there is a leading super large Mn deposit in the west area; the thickness of its Mn ore layers broadly ranges from 1 to 3 m, and the maximum and average thicknesses are 6.53 and 2.71 m, respectively. Moreover, secondary Mn sedimentary basins have developed in the area, and turbidity current channels in the occlusive "sedimentary trough" are densely distributed. Consequently, the metallogenic geological conditions for Mn deposits are superior. In the east area, two small Mn sedimentary basins have been discovered: one is the Yezhu-Dalong Mn sedimentary basin in Guzhang County and the other is the Duye-Tangtuo Mn sedimentary basin in Fenghuang County. The Mn deposits in the study area were mainly formed in the Datangpo Period of the Middle Nanhua Period, distributed in the Lower Member of the Datangpo Formation in the west area, and occurred in the Wuling secondary rift basin of the Nanhua Period Datangpo Formation.

    Figure 3.  Lithofacies paleogeographic map of the Middle Nanhua Period (Datangpo Formation) in Songtao-Huayuan area.

    There has been some controversy over the genetic type of the sedimentary Mn deposits in the Huayuan area, Hunan Province. Tang (1990) considered that the sulfur in the Minle Mn deposit is mainly derived from the weathering separation of continental rocks, rather than from the upper mantle. Liu and Zhang (1986) held the opinion that the deposits in the area belong to chemical and biochemical sedimentary genesis. Additionally, by studying the distribution and characteristics of the volcanic detrital materials in the deposits, Yang et al. (2006) considered the Mn deposits in northwestern Hunan as submarine volcanic eruption-sedimentary Mn deposits far from the volcanic eruption center (Yang and Lao, 2006). Figure 4a shows the metallogenic pattern of the submarine volcanic-sedimentary Mn deposit. Based on a research on the carbon and sulfur isotopes and algae fossils in the Mn deposits from the Datangpo Period in Guizhou Province, Yang et al. (2002) proposed that the carbonate cap (manganese carbonate), formed by the reaction of a high amount of CO2 in the atmosphere with Ca2+ and Mn2+ in the ocean after the glacial period, led to the sedimentation of Mn deposits. Zhou et al. (2013) discovered a bubble-like structure and a hole structure filled with asphaltene in the rhodochrosite orebodies of the Datangpo-type Mn deposits. In addition, many sedimentary characteristics, including the diapir structure, leakage tube structure, mud-volcanic structure, and soft-sediment deformation structure, have been observed in the ore-bearing layers and their underlying strata, indicating that this type of Mn deposit is related to the seepage of ancient natural gas. Figure 4b shows the metallogenic system and metallogenic pattern of this Mn deposit in the rift basin.

    Figure 4.  (a) Metallogenic pattern of submarine volcanic-sedimentary Mn deposit (Yang and Lao, 2006). (b) Metallogenic system and metallogenic pattern of Mn deposit characterized by an ancient natural gas seepage in the rift basin (Zhou et al., 2013) (b. section c. plan). 1.1st member of Datangpo Group of lower Nanhua System (black series of strata with manganese); 2. Liangjiehe Group and Tiesiao Group of lower Nanhua System; 3. Bubble-shaped rhodochrosite; 4. Massive rhodochrosite; 5. Banded rhodochrosite; 6. Tuff or tuffaceous sandstone; 7. Dolomite lenses; 8. Carbonaceous shale; 9. Ancient fracture.

    Based on literature related to the study area, field investigations, and basic data of the study area, a conceptual model for prospecting Mn deposits is constructed (Table 1).

    Conceptual model for prospecting Mn deposits
    Geological factors Contents Classification
    Metallogenic epoch Datangpo Period of Middle Nanhua Period Necessary
    Geotectonic position Zhangjiajie-Huayuan fold thrust belt, Huayuan-Minle fault-bend fold belt Necessary
    Paleogeography Extensional rift basin Necessary
    Sedimentary facies Semi-restricted gulf manganese-bearing shale subfacies Necessary
    Sedimentary sequence Mainly distributed in the third sequence of the Nanhua Period (NHS3) and mainly occurred in the two system tracts of transgressive systems tract (TST) and condensed section (CS) Necessary
    Paleoclimate Semi-restricted gulf environment, the climate warmed up and turned into interglacial warm-wet climate; consequently, ablation-induced transgression emerged Important
    Sedimentary formation Black shale formation Necessary
    Tectonics Tectonic intersection area, deep fracture, and basement syngenetic fracture Important
    Manganese-bearing rock series The manganese-bearing rock series consists of black silty carbonaceous shale and banded rhodochrosite layers, when the thickness of the rock series is greater than 35 m, the thickness of the Mn orebodies can reach up to 5–7 m, and the corresponding Mn grade is over 24% (Minle); when the thickness is less than 10 m, the Mn orebody with a certain scale is hardly formed (Shanmuzhai) Necessary
    Rock formation indication mark Thick-layer moraine conglomerate Important

    Table 1.  Conceptual model for prospecting Mn deposits in Huayuan area of Hunan Province

  • Figure 5 shows the 3D CNN-based framework of the 3D MPM proposed in this research, comprising three main parts.

    Figure 5.  Flowchart of the technique used in this research.

    Part one: Data discovery and modeling. The collected data include textual big data, lithofacies paleogeographic maps, borehole data, exploration line sections and 23 cutting sections, standard column charts, and geological maps. Because of problems, including diverse formats and inconsistent coordinates, it is necessary to conduct text mining processing on the textual big data to extract the key prospecting information, and to subsequently carry out coordinate unification, format registration, and conversion of the other data. Accordingly, the entity model can be constructed on the basis of the above data. After assigning a value to the block attribute, the calculation is imposed on the various characteristic variables. The attribute information included in each block model contains the third sequence, fracture, fracture buffer zone, Nantuo moraine layer, favorable buffer zone of the moraine layer, Datangpo Formation, the interlaminar anomalous body of the ancient landform of Nanhua Period, the interlaminar anomalous body of the ancient landform of Nantuo Formation, the interlaminar anomalous body of the ancient landform of Datangpo Formation, the interlaminar anomalous body of the ancient landform of Fulu Formation, equidensity, azimuth anomalous degree, intersection number, frequency number, anomalous azimuth, and centrosymmetry degree. Additionally, the known positive and negative samples served as the training set, and the unknown bodies to be predicted served as the unlabeled (input) set.

    Part two: three-dimensional CNN model prediction. In this research, 662 positive and 1 050 negative samples were obtained, where 80% of the preprocessed positive and negative samples used as the training set, and the rest 20% served as the validation set. The block model was stored in the form of a central point. We expanded five blocks to the front, back, left, and right for each centroid point. If the size of each block is 100 m×100 m×100 m, each unit to be convoluted will become a cube with a size of 1 100 m×1 100 m×1 100 m after expansion, namely 11×11×11 blocks. Subsequently, we inputted various attributes of each sample block to the model and applied the spatial distribution characteristics of the different factors to the training prediction model based on the extraction capability of the network structure in terms of its excellent spatial characteristics. Consequently, the model also covers the potential relevance between the different factors. Finally, we employed two indexes, namely the accuracy rate and recall rate, to check the classification accuracy of the 3D CNN model. The test set eventually contains two types of values of each test sample through the network, namely the ore-bearing and non-ore-bearing scores.

    Part three: Outputting the prediction results and ore-bearing probability. After imposing the normalization of the softmax layer on the scores outputted from the dense layer, the values ranging from 0 to 1, namely of the ore-bearing probability and non-ore-bearing probability, can be eventually determined and outputted in the form of a list in the CSV format. The position of each block can be determined by the coordinates (X, Y, Z), and the 3D display of the prediction results can be consequently achieved by importing them into Surpac.

    With the help of the above technique, the multivariate and massive 3D block model data can be more intelligently processed, and the spatial distribution characteristics of the data and their potential relevance can be applied to train the classification model for prospecting and prediction. As a result, the localization and probability determination of the 3D prediction process can be realized, while providing new insights into geological big data-based prospecting and prediction.

  • Three-dimensional geological modeling is an important basis for 3D geological mapping, deep geological survey, and MPM. It is also an important method to solve some deep geological problems and to study geological evolution. Moreover, a 3D model of the geological units (objects) in a region, constructed based on the geological survey data and exploration engineering and lithofacies paleogeographic data, can intuitively describe the spatial distribution of the geological units and the evolutionary relationship between them. We construct a real 3D time-space geological model by integrating the relevant data related to remote sensing, DEM, and chronology.

    Based on several geological datasets, we established 3D digital models of the Huayuan Mn deposit using the Surpac 6.3 software, including the construction of 3D digital models of the target strata, favorable rock formations, faults, and orebodies. The geoscience datasets consist of the following contents: 39 exploration line sections of the Minle Mn deposit and its periphery, 23 cutting sections of the Huayuan area, 212 sets of borehole data, 1 : 100 000 lithofacies paleogeographic map of the Songtao-Huayuan area, 1 : 200 000 geological and mineral maps of the Songtao-Huayuan area, 1 : 50 000 geological maps of the Heku sheet and Malichang sheet in the Huayuan area, hypsographic map of the Huayuan area, Aster remote sensing data with a 30 m level resolution, and an exploration report of the study area. Based on the collected borehole depth data and other data, the modeling depth of the entity model is determined to be shallower than 1 500 m. In the Huayuan study area, the models at locations with drilling engineering and exploration line sections, such as the Minle Mn deposit and Huomachong Mn deposit, were constructed on the basis of the deepest exploration depth of the boreholes, and the current deepest borehole depth collected from the Minle site is 521 m. While at other locations without drilling engineering, the models were extended on the basis of the surface attitude data of the 1 : 50 000 geological map, with the deepest depth of the cutting sections being 1 500 m.

    Further, we performed the 3D space reconstruction of the ancient landform, ore-bearing horizon, and other prediction factors. The 3D quantitative analysis of the metallogenic geological anomalies in the 3D space is mainly achieved with the help of a "cube model." Considering the size of the study area and software operation capability, the row×column×layer of the selected voxel is 100 m×100 m×100 m. The total number of blocks contained in the model is 2 606 100 (238×365×30), a total of 22 factors is initially set as the 3D prediction layers of the Huayuan sedimentary Mn deposit, and all the predictor factors are assigned to the blocks as attributes.

  • The construction of a 3D digital model involves digitally expressing the space and attribute characteristics of the geological bodies. Based on the basic data and prospecting geological model of the study area, in this research, we constructed 3D digital models of the surface scope, fracture, Mn orebodies, Nantuo moraine layer, and Datangpo Formation corresponding to the topography, tectonics, orebodies, rock formation indication mark, and strata of the study area, including prospecting digital models of the Huayuan study area (Table 2).

    Ore-controlling factors Metallogenic geological anomalies Prospecting digital models
    Strata Datangpo Formation Digital model of Datangpo Formation
    Rock formation indication mark Thick layer of moraine conglomerate serving as the ore layer roof, indicative of mineralization. Digital model of Nantuo moraine layer
    Tectonics Deep fracture and tectonic intersection (submarine volcanic eruption-sedimentary Mn deposit, ancient natural gas seepage Mn deposit) Digital model of fracture
    Lithofacies palaeogeography Secondary rift basin 3D digital model of the ancient landform of the Nanhua Period Datangpo period of Songtao-Huayuan area
    Orebodies Mn orebodies 3D digital model of Mn orebodies

    Table 2.  Prospecting digital models of the Huayuan study area

  • The 3D digital visualization of the ancient landform characteristics and sequence stratum characteristics cannot be realized through the conventional 3D modeling method; therefore, we introduced the concept of 3D spatial reconstruction. The reconstruction work mainly includes a 3D spatial reconstruction of the ancient landform, sequence strata, and digital model-based mineralized anomalous bodies (Table 3).

    Ore-controlling factors Metallogenic geological anomalies 3D spatial reconstruction of metallogenic anomalies
    Strata Ore-host strata information 3D spatial reconstruction of metallogenic ore-host strata (Datangpo Formation)
    Sequence strata Favorable sequence strata 3D spatial reconstruction of favorable three-level sequence strata
    Rock formation indication mark Favorable rock formation indication mark 3D spatial reconstruction of Nantuo moraine layer buffer zone
    Tectonics Channels of ancient natural gas and magmatic hydrothermal solution 3D spatial reconstruction of fracture buffer zone
    Vents of ancient natural gas and magmatic hydrothermal solution 3D spatial reconstruction of fracture intersection area
    Ancient landform Ancient landform of geological evolution period related to mineralization 3D spatial reconstruction of ancient landform
    Lithofacies paleogeography Favorable sedimentary facies Secondary rift basin

    Table 3.  List of 3D spatial reconstruction data of the Huayuan study area

    (1) Three-dimensional spatial reconstruction of ancient landform

    The 3D spatial reconstruction of the ancient landform involves methods of divisional statistics and spatial analysis to recover the ancient landform interface related to the mineralization based on the remote sensing and ancient landform marks, and accordingly to realize the 3D spatial reconstruction of the ore-bearing horizons of a specific period with the help of 3D visualization software. Moreover, the recovery of the ancient landform is based on the layered recovery sequence "from young to old", as the older strata are typically covered by the later sedimentary strata. While recovering the ancient landform of a specific period, the strata deposited after this period need to be stripped completely, so that the characteristics of the ancient landform can be recovered to the maximum extent. In this research, the 3D spatial reconstruction of the ancient landform is mainly directed at the ancient landform of the various periods of the Nanhua Period; Fig. 6 shows the construction flow.

    Figure 6.  (a) Method flowchart for the 3D spatial reconstruction of ancient landform; (b) ancient landform interface; (c) ore-bearing horizon of each period.

    (2) Three-dimensional spatial reconstruction of sequence strata

    The 3D spatial reconstruction of the sequence strata is different from the previous 3D modeling, and it is performed under the guidance of the sequence stratigraphy theory based on the characteristics of sedimentary deposits. In this research, we first imported the coordinate data of the third sequence interface points acquired from the boreholes into MapGIS to obtain the cloud data layers of the upper and lower interface points of the third sequence. Subsequently, we imported the upper and lower interfaces of the third sequence acquired with the help of the Grad interpolation function of Surfer into the Surpac platform to complete the 3D spatial reconstruction of the sequence strata.

    (3) Three-dimensional spatial reconstruction of mineralized anomalous bodies

    The 3D spatial reconstruction of the mineralized anomalous bodies involves extracting the strata, fracture, and other favorable metallogenic information on the basis of the 3D digital model. Based on a comprehensive research of the metallogenic geological setting, metallogenic epoch, genetic type, and mineralization type, we determined the favorable ranges of the metallogenic factors and completed the 3D spatial reconstruction of the fracture buffer zone, Datangpo Formation, and Nantuo moraine layer.

  • Based on the statistical analysis of all the potential ore-controlling factors in the study area and combined with the data of the study area, 22 predictor factors are preliminarily proposed as the 3D prediction layers for the mineralization of the Huayuan Mn deposit in Hunan Province. The value corresponding to the prediction variable in the block model is assigned 1 and that which does not exist in the block model is assigned 0. Based on the analysis and statistics of the distribution of the various prediction variables in the block model, the model is composed of 2, 606, 100 voxels with an individual size of 100 m×100 m×100 m. Each voxel is endowed with the attribute of prospecting the geological model. Figure 7 shows the spatial distribution of these 3D prediction layers. The weight values of the various ore-controlling factors were determined using WofE modeling from large to small (Table 4).

    Figure 7.  Three-dimensional predictor layers in the Huayuan ore cluster.

    Predictor numbers Evidence item W+ W- C
    Predictor 1 Third sequence 6.152 488 -2.545 18 8.697 668
    Predictor 2 Datangpo Formation 5.626 796 -2.088 96 7.715 756
    Predictor 3 Favorable metallogenic buffer zone of Nantuo moraine layer 5.087 679 0.013 965 5.073 714
    Predictor 4 Interlaminar anomalous body of ancient landform of Datangpo Formation 2.252 144 -0.588 68 2.840 823
    Predictor 5 Interlaminar anomalous body of ancient landform of Nantuo Formation 2.031 88 0.072 054 1.959 825
    Predictor 6 Interlaminar anomalous body of ancient landform of Nanhua Period 1.716 126 -0.628 69 2.344 812
    Predictor 7 Fracture 1.700 959 0.245 48 1.455 479
    Predictor 8 Fracture buffer zone 200 1.600 513 -0.212 97 1.813 482
    Predictor 9 Fracture buffer zone 400 1.406 503 -0.671 6 2.078 101
    Predictor 10 Fracture buffer zone 600 1.285 782 -1.660 49 2.946 273
    Predictor 11 Fracture buffer zone 800 1.128 361 -3.047 12 4.175 481
    Predictor 12 Fracture buffer zone 1 000 0.981 231 -8.157 14 9.138 369
    Predictor 13 Interlaminar anomalous body of ancient landform of Fulu Formation 0.856 049 0.395 81 0.460 239
    Predictor 14 Fracture buffer zone 1 200 0.853 327 -7.941 28 8.794 611
    Predictor 15 Fracture buffer zone 1 400 0.752 675 -7.702 41 8.455 083
    Predictor 16 Equidensity 0 0 0
    Predictor 17 Azimuth anomalous degree 0 0 0
    Predictor 18 Anomalous azimuth 0 0 0
    Predictor 19 Centrosymmetry degree 0 0 0
    Predictor 20 Normalization frequency 0 0 0
    Predictor 21 Number of normalization intersections 0 0 0
    Edictor 22 Nantuo moraine layer -0.135 61 0.450 304 -0.585 91

    Table 4.  Three-dimensional predictor layers and their weights (W+, W-) and spatial contrast (i.e., W+ – W-) in the weight-of-evidence (WofE) modeling in the study area

    The basic method of the 3D fuzzy evidence weight adopted in this work is as follows,

    D—research event, e.g., mineralization; V—total volume of the study area; X—the set of voxels contained in an evidence layer, Xi (i=1, 2, 3, …, 22) represents the set of voxels contained in evidence i; μD(x)—the appearance or occurrence degree of event D at location x (xX, namely, the subordination degree related to event D in unit x of layer X).

    In the conventional evidence weight model: μD(x)∈{0, 1};

    In the fuzzy evidence weight model: μD(x)∈[0, 1].

    In other words, the subordination degree of an event in the fuzzy evidence weight model can be linearly assigned a value ranging from 0 to 1. Since the evidence weight can be calculated by the fuzzy evidence weight method to the classification of the assigned values of Xi, the numerous assigned values of Xi will lead to results containing noise, consequently affecting the reliability of the weighted value. Therefore, it is necessary to reclassify the assigned values. However, the reclassification will require the linearly assigned values in the original interval [0, 1] to be reduced to several classes again, resulting in information loss. Therefore, this study adopts the double fuzzy method, which does not require reclassifying the evidence layer, but requires considering the evidence layer as the fuzzy set related to event i, and the calculation model of the fuzzy probability, conditional fuzzy probability, and fuzzy evidence weight is defined.

  • A 3D CNN typically contains the 3D convolutional layer, the 3D pooling layer, and the dense layer to extract images and to subsequently obtain a score by connecting with the softmax layer (Kamnitsas et al., 2017; Chen et al., 2016). Moreover, each layer has a number of channels, where each channel represents a type of feature. As for the 3D CNN, the convolution and pooling involve cubic 3D characteristic blocks. Unlike 2D features, 3D features are presented as a set of neurons in a 3D form. In this study, the 3D spatial distribution of the 22 ore-controlling factors served as the input to the 3D CNN prediction model. The ore-bearing probability of each voxel could be eventually generated after the processing of the two convolutional layers and two pooling layers, as well as the flatten layer, dropout layer, dense layer, and softmax layer (Fig. 8).

    Figure 8.  First layer is the input layer with 22 voxels, and the size of the voxels is 100 m×100 m×100 m. Conv3D1 and Conv3D2 are the convolutional layers, both with a filter size of 11. MaxPooling3d1 and MaxPooling3d2 are 3D maxpooling layers, both with a size of 2×2×2. We apply dropout between the flatten and dense layers and set the fraction of the input units to drop as 0.5. Note that we apply the regularization method to the dense layer.

    Three-dimensional convolutional layer: To construct a 3D convolutional layer, a series of 3D characteristic extraction blocks, namely the 3D convolution kernel, should be first built to scan all the inputs. Moreover, for generating a 3D characteristic block, different 3D convolution kernels are used to convolve different characteristic input blocks, and each characteristic block respectively corresponds to an independent convolution kernel. Subsequently, this research adds a bias term and a nonlinear activation function and finally sums the operations of the different 3D convolution kernels. The formula for the 3D convolution is as follows

    where $ {h}_{i}^{l} $ and $ {h}_{k}^{l-1} $ respectively refer to the ith 3D characteristic block of layer l and the kth 3D characteristic block of the layer l-1; $ {W}_{ki}^{l} $∈$ {R}^{2} $ is the 3D convolution kernel connecting $ {h}_{i}^{l} $ and $ {h}_{k}^{l-1} $; $ {h}_{i}^{l}(x, y, z) $, $ {h}_{i}^{l-1}(x-u, y-v, z-w) $, and $ {W}_{ki}^{l}(u, v, w) $ are respectively the element value of $ {h}_{i}^{l} $ at the coordinate (x, y, z), the element value of $ {h}_{k}^{l-1} $ calculated by the 3D convolution kernel $ {W}_{ki}^{l}(u, v, w) $ at the coordinate of $ (x-u, y-v, z-w) $, and the element value of the 3D convolution kernel $ {W}_{ki}^{l} $ itself at the coordinate $ (u, v, w) $; $ {b}_{i}^{l} $ refers to the bias item. $ \sigma (.) $ is the nonlinear activation function, e.g., the leaky ReLU.

    Three-dimensional pooling layer: A 3D pooling layer is inserted after a continuous convolution operation. The 3D characteristic block is employed to reduce the operation of data volume on the premise of retaining the original feature information by continually reducing the scale of the characteristic graph after decreasing the image dimension. If the layer l is the convolutional layer, then the layer l+1 immediately following it is a pooling layer. The concept of pooling can be described using a 4D tensor $ T=[{h}_{1}^{l}, {h}_{2}^{l}, \dots, {h}_{K}^{l}]\in {R}^{X\times Y\times Z\times K} $. As for the pooling operation, we select the maxpooling, then remove the maximum value from a scanned 3D cubic block, and finally generate the output of $ T\in {R}^{X\times Y\times Z\times K} $. Both $ (X, Y, Z) $ and $ ({X}^{{'}}, {Y}^{{'}}, {Z}^{{'}}) $ are the numbers of characteristic blocks generated after the convolution operation, which remain unchanged. If the size and stride of the pooling kernel are M and S, respectively, the magnitude of $ {X}^{{'}} $ after the pooling operation can be expressed as $ {X}^{{'}}=ceil(X/S) $, and the same operation is also imposed on $ {Y}^{{'}} $ and $ {Z}^{{'}} $.

    Dense layer: The dense layer has more connections than the convolutional layer. Each neuron is connected to all the neurons in the adjacent layer. As a result, these neurons enhance the representative capability of extracting the characteristics. The dense layer is obtained by first conducting a product operation between the 1D vector stretched from the cubic characteristic block and the neuron, then adding a bias term, and finally applying a nonlinear activation function, namely

    where $ {h}^{f-1} $ refers to the outputted 1D characteristic vector after the 3D characteristic block of the first layer $ f-1 $ is stretched into the 1D vector; $ {h}^{f} $ is a characteristic output of the layer $ f $; $ {W}^{f} $ and $ {b}^{f} $ are the weight matrix and bias term, respectively.

    (1) Rectified linear unit (ReLU) activation function

    AlexNet adopts the ReLU activation function to replace the previously adopted sigmoid nonlinear activation function. As a result, the calculated amount of the entire process can be significantly reduced by adopting the ReLU activation function. Moreover, the application of the unsaturated nonlinear ReLU activation function can help avoid the problem as well as accelerate the training by several times. With respect to the deep network, the gradient can easily disappear during the back propagation of the sigmoid function (when the sigmoid approaches the saturation area, the transformation is too slow, and consequently, the derivative is approximated to 0, resulting in the loss of information). Accordingly, the training of the deep network cannot be completed. In comparison, the ReLU can assign the output of some neurons to 0, which leads to the sparsity of the network, reduces the interdependence of the parameters, and alleviates the overfitting problem. The ReLU activation function can be expressed as follows,

    (2) Preventing overfitting by dropout layer

    The overfitting can be controlled through the dropout method with the introduction of a combination of various weights. During the training process, the activation status of the hidden neurons is controlled by a specific norm threshold; both the forward and back propagations of the neurons exceeding the threshold will be restrained. In this training process, a probability of 0.5 is adopted to randomly deactivate the neurons.

    (3) Softmax classifier

    After the CNN undergoes a series of convolutions, pooling, and other operations, the characteristics obtained eventually through the dense layer should be classified, and the Softmax function is generally used for multiple classification tasks. For multiple categories, this type of classifier outputs a set of probability vectors with the probability sum being equivalent to 1, where each assigned value of the vector is the predicted probability of its corresponding category. Suppose the training set is $ \left\{({x}^{1}, {y}^{1})\right\}, \dots, \left\{\right({x}^{m}, {y}^{m}\left)\right\} $, the category label y has K different assigned values, namely, $ y\left(i\right)\in \{1, \dots, K\} $. For a given test sample, the adopted Softmax classifier has K dimensions, and the value of each dimension corresponds to a probability value, then the Softmax classifier can be expressed as

    where $ {\theta }^{\left(1\right)}, {\theta }^{\left(2\right)}, \dots, {\theta }^{\left(K\right)}\in {R}^{n} $ are the model parameter, $ \frac{1}{{\sum }_{j=1}^{K}\;\mathrm{e}\mathrm{x}\mathrm{p}\left({\theta }^{\left(j\right)T}\;x\right)} $ belongs to the normalizing factor of the parameter, then the Softmax classifier can use the following cross entropy loss function,

    where I(.) refers to the indicator function. When the value in parentheses is true, the result is 1; otherwise, it is 0, the probability of the sample x belonging to j is

    Since it is impossible to determine the minimum analytical solution $ J\left(\theta \right) $, an iterative optimization algorithm is generally used for solving. The derivative of the loss function is

    The minimum value of the loss function can be determined by plugging the acquired partial derivative into the iterative optimization algorithm, e.g., the gradient-descent algorithm.

  • Figure 9 shows the super-parameter setting for each layer of the 3D CNN model adopted in this study. (1) The first layer (convolutional layer): The size of the convolutional kernel=[5, 5, 5], stride=[1, 1, 1], output channel=32, padding=same (expanded edge, the input equals to the output); (2) The second layer (pooling layer): pool_size=[2, 2, 2], stride=[2, 2, 2], output channel=32 (default), padding=same; (3) The third layer (convolutional layer): The size of the convolutional kernel=[5, 5, 5], stride=[1, 1, 1], output channel=32, padding=same; and(4) The fourth layer (pooling layer): pool_size=[2, 2, 2], stride=[1, 1, 1], output channel=32, and padding=same. Here, each convolutional layer has experienced the processing of the ReLU activation function and subsequently the downsampling processing (pool processing). As the activation function of the CNN, the ReLU function outperforms the sigmoid function in terms of the verified effect in deeper networks, and it can successfully solve the gradient diffusion problem observed in the case of the sigmoid function when applied to deeper networks. Subsequently, the output results of the 3D CNN are fed into the dense layer after the flatten operation, and the dropout layer is imposed on the subsequent dense layers to prevent overfitting. Finally, the ore-bearing and non-ore-bearing probabilities of each block can be outputted through the Softmax operation.

    Figure 9.  Schematic of the network structure and parameters of the 3D CNN.

  • By acquiring the coordinates of the prediction results, we assign the predicted ore-bearing areas and the areas developing known deposits (occurrences) with different colors for outputting. The ore-bearing probability can be determined by the Softmax activation function, the details of which are described in Section 2.2.1. However, the Softmax activation function can only be applied to neurons with more than one output; this ensures that the sum of all the output neurons is 1.0, so the output is the probability value less than or equal to 1, making it easy to intuitively compare the various output values. If Pk is considered the ore-bearing or non-ore-bearing "probability, " for example, if the output of type A="ore-bearing" is 0.8, the ore-bearing probability of the area delineated by the prediction model is 80%.

  • Based on the difference in the input ore-controlling factor combinations, we divide the comparative experiments into six groups, and the two prediction methods, namely the 3D CNN and WofE models, are applied to each group (Table 5). The objective is to determine the optimal ore-controlling factor combination and combination number by comparing the training loss, training accuracy, validation accuracy, and validation loss of the 3D CNN model trained on different factor layer combinations, and to analyze the feasibility and superiority of the 3D CNN model applied to 3D MPM by comparing the prediction results of the 3D CNN and WofE models.

    Serial number Number of layers 3D Predictor layers Size of voxel (m) Step (time) Train accuracy (%) Train loss Valid accuracy (%) Valid loss
    Experiment 1 22 1–22 100×100×100 215 100 0.000 021 100 0.000 116
    Experiment 2 21 1–21 (remove 22) 100×100×100 215 100 0.000 203 100 0.000 299
    Experiment 3 15 1–15 (remove 16–22) 100×100×100 215 100 0.000 576 100 0.000 741
    Experiment 4 13 1–13 (remove 14–22) 100×100×100 215 100 0.000 004 100 0.000 099
    Experiment 5 12 1–12 (remove 13–22) 100×100×100 215 100 0.000 105 100 0.000 079
    Experiment 6 6 1–6 (remove 7–22) 100×100×100 215 100 0.000 022 100 0.000 022

    Table 5.  Comparison of the model indicators used in the multiple experiments

    A comparison of the training loss, training accuracy, validation accuracy, and validation loss of the 3D CNN model in the six groups of experiments (Figs. 10a10f) shows that the training accuracy and verification accuracy of the model finally converge to 100% (given the limited sample size of the study area, the verification accuracy is likely to reach 100%), and the loss value gradually decreases and approach 0. Accordingly, the performance of the model is good. However, in experiment 2, the accuracy decreases, and the loss value increases with increasing iteration, indicating a poor stability and robustness of this model. The corresponding ore-controlling factor layers of experiment 2 are the 21 factors exclusive of the Nantuo moraine layer. Figure 10g shows the six training accuracy curves. After the training model converges to 100%, the iterations of the characteristic point approaching stabilization are 112, 179, 111, 79, 103, and 83, among which the latter three groups slightly outperform the former three groups in terms of the model robustness and convergence speed. The loss value of experiment 5 is relatively high, reaching 0.000 105 (Fig. 10h). The trends in the verification accuracy and loss value curves are consistent with those of the training (Figs. 10i, 10j). Thus, it can be considered that the latter three groups of the 3D CNN models exhibit a better performance. In addition, the serial numbers for the input ore-controlling factor layers of the latter three groups of the models are 1–13, 1–12, and 1–6, respectively. However, a further analysis of the prediction results should be carried out to evaluate the prediction effect of the six groups of models in the Huayuan Mn deposit, and it is highly likely that the prediction area with the maximum ore-bearing probability generated by the model may contain undiscovered ore bodies.

    Figure 10.  Accuracy and loss of prediction models trained through experiment 1–6 under different ore-controlling factors. (a)–(f) Training loss, training accuracy, validation accuracy, and validation loss of six groups of the 3D CNN models, respectively; (g)–(j) Summary contrast diagrams showing the training accuracy, training loss, validation accuracy, and validation loss of the six experiments.

  • By plotting the success rate curves and ore-controlling rate curves, we further quantitatively evaluated the performance of the two models (Fig. 11). The calculation process for the success rate curves is as follows: First, we sequence the predicted ore-bearing probabilities of all the blocks in descending order and extract blocks with a predicted ore-bearing probability not less than 0.5. Subsequently, we reclassify the extracted probability by setting various thresholds. Finally, we calculate the success rate by carrying out statistics on the number of known blocks in the various segments (Agterberg and Bonham-Carter, 2005). The calculation process of the ore-controlling rate involves conducting the statistics and calculation of all the blocks in the study area.

    Figure 11.  MPM performance evaluation curves for the WofE and 3D CNN models applied to the six groups of experiments. (a)–(d) Success rate curve chart and ore-controlling rate curve chart, respectively; (b)–(c) plots obtained by extracting the success rate between 0.95 and 1 from (a), where (b) and (c) are the success rate curves for the WofE and 3D CNN models, respectively; (e)–(f) plots obtained by extracting the ore-controlling rate between 0.95 and 1 from (d), where (e) and (f) are the ore-controlling rate curves for the WofE and 3D CNN models, respectively.

    Figures 11a, 11d show the success rate curves and ore-controlling rate curves of the 12 experiments; clearly, when the threshold is 50%, the success rate exceeds 95%. To analyze the differences between the 12 experiments more carefully, we analyze the variation trend in the success rates for different experiments by extracting success rates belonging to the interval of 95%–100% (Figs. 11b11c). The point that first reaches 100% is taken as the critical point and marked in the figure, where it can be seen that the success rate of the WofE model reaches 100% within the threshold range of 80%–100%, whereas that of the 3D CNN model reaches 100% within the threshold range of 20%–50%. In other words, the first 20%–50% of the ore blocks predicted by the 3D CNN model covers all the known ore blocks, whereas the first 80% or even 100% of the ore blocks predicted by the WofE model are required to cover all the known ore blocks, indicating that the effectiveness of the 3D CNN is better than that of the WofE model. A comparison between the different experimental groups shows that experiment 5 is the one where the success rates of all the WofE and 3D CNN models first reach 100%, and the corresponding ore-controlling factor condition is 1–12. This includes the third sequence, Datangpo Formation, favorable metallogenic buffer zone of the Nantuo moraine layer, interlaminar anomalous body of the ancient landform of Datangpo Formation, interlaminar anomalous body of the ancient landform of Nantuo Formation, and interlaminar anomalous body of the ancient landform of Nanhua Period. In addition, the buffer zones within 1 000 m of the fractures (200, 400, 600, 800, and 1 000 m) are included, whereas the following areas are removed: interlaminar anomalous body of the ancient landform of Fulu Formation, buffer zones outside the 1 000 m range of the fractures, Nantuo moraine layer, and some parameter indexes related to the fractures. The removed factors are interference terms in the MPM.

    Figure 11d shows that the first 20% of the predicted probability for the entire study area covers more than 95% of the known orebodies. Figures 11e, 11f show the plots based on the extracted ore-controlling rate interval of 95%–100%. Clearly, all the known ore blocks are included in the top 10% of the blocks with a high predicted ore-bearing probability by the 3D CNN, whereas only approximately 96% of the blocks are included in the top 10% of the blocks with a high predicted ore-bearing probability by the WofE model. Additionally, only when the threshold is increased to more than 50%, or even 100%, can the results of the WofE model contain all the known ore blocks. A further observation reveals that even if the WofE model is adopted in the research, experiment 5 presents certain advantages. In general, the ore-bearing probability distribution and prediction effect of the 3D CNN model are better than those of the WofE model, where the prediction ability of experiment 5 is better than those of the other groups of experiments.

    Based on a comparison of the predicted probability distribution and prediction performance of the 3D CNN and WofE models under the six groups of different ore-controlling factors, it is considered that the 3D evidence layers 1–12 in the case of experiment 5 are consistent with the mineralization model of the sedimentary Mn deposits in the Huayuan area. Furthermore, the prospecting model of the study area can be accordingly determined, and the interference factors can be eliminated as well. Under the conditions with the same dataset, block size, and variables, the 3D metallogenic prospect map acquired in experiment 5 with the help of the 3D CNN and WofE models is shown in Fig. 12. Seen from the earth surface, blocks with higher probability values are mainly distributed in the outcrop area of the Datangpo Formation (Figs. 12a, 12b). In the sections, Figs. 12c12e show that the known orebodies are all closely contained in the blocks with the 3D CNN-predicted probability of 0.8–1.0, the distribution of the predicted ore blocks is very concentrated, and the probability values of the other non-predicted areas are very low.

    Figure 12.  Predictive 3D mineral prospectivity maps of the probability values obtained using the 3D CNN model (a), (c), (e) and WofE model (b), (d), (f). The prospective 3D voxels, with a probability value threshold of 0.65, obtained from (g) 3D CNN model and (h) WofE model.

    As for the prediction results of the WofE model, the probability interval of 0.5–0.7 covers many predicted ore blocks significantly affected by the fracture. The overlapping display, shown in Figs. 12g, 12h, and the 12 ore-controlling factor layers of experiment 5 confirm that the following areas are the ones with a high prospecting potential: blocks distributed in the third sequence, Datangpo Formation, favorable metallogenic buffer zone of the Nantuo moraine layer, interlaminar anomalous body of the ancient landform of Datangpo Formation, interlaminar anomalous body of the ancient landform of Nantuo Formation, interlaminar anomalous body of the ancient landform of Nanhua Formation, and side of fractures. In general, although the corresponding relationship with the probability values of the 3D CNN and WofE models is good, the blocks with high probability values (yellow) in the 3D CNN results are fewer and intensively distributed. The known ore blocks occur in the predicted high-value areas, indicating that the 3D CNN model has a good prediction effect for the 3D MPM of the study area.

  • In this research, we carried out a 3D CNN model-based 3D MPM of the Huayuan Mn deposit, Hunan Province. We constructed a 3D digital model based on the prospecting model of the study area and conducted a 3D spatial reconstruction of the ancient landform, sequence strata, and mineralized anomalous bodies, aiming to determine the 3D predictor layers. Subsequently, the proposed CNN, as a data-driven predictive modeling technique, was applied to estimate the probability of mineral occurrence.

    Based on various geoscience datasets, including geological maps, geological sections, and boreholes, we established a 3D model of the study area and divided the entire study area into 2 606 100 voxels with a size of 100 m×100 m×100 m. When the 2D grid units are replaced by 3D voxels, the advantages of the 3D MPM are evident: the 3D prediction gives a more realistic picture of the mineralization process; moreover, the sample number of the 3D prediction is several times higher than that of the 2D prediction, consequently providing an application scope for deep learning. When all the potential ore-controlling factor layers are inputted to the models, good deep learning prediction models can overcome the typical "interferences" encountered when selecting the real ore-controlling factors. To demonstrate the effectiveness of the 3D CNN model in 3D MPM, we carried out a comparison and analysis of the results predicted using the 3D CNN and WofE methods. For this, we inputted 22 evidence factor layers and designed six groups of comparison experiments with different factor combinations.

    From the comparison of the CNN model performance in the six groups of experiments, we found that the performance and stability of the latter three models is better than those of the former three. Additionally, the success rate curves and ore-controlling rate curves showed that the 3D CNN model outperforms the WofE model in terms of the effectiveness and probability distribution of the 3D MPM of the study area. In particular, the prediction effect of 1–12 ore-controlling factors adopted in experiment 5 was superior to those of the other factors. Thus, we believe that the Mn deposit in the study area is not only related to the stratum and interlaminar anomalous bodies, but also to the spatial distribution of the faults. Compared with the conventional WofE prediction method, the 3D CNN model is more effective and has more useful for big data-driven 3D MPM.

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