Development Stages of Quantitative Evaluation of Mineral Resources

Quantitative assessment of mineral resources involves multiple aspects, such as delineating prospective areas, estimating the likelihood of mineral deposit occurrence and predicting mineral resources (Carranza, 2008, 2011a, 2011b; Cheng, 2008; Carranza & Sadeghi, 2010; Porwal & Carranza, 2015; Yousefi & Nykänen, 2017; Yousefi et al., 2019, 2021; Kreuzer et al., 2020; Zuo 2020). The developments of quantitative assessment of mineral resources have undergone several stages in history (Fig. 1). In this section, we introduce mainly the stages of development of quantitative assessment of mineral resources from a perspective of mineral prospectivity mapping (Fig. 1). Other relevant methods/theories as shown in The initial formative stage can be traced back to the period of 1950s to 1970s, as manifested by the widespread applications of mathematical methods in geology (e.g., Agterberg, 1970; Singer, 1971; Prelat, 1977). Notably, Allais (1957) estimated the probability of deposit occurrence in the Algerian Sahara based on Poisson distribution, Harris (1965) evaluated metallic mineral deposits based on geological maps that were produced by multivariate statistical analysis, and Dahlberg (1967) applied multivariate analysis to explore trace metals in stream sediments for locating mineral deposits. In that period, mathematical methods with relevant applications in geology were investigated systematically by geologists, forming ultimately a set of statistical analysis-based mineral resource assessment system.

Figure 1
figure 1

Stages of development of quantitative assessment of mineral resources

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The mature stage was from the 1980s to the 2000s, during which, with rapid advancements in computer hardware and software as well as increasing demand for mineral resources all over the world, GIS-based mineral resource assessment systems have been developed rapidly (e.g., Agterberg, 1989; Bonham-Carte et al., 1989; Wang & Wang, 1989; Agterberg et al., 1990; Bonham-Carte, 1994; Singer & Kouda, 1996; Carranza & Hale, 2000; Cheng, 2000; Zhao et al., 2000; Zhao, 2002; Zuo, 2020). The GIS-based mineral resource prediction and evaluation during this period had three main characteristics. First, a series of well-developed mineral deposit models (e.g., Cox & Singer, 1986; Roberts et al., 1988) provided unprecedented geological fundamentals for mineral potential evaluation. Second, the rapid developments in mineral resource evaluation technology produced a series of advanced methods for spatial identification and quantitative simulation of potential mineralization targets (Wilson et al., 2021). Third, the widely used GIS technology in mineral exploration made it possible to integrate multisource geospatial datasets (e.g., geophysical, geochemical and geological data) for quantitative assessment and modeling of mineral resource potential. During this period, various data integration methods have been developed for mineral prospectivity mapping (MPM; Carranza, 2021b), of which the most prominent were weights of evidence (WofE; Agterberg, 1989; Bonham-Carter et al., 1989; Carranza & Hale, 2000; Porwal et al., 2006a; Baddeley et al., 2021), fuzzy logic (Carranza & Hale, 2001a; Porwal et al., 2003b; Yousefi & Carranza, 2015), logistic regression (LR; Agterberg & Bonham-Carter, 1999; Carranza & Hale, 2001b), and evidential belief functions (EBF; Carranza & Hale, 2003; Carranza et al., 2005, 2008; Carranza, 2011a, 2015; Liu et al., 2015).

The rapid development stage started from the 2010s and continues to the present, during which, with the introduction of big data technology and artificial intelligence into geosciences, various machine learning methods have been developed for quantitative assessment and modeling of mineral resources, the most notable of which were artificial neural network (ANN; Koike et al., 2002; Porwal et al., 2003a), support vector machine (SVM; Zuo and Carranza, 2011; Geranian et al., 2016; Chen et al., 2019; Ghezelbash et al., 2019, 2021), random forests (RF; Rodriguez-Galiano et al., 2014; Carranza & Laborte, 2015a, 2015b, 2016), Boltzmann machine (Chen, 2015), extreme learning (Chen & Wu, 2017), maximum entropy (MaxEnt; Liu et al., 2018a, b), isolation forest (Chen & Wu, 2019; Zhang et al., 2021a) and wavelet-based neural network (Chen et al., 2022). In recent years, deep learning models based on multilayer neural networks, which are a special branch of machine learning theory, have emerged as a research hotspot in the realm of exploration criteria identification and mineral prospectivity mapping (Xiong et al., 2018; Zhou et al., 2018, 2021; Zuo et al., 2019, 2021a). Typical deep learning algorithms, such as convolutional neural network (Sun et al., 2020; Yang et al., 2021; Li et al., 2022a), deep autoencoder network (Xiong & Zuo, 2016; Zhang et al., 2021b), GMDH neural network (Parsa et al., 2021) and extreme gradient boosting (Parsa, 2021), have been used to handle complex and nonlinear relationships among multisource geospatial datasets in modeling of mineral prospectivity. Many recent successful case studies have made the use of machine learning the most typical data mining paradigm in mineral resource assessment.

Overview of Geomathematical Methods in Mineral Resource Assessment

Geostatistics, as a branch of spatial statistics, was introduced by Krige (1951) for applications in mining engineering. Later, Matheron (1963) proposed the concepts of regionalized variable and variation function. With the help of geostatistics, one can describe spatial patterns of samples and then interpolate unknown values based on given geochemical survey data. However, interpolation based on traditional geostatistics has some disadvantages, such as serious smoothing effects. Thus, the geostatistical stochastic simulation theory developed rapidly into a new research field and it led into a series of stochastic simulation methods (Alabert, 1987; Johnson, 1987; Isaaks 1990), such as sequential Gaussian simulation (SGS), sequential indicator simulation (SIS) and sequential indicated co-simulation (SIcS). Geostatistical stochastic simulation can reproduce the global spatial correlation and local variability characteristics of a dataset. Geostatistical modeling has become an important tool for mineral resource uncertainty assessment. For example, geostatistical stochastic simulation combined with multifractal model has been applied for uncertainty analysis of mineralization-related geochemical anomalies (Wang & Zuo, 2018, 2019; Ersoy & Yunsel, 2019; Liu et al., 2019c, 2019d; Madani & Carranza, 2020; Ramezanali et al., 2020; Liu & Carranza, 2022).

Extraction of spatial features or spatial recognition criteria related to mineralization or representing controls on mineralization from GIS-stored multisource geospatial datasets is an essential stage in quantitative assessment of mineral resources. Among various spatial recognition criteria, geochemical anomalies are direct indicators of mineral prospectivity. Delineation of geochemical anomalies to target mineral deposits is most commonly done in mineral resource assessment (Carranza, 2008, 2017a, b; Grunsky, 2010; Cheng & Zhao, 2011; Zuo et al., 2016, 2021b; Grunsky & Caritat, 2020; Sadeghi, 2021). Traditional statistical analysis (e.g., principal component analysis, cluster analysis and correlation analysis) and exploratory data analysis (EDA) (e.g., probability graphs, Chi-square plot, histogram, box plot) have been used frequently to assist in geochemical exploration (Sinclair, 1974; Govett et al., 1975; Fletcher, 1981; Howarth, 1984, 2013; Stanley & Sinclair, 1987; Grunsky & Agterberg, 1988; Yusta et al., 1998; Camizuli & Carranza, 2018; Carranza, 2021a). Since the 1990s, fractal/multifractal theory with related models have been applied gradually for geochemical anomaly identification and mineral resource assessment (Cheng et al., 1994, 1996, 2000; Cheng, 1999, 2007, 2012, 2021). Because the distribution patterns of geochemical element concentrations in the Earth’s crust are caused by various nonlinear geological/geochemical processes, the nonlinear properties of singular mineralization processes can thus be applied to predict undiscovered mineral deposits. Based on the principle of multifractal modeling, particularly that of singularity, generalized self-similarity and fractal spectrum, Cheng (2006) summarized multifractal mineralization prediction theory and models for applications to assessment of mineral resources and modeling of mineral exploration targets. Methods of compositional data analysis (CoDA) have also been developed for geochemical pattern recognition because of the closure problem with geochemical data (Chayes, 1960; Aitchison, 1986; Filzmoser et al., 2018). These methods include ilr-based univariate analysis (Carranza, 2017a), clr-based principal component analysis (PCA) (Grunsky et al., 2014; Wang et al., 2014), clr-based factor analysis (Liu et al., 2016) and compositional balance analysis (Liu et al., 2018c, 2019a). Recently, machine learning models are gradually being applied in geochemical anomaly mapping (Zuo et al., 2019, 2021a; Chen et al., 2021a).

As finding surface or near-surface mineral deposits becomes progressively difficult, GIS-based 3D geological modeling has been increasingly applied to explore sub-surface mineral deposits. Nowadays, searching for deep mineral resources has become a key research direction in quantitative evaluation of mineral resources, whereby 3D geological modeling and 3D spatial analysis technology play an important role in deep mineral exploration (Wang et al., 2011, 2015; Chen et al., 2014; Perrouty et al., 2014; Yuan et al., 2014, 2019; Nielsen et al., 2015; Li et al., 2015, 2018, 2019a, 2019b). Since 2016, China has carried out deep exploration projects that are supported by its national key research and development program. The main objective of this project is to rebuild 3D prediction model for subsurface mineral exploration through the assembly of district-scale geoscience datasets from the surface to depths of 3 km, thus promoting greatly the progress of deep mineral exploration in China.

Developments in Quantitative Assessment of Mineral Resources

Here, we summarize the developments in quantitative assessment and modeling of mineral resource potential to provide insights into advanced theoretical methods and their applications. Three research fields of mineral resource assessment are reviewed, namely nonlinear mineralization prediction theory, machine learning-based mineral prospectivity mapping, and GIS-based 3D modeling for deep mineral exploration.

Multifractal Theory for Mineral Resource Assessment

Mandelbrot (1975) proposed the fractal/multifractal theory in the 1970s. After that, the theory has been developed further and applied extensively in mineral resource assessment over the last three decades (e.g., Turcotte, 1986; Bølviken et al., 1992; Agterberg et al., 1993; Cheng et al., 1994, 1996; Cheng, 1999; Agterberg, 2007, 2014; Zuo et al., 2009; Xie et al., 2010; Zhao et al., 2012; Liu et al., 2013; Wang et al., 2013; Sadeghi et al., 2015; Chen & Cheng, 2016). Physically, multifractals consist of a set of fractals that are spatially intertwined with each other in space (Halsey et al., 1986; Evertsz & Mandelbrot, 1992; Cheng, 1999). Developments in the application of the fractal/multifractal theory have manifested that many geological processes such as mineralization, volcanism and igneous activity can be characterized by the properties of self-similarity and scale invariance (Cheng et al., 1994, 1996; Cheng, 1999).

Mineral deposits, which characterized by high metal concentrations, are end products of multiple nonlinear geological processes, especially the singular mineralization process. Previous studies have shown that singular mineralization processes can be revealed by fractal/multifractal or power-law models (Cheng, 2007; Cheng & Agterberg, 2009; Cheng & Zhao, 2011). Turcotte (1986) has shown that the relationship between tonnage and mean grade often exhibits a fractal behavior. Cheng (2012) stated that the nonlinear properties of singular mineralization processes can be used to predict undiscovered mineral deposits. Nowadays, many power-law models derived from the fractal/multifractal theory have been developed and applied for mineral resource prediction, and such models have been verified to be particularly useful in recognition of concealed and weak geochemical anomalies especially in covered areas (Goncalves et al., 2001; Cheng, 2007, 2012; Agterberg, 2012; Arias et al., 2012; Xiao et al., 2012; Liu et al., 2013; Wang et al., 2013; Zuo et al., 2015; Chen et al., 2016; Sadeghi & Cohen, 2021; Ghasemzadeh et al., 2022).

The distribution patterns of geochemical elements in the Earth’s crust are the end products of nonlinear processes. Understanding ore-forming processes and the spatial-frequency distributions of geochemical elements is no less necessary for the application of power law-based mathematical models in quantitative assessment of mineral resources. Multifractals caused by extreme geochemical dispersion processes under complex geological processes can be depicted by multiple probability distribution patterns (e.g., normal, lognormal and power-law distributions) through a quantile–quantile plot analysis of singularity indices (Liu et al., 2017, 2019b). The power-law distribution of geochemical data is a useful tool not only for identifying geological anomalies but also for delineating mineral exploration targets (Cheng, 2008). In the past two decades, various power-law models have been developed for mineral exploration, such as the concentration–area fractal model (C–A; Cheng et al., 1994), spectrum–area model (S–A; Cheng et al., 2000), concentration–distance model (C–D; Li et al., 2003), local singularity analysis (LSA; Cheng, 2007), concentration–volume model (C–V; Afzal et al., 2011), singularity-quantile analysis (S–Q; Liu et al., 2017) and weighted singularity mapping (Xiao et al., 2018). These nonlinear models are powerful tools for quantitatively processing geo-information in terms of identifying anomalies, decomposing compounded anomalies and evaluating the relationships between geological anomalies and mineral deposits (Cheng & Zhao, 2011).

Singularity, as defined by Cheng (2007) from the perspective of geological application, is a special phenomenon of mass of energy release or mass accumulation in relatively narrow spatial–temporal intervals. Local singularity analysis, as one of the most important multifractal model, is effective for identifying geochemical anomalies, especially weak and concealed ones at covered areas or linked to deep sources (Cheng, 2012). Singularity indices calculated from LSA can be divided into three groups based on their frequency distribution patterns: (i) singularity indices with α < 2 indicate element enrichment that is suggestive of the presence of metal mineralization; (ii) singularity indices with α > 2 indicate element depletion that is suggestive of the absence of mineralization; (iii) singularity indices with α close or equal to 2 indicate geochemical background. Based on LSA and Q–Q plot analysis, the singularity-quantile (S–Q) analysis was developed to partition mixed geochemical anomalies by plotting singularity index quantiles vs. standard normal quantiles in frequency domain (Liu et al., 2017). Recent studies show that the S–Q method is a useful tool in delineating geochemical exploration targets (Liu et al., 2017; Xu et al., 2020; Mondah et al., 2021; Zhao et al., 2021).

Machine Learning-based Mineral Prospectivity Mapping

Applications of machine learning to mineral resource assessment can be traced to the 1990s (Singer & Kouda, 1996; Harris & Pan, 1999). Nowadays, with the introduction of big data and artificial intelligence into mathematical geosciences, the rapid developments of machine learning are changing the model of mineral resource assessment (Xiong et al., 2018; Zuo et al., 2019; Zhou et al., 2021). Up to now, various advanced machine learning methods, especially ANN (Singer & Kouda, 1996), SVM (Zuo & Carranza, 2011) and RF (Carranza & Laborte, 2015a, b, 2016) have been developed to integrate multisource geospatial datasets for mineral prospectivity analysis.

ANN was first introduced by McCulloch and Pitts (1943). The basic idea of an ANN is to learn and classify complex patterns based on emulation of the human brain and nervous system (Abiodun et al., 2018). Training an ANN model requires defining multiple parameters such as number of hidden layers, nodes per layer, initialization weights, regularization parameters and learning rate to decrease overfitting (Rodriguez-Galiano et al., 2015). The aim of an ANN algorithm is to find a set of weights that ensures each input vector is the same or close to the output vector. ANNs have high efficiency in generalization, self-learning and nonlinear approximation. Several forms of ANN methods have been applied in the geosciences over the years (Harris & Pan, 1999; Koike et al., 2002; Porwal et al., 2004, 2006b; Nykänen, 2008; Leite et al., 2009; Oh & Lee, 2010; Hong et al., 2020; Maepa et al., 2021), notably radial basis functional neural network (RBFNN), probabilistic neural network (PNN) and multi-layer perception (MLP). With the developments and applications of deep learning in geosciences, ANN is becoming relatively competitive with other machine learning algorithms and conventional regression models regarding applicability and efficiency for MPM. However, there are still some key challenges or issues with ANN modeling (Koike et al., 2006; Fan et al., 2012; Abiodun et al., 2018), including (1) improving model transparency, (2) allowing useful knowledge from trained ANN models, (3) improving extrapolation and convergence abilities, (4) identifying factors that influence spatial distribution based on sensitivity analysis, and (5) exploring new approaches to uncertainty.

The SVM algorithm was developed in Russia in the 1960s (Vapnik & Lerner, 1963), which can be applied for dichotomy classification of higher-dimensional features. The basic idea of the SVM is to transform input features into a multidimensional space, in which a hyper-plane can be used to separate two classes (e.g., presence or absence of mineral deposits). In the SVM model, the relationships between dependent variables and independent variables are determined by a subset of the data termed support vectors. The SVM regression model is determined by the quadratic programming-based numerical optimization and Lagrange multipliers. Actually, an optimal SVM model is established when the optimization algorithm finds a global minimum (Cristianini & Shawe-Taylor, 2000; Vapnik, 2000). Besides, one of the advantages of the SVM is its less tendency to overfit regression functions because of the applications of the ε-insensitive loss function and structural risk optimization (Vapnik, 2000; Achieng, 2019).

Breiman (2001) developed the RF algorithm, which is a kind of ensemble learning method that solves a single prediction problem by combining several models. The RF method combines multiple decision trees and performs repeated predictions of the training data from the root node to a terminal node (Breiman, 2001; Rodriguez-Galiano et al., 2014; Carranza & Laborte, 2015a, b, 2016). The basic idea of the RF model is to grow multiple decision trees on random subsets. The advantages of the RF for MPM include: (1) it is relatively robust to outliers; (2) its ability to combine continuous and/or categorical data as variable inputs; (3) its ability to overcome the ‘black-box’ limitations of artificial neural networks, and (4) its ability to assess the relative importance of the independent variables. Previous studies show that the RF model can achieve higher predictive accuracy and efficiency in MPM compared to other machine learning algorithms (e.g., ANN, SVM and maximum entropy) (Rodriguez-Galiano et al., 2015; Sun et al., 2019; Zhang et al., 2019).

Deep learning, as a kind of multilayer neural network, is a type of machine learning that has become one of the most popular hotspots in mathematical geosciences (Zuo et al., 2019; Zhou et al., 2021). Over the past few years, several typical deep learning algorithms have been developed for mineral resource assessment, due to their powerful ability to mine or extract mineralized information automatically from complex data structures. For example, Xiong and Zuo (2016) applied deep auto-encoder network to recognize Fe polymetallic mineralization associated multivariate geochemical anomalies in the southwestern Fujian district, China. Yang et al. (2021) introduced a GoogLeNet-based convolutional neural network for mapping gold prospectivity in the Fengxian study area, China, and Li et al. (2022a) reported a GAN-based data augmentation method for assisting REE prospectivity mapping in the Southern Jiangxi, China.

GIS-based 3D Modeling for Mineral Resource Assessment

In the late 1980s, with the gradual development and growth of computer graphic technology, information visualization was introduced into the geosciences and it promoted the growth of 3D geological modeling. The aims of 3D geological modeling are to characterize the spatial distribution of geological units and reveal the evolutionary relationships among geological units based on integration of multisource information from boreholes, geophysical and geochemical data, and other relevant data. Traditional 3D modeling for MPM is commonly based on a set of stacked geological profiles obtained from field exploration, which provides a visual representation to detect the 3D geological configuration in the subsurface, as well as insights into geophysical and geochemical characteristics of the subsurface, but it cannot represent the successions between two cross-sections (Li et al., 2019a). Over the years, the developments of 3D GIS technology have promoted significant developments in 3D MPM and deep mineral exploration. As the likelihood of finding new ore bodies at or near surface decreases over time, 3D geological modeling for deep mineral exploration is increasingly conducted in maturing mining camps and ore districts to explore for blind mineral deposits (Wang et al., 2011, 2021; Li et al., 2015; Martin-Izard et al., 2015; Yuan et al., 2019; Mao et al., 2020; Jia et al., 2021; Zhang et al., 2021c).

3D GIS technologies provide powerful tools to integrate multi-source and multi-dimension geospatial datasets for understanding the depth extent of deep ore-controlling or ore-bearing geological bodies and for characterizing geological relationships in a more interpretive environment (De Kemp et al., 2011). In the last two decades, a series of commercial 3D GIS platforms have been developed for 3D geological modeling (Wang et al., 2021), such as the SKUA-GOCAD platform for 3D geological modeling, the Encom Modelvision software for geophysical constrained 3D geological modeling, the FLAC3D software for 3D dynamic simulation, and the GeoCube3.0 software for data integration and modeling. These software programs are nowadays applied frequently to build 3D spatial geometry model and 3D feature model of critical geological body.

Over the past 40 years, a lot of 3D geological modeling methods have been developed and applied to rebuild the 3D geometries of concealed geological bodies, which can be classified into explicit modeling and implicit modeling (Li et al., 2019a). Implicit modeling relies mainly on multivariate statistic methods to build 3D geological based on observed or measured data such as foliation measurements, structural directions, stratigraphic positions and relationships among the geological bodies (Lajaunie et al., 1997; Hillier et al., 2014). However, explicit modeling depends highly on reliable knowledge of geologists to restructure subsurface based on polynomial equations and smoothed interpolation technology (Mallet, 1992; Caumon et al., 2009).

In the applications of 3D geological modeling in MPM, a reliable 3D model relies on how much data are obtained from the ground surface and deep. Previous studies show that many cases of 3D prospectivity modeling focus on deposit- and district- scales (e.g., Wang et al., 2011, 2015; Xiao et al., 2015; Martin-Izard et al., 2015; Li et al., 2015, 2018, 2019a, 2019b; Mao et al., 2018, 2019; Yuan et al., 2019; Zhang et al., 2020; Farahbakhsh et al., 2020; Qin et al., 2021; Liu et al., 2021; Zhang et al., 2021d). That is because datasets for 3D modeling, such as drill-holes, cross-sections, geochemical and geophysical data, are available mostly at deposit- and district- scales. However, few studies have investigated 3D prospectivity modeling at a regional scale (Perrouty et al., 2014; Nielsen et al., 2015; Lee et al., 2019) due to sparse datasets, high costs of collecting relevant data, and lack of detailed understanding on subsurface geological structures (Jessell et al., 2014). The main challenge for regional scale 3D MPM is the building of a meaningful conceptual model of prospectivity when the above-mentioned constraints exist. Thus, uncertainties in 3D geological modeling for mineral exploration typically increased from deposit- to district- to regional-scale (Wang et al., 2017).

In recent years, the growth of big data analytics and artificial intelligence has promoted innovation to integrate mineral resource exploration and evaluation (Zuo et al., 2019; Wang et al., 2021; Zhao & Chen, 2021; Zhou et al., 2021), leading to developments of various machine learning methods for 3D mineral exploration. For example, Mao et al. (2020) adopted a hybrid GA-SVR model for 3D gold exploration in the Axi deposit, northwestern China, and demonstrated that this model was superior to fuzzy WofE and multiple nonlinear regression. Zhang et al. (2021c) proposed a 3D bagging-based PUL algorithm to evaluate gold potential based on unlabeled data and positive samples, as well as compared with WofE, one-class SVM and RF. Liu et al. (2021) applied a multilayer perceptron neural network to explore the relationships between Au mineralized targets and ore-controlling factors and to recognize deep mineral exploration targets in the Xiadian Au deposit of the Jiaodong Peninsula, China. Additionally, a GeoCube software was developed by Wang et al. (2015) and Li et al. (2016), in which multiple integration modules were embedded for extraction and integration of 3D exploration criteria such as the WofE, Fuzzy WofE, Boost WofE, LR and RF models.

Organization of The Special Issue

The 17 papers comprising this special issue can be grouped into three themes, arranged according to their sequence in this special issue.

Theme 1: Geomathematical Methods for Geo-Anomaly Recognition

This theme is represented by the following seven papers, arranged according to their sequence in this special issue:

(1–1) “Mapping of regional-scale multi-element geochemical anomalies using hierarchical clustering algorithms” by Geranian & Carranza (2021);

(1–2) “Identification of multi-element geochemical anomalies for Cu–polymetallic deposits through staged factor analysis, improved fractal density and expected value function” by Zhao et al. (2021);

(1–3) “Uncertainty analysis of geochemical anomaly by combining sequential indicator Co-simulation and local singularity analysis” by Liu & Carranza (2022);

(1–4) “Joint modeling based on singularity mapping and U-statistical methods for geo-anomaly characterization” by Wang et al. (2022a);

(1–5) “A ‘weighted’ geochemical variable classification method based on latent variables” by Liu et al. (2022);

(1–6) “Depiction of different alteration zones using fractal and simulation algorithm in Pulang porphyry copper deposit, Southwest China” by Wang and Xia (2021); and.

(1–7) “Extraction of gravity–magnetic anomalies associated with Pb–Zn–Fe polymetallic mineralization in Luziyuan ore field, Yunnan Province, Southwestern China” by Shang et al. (2021).

Paper (1–1) demonstrated that the BIRCH and BHC algorithms performed better in the classification of regional geochemical exploration data compared to conventional AHC algorithms such as OS-AHC. Paper (1–2) proposed an improved fractal density model based on fractal topography theory and proved its effectiveness to enhance Cu anomalies in the Zhongdian area, Yunnan Province, China. Paper (1–3) introduced a new method by combining sequential indicator co-simulation (SIcS) and LSA to measure uncertainties of geochemical anomalies, in which the spatial structure of the primary variable can be rebuilt by introducing an auxiliary variable. Paper (1–4) discussed a joint modelling method by integrating U-statistics and multi-scale window optimized LSA to explored geochemical anomaly heterogeneity of ore-forming elements W and Sn in the Malipo district, southeastern Yunnan, China. Paper (1–5) reported a weighted clustering method that was demonstrated by using a classic geochemical dataset from western Meguma Terrain, Nova Scotia, Canada. Paper (1–6) reported the SGS and C-V fractal model to identify copper alteration zones based on drillhole data from the Pulang deposit, China. Paper (1–7) focused on applying BEMD and entropy weight–TOPSIS techniques to decompose gravity–magnetic anomalies and to extract Pb–Zn–Fe mineralization-related anomalies in the Luziyuan ore district and surrounding areas, Yunnan, China.

Theme 2: Machine Learning for Mineral Prospectivity Mapping

This theme is represented by the following six papers, arranged according to their sequence in this special issue:

(2–1) “Mineral prospectivity mapping based on isolation forest and random forest: Implication for the existence of spatial signature of mineralization in outliers” by Zhang et al. (2021a);

(2–2) “Application of AdaBoost algorithms in Fe mineral prospectivity prediction, a case study in Hongyuntan–Chilongfeng mineral district, Xinjiang Province, China” by Zhao et al. (2022);

(2–3) “Gold prospectivity modeling by combination of Laplacian Eigenmaps and least angle regression” by Chen et al. (2021b);

(2–4) “A hybrid logistic regression: gene expression programming model and its application to mineral prospectivity mapping” by Xiao et al. (2021);

(2–5) “Mineral prospectivity mapping via gated recurrent unit model” by Yin et al. (2021); and.

(2–6) “Determination of predictive variables in mineral prospectivity mapping using supervised and unsupervised methods” by Wang et al. (2022b).

Paper (2–1) introduced two algorithms, namely isolation forest and random forest, for orogenic gold prospectivity mapping in the Hezuo–Meiwu district, West Qinling orogen, China. Paper (2–2) investigated Boosting algorithms for volcanic–sedimentary Fe prospectivity analysis in the Hongyuntan–Chilongfeng mining district, China. Paper (2–3) developed a methodology by integrating the Laplacian Eigenmaps (LEMS) with least angle regression (LARS) to map Au-prospective areas in the Jinchanggouliang area, Inner Mongolia, China. Paper (2–4) developed a hybrid model by integrating logistic regression (LR) with gene expression programming (GEP) for MPM in the Eastern Tianshan Cu–Mo polymetallic belt, China. Paper (2–5) employed a gated recurrent unit (GRU) model to map mineral potential in the Baguio District, Philippines. Paper (2–6) explored the performance of the recursive feature elimination (RFE) and sparse principal components analysis (SPCA) to determine optimum PVs, and concluded that PV selection was a critical step in improving the predictive ability of MPM.

Theme 3: GIS-based 3D Modeling for Mineral Exploration

This theme is represented by the following four papers, arranged according to their sequence in this special issue:

(3–1) “Generalized mathematical morphological method for 3D shape analysis of geological boundaries: application in identifying mineralization-associated shape features” by Deng et al. (2021);

(3–2) “Modeling-based multiscale deep prospectivity mapping: a case study of the Haoyaoerhudong gold deposit, Inner Mongolia, China” by Li et al. (2022b);

(3–3) “Three-dimensional pseudo-lithologic modeling via adaptive feature weighted k-means algorithm from multi-source geophysical datasets, Qingchengzi Pb–Zn–Ag–Au district, China” by Zhang et al. (2021d); and.

(3–4) “An improved GWR approach for exploring the anisotropic influence of ore-controlling factors on mineralization in 3D Space” by Huang et al. (2021).

Paper (3–1) reported a general shape analysis method termed mathematical morphology (MM) to explore the 3D shapes of boundaries of the Fenghuangshan Cu ore field, Eastern China. The Paper (3–1) introduced several steps on how to transfer and integrate multisource ore-controlling information for modeling-based 3D MPM based on multiscale geodatasets. Paper (3–1) proposed an adaptive feature weighted k-means (AFW k-means) method to construct a 3D pseudo-lithology model for deep mineral exploration in the Qingchengzi polymetallic district, China. Paper (3–4) investigated the 3D spatial non-stationary relationships of mineralization targets with ore-controlling factors based on an improved geographically weighted regression (GWR) model.

Conclusions

In this special issue, we reviewed quantitative assessment and modeling of mineral resource potential with a series of case studies over the past seventy years. Three research themes of mineral resource assessment are reviewed in detail, namely (1) multifractal mineralization prediction theory, (2) machine learning-based MPM, and (3) GIS-based 3D modeling for deep mineral exploration. In addition, we introduced briefly the 17 papers forming this special issue, which can be grouped into the aforementioned three themes. It is believed that GIS-based 3D analysis and integration of relevant multi-source data will become increasingly indispensable in assisting mineral exploration in deep and surroundings of known deposits in the future. Moreover, with the explosive increase in volume of geoscientific data, deep machine learning algorithms will be increasingly used for extracting and integrating ore-associated features from multisource data in order to model and assess quantitatively mineral resource potential.