Comparative Machine Learning-Based Prediction of Gold Enrichment in a Sulphide-Hosted Orogenic System Using Multielement Geochemistry

1. Introduction

Orogenic gold deposits (OGDs) are among the most economically significant gold systems globally, particularly within Precambrian terranes such as the West African, Yilgarn, and Superior cratons [1,2,3]. These structurally controlled, epigenetic systems are typically associated with compressional tectonics in metamorphic belts and are characterized by quartz-carbonate veins containing gold in both visible and invisible forms, often within sulfide minerals such as arsenopyrite, pyrite, and pyrrhotite [4,5,6]. Pathfinder elements such as As, Sb, Fe, Ni, and Co are strongly associated with gold, enabling more effective geochemical exploration [7,8]. Mineral zoning in sulphide minerals has also been employed to differentiate mineralized from barren zones, reflecting fluid evolution during ore formation [9,10]. Recent advances have highlighted the importance of integrating multielement geochemistry with machine learning (ML) to better delineate mineralized zones, especially in complex and covered terrains [11,12,13].

Over the last two decades, the mineral exploration landscape has been transformed by the convergence of improved geoscientific data acquisition, computational capabilities, and ML tools [14,15]. Traditional exploration techniques, although foundational, are increasingly challenged by limitations of cost, time, and subjectivity, especially in geologically complex areas where indicators are obscured [16,17]. Sulphide-hosted OGDs in greenstone belts and shear zones typify this complexity, underscoring the need for predictive modelling in regions like the West African Craton [18,19].

The widespread availability of multielement geochemical datasets from soil and rock sampling campaigns provides a rich resource for ML applications. These algorithms are particularly adept at modelling nonlinear and high-dimensional relationships, offering great promise in mineral prospectivity analysis [20,21]. Emerging analytical technologies such as LA-ICP-MS, portable XRF, and high-resolution elemental mapping have further expanded data access [22,23]. Techniques like Random Forest (RF), Support Vector Regression (SVR), and Convolutional Neural Networks have been applied to anomaly detection and predictive modelling tasks, enabling higher confidence in target delineation [24,25,26]. Geochemical indices and elemental ratios also continue to support anomaly classification and mineral potential mapping [27,28].

ML has enabled a shift from deterministic to probabilistic modelling, improving flexibility and accuracy in mineral systems analysis. Ensemble learning strategies, including bagging and boosting, are now widely used and recognized for superior predictive power in geoscientific contexts [29,30]. Nonetheless, many studies emphasize advanced algorithms without benchmarking against elementary baselines such as linear regression models, limiting the ability to evaluate true ML gains under consistent preprocessing and geological settings [31,32].

Geochemical datasets pose unique challenges as they are inherently compositional, constrained by closure to a constant sum, and thus require log-ratio transformations to avoid spurious correlations [33]. Without compositional data analysis (CoDA), interpretations may lack subcompositional coherence and risk misleading geological conclusions [34]. Multicollinearity, redundancy, and sparsity in geochemical data further complicate modelling tasks [35,36].

While integrating geophysical and structural datasets into predictive models can improve accuracy, these datasets are often unavailable in early-stage exploration, making it essential to assess the predictive utility of geochemical data on its own [37,38]. The demand for interpretable machine learning solutions has increased the adoption of explainable artificial intelligence (XAI), with SHapley Additive exPlanations (SHAP) emerging as a leading method. SHAP enhances model transparency by assigning importance scores to each feature, thereby linking model outcomes to geological processes [39,40,41,42,43].

In mineral exploration, SHAP has helped validate pathfinder elements including Al₂O₃, MgO, Sr, S, Fe, and As, particularly in sulphide-rich systems [35,39]. It has also been employed in unsupervised learning workflows and anomaly detection, enabling the delineation of lithological boundaries and mineralized zones [44,45]. Although computationally intensive, SHAP represents a significant breakthrough in the fusion of ML with geological understanding [46,47].

This study responds to the need for robust, interpretable, and geology-informed predictive models in mineral exploration by: (1) benchmarking linear baselines—Ordinary Least Squares (OLS), Ridge, Lasso, and Huber—against non-linear ML algorithms (RF, SVR, kNN, and MLP) within a CoDA-correct preprocessing workflow; (2) applying SHAP to interpret RF outputs and identify key geochemical predictors; and (3) ensuring reproducibility by publishing full code, hyperparameter grids, and a synthetic proxy dataset. By tackling these objectives, this research contributes to best practices in model selection, preprocessing, and interpretation in ML-based geochemical targeting.

2. Materials and Methods

This study employed a structured compositional data analysis (CoDA) framework following Aitchison [48], in which the response variable was defined as y = ln(Au/G₁₀), where G₁₀ is the geometric mean of the predictor elements. This formulation represents gold enrichment relative to the multielement geochemical background and ensures that the predictor variables are independent of Au, thereby eliminating circularity and enabling valid application to unseen samples [49,50]. The computational workflow was implemented in Python 3.10 within a Jupyter Notebook environment. The pipeline incorporated systematic preprocessing of geochemical assays using a CoDA-correct approach (multiplicative replacement of below-detection values, closure to constant sum, and centered log-ratio transformation with robust outlier screening), ensuring statistically valid treatment of compositional data.

Modelling included both elementary baselines (Ordinary Least Squares, Ridge, Lasso, Huber) and advanced non-linear algorithms (Random Forest, Support Vector Regression, k-Nearest Neighbors, and Multi-Layer Perceptron) to benchmark ML performance gains. A rigorous experimental design with stratified splits and five-fold cross-validation was adopted to guarantee robust evaluation. Performance metrics (R², RMSE, MAE) were compared across baselines and non-linear models, while SHAP analysis provided geological interpretability by linking predictive features to sulphide-associated mineralization.

2.1. Study Area and Data Description

The dataset comprises 53,126 multielement geochemical samples collected from a sulphide-hosted orogenic gold system within a Paleoproterozoic Birimian greenstone belt. The geological setting is characterized by structurally controlled gold mineralization associated with sulphide phases, particularly pyrite and arsenopyrite, consistent with typical orogenic gold deposit models.

Each sample contains concentrations of Au and a suite of major and trace elements, including S, Fe, Al, Si, Mn, Sr, Ni, Cu, K, and Ti. These elements were selected based on their geological relevance to mineralization processes, association with sulphide phases, and data completeness across the dataset. The final dataset provides a robust multivariate geochemical representation suitable for machine learning-based predictive modelling. A summary of the dataset is shown in Table 1.

2.1.1. Sample Preparation and Analytical Methods

All drillhole samples were prepared using industry-standard laboratory protocols. Sample preparation included crushing to <2 mm followed by pulverization to approximately 75 μm to ensure analytical homogeneity. Gold (Au) was analysed using fire assay with atomic absorption spectrometry (AAS) finish. Major and trace elements (S, Fe, Al, Si, Mn, Sr, Ni, Cu, K, Ti) were analysed using X-ray Fluorescence (XRF) following multi-acid digestion. All analyses were conducted at a single accredited commercial laboratory using consistent analytical methods and detection limits throughout the dataset.

2.1.2. Rationale for Element Selection

Element selection was guided by geochemical relevance, data completeness, and analytical consistency. The selected elements (S, Fe, Al, Si, Mn, Sr, Ni, Cu, K, Ti) are commonly associated with sulphide-hosted orogenic gold systems and exhibited low censoring rates (<25%) across the dataset. Sulphur and iron were specifically retained as key proxies for sulphide abundance, given their strong mineralogical association with gold-bearing phases such as pyrite and arsenopyrite. Although arsenic (As) is a well-known pathfinder element in orogenic gold systems, it was excluded due to high censoring rates and inconsistent detection limits within the available dataset. The retained element suite captures the dominant sulphide-controlled geochemical signal while ensuring CoDA robustness.

2.2. Data Preprocessing

Geochemical data are inherently compositional, meaning that only relative relationships between components carry meaningful information. To ensure statistically valid analysis and avoid spurious correlations, preprocessing was conducted within a CoDA framework.

2.2.1. Treatment of Below-Detection-Limit Values

Below-detection-limit (BDL) and zero values among the predictor elements were treated using a multiplicative replacement strategy. A small constant (δ = 1×10⁻⁶ of the row total) was distributed proportionally across components, ensuring strictly positive values while preserving the relative structure of the data.

2.2.2. Closure and CLR Transformation

To account for the compositional constraint, predictor-element vectors (S, Fe, Al, Si, Mn, Sr, Ni, Cu, K, Ti) were closed to a constant sum and transformed using the centred log-ratio (CLR) transformation as used by Aitchison [48]: CLR(xᵢ) = ln(xᵢ/g(x)), where g(x) is the geometric mean of the predictor-element vector. Gold (Au) was excluded from this transformation to avoid circularity in the predictive framework.

2.2.3. Outlier Detection

Outliers were identified in the transformed predictor space using the Minimum Covariance Determinant (MCD) estimator. Mahalanobis distances were computed and compared against a chi-square threshold at α = 0.999. Samples exceeding this threshold were removed, resulting in a filtered dataset of 41,626 samples. This procedure ensures robust modelling by removing multivariate anomalies without biasing high-grade mineralization trends.

2.3. Target Variable Definition

To eliminate circularity, the response variable was defined independently of the predictor transformation as y = ln(Au/G₁₀), where G₁₀ is computed from the predictor elements only. This formulation ensures that Au is not embedded within the predictor space and allows the model to be applied to unseen samples using only measured predictor-element concentrations. The formulation represents gold enrichment relative to the multielement geochemical background and provides a methodologically sound and non-circular predictive framework.

2.4. Exploratory Compositional Analysis and Predictor Selection

Before model development, exploratory compositional data analysis was conducted to evaluate relationships among predictor elements and justify their inclusion. A CLR-based correlation matrix was examined to assess inter-element associations and potential redundancy within the predictor set as shown in Figure 1. Additionally, geological relevance was considered, particularly the role of sulphur and iron as key indicators of sulphide mineralization and gold deposition. This approach preserves the compositional structure of the data and avoids spurious correlations associated with raw concentrations.

The CLR-based correlation matrix (Figure 1) reveals distinct geochemical associations among predictor elements. Strong relationships between Fe and Ti, as well as Al and K, reflect lithological controls, while associations involving sulphur (S) highlight sulphide-related mineralization processes. The absence of extreme redundancy among variables indicates that the selected predictor set retains meaningful compositional information suitable for machine learning modelling.

To further investigate compositional structure and validate element selection, principal component analysis (PCA) was performed on CLR-transformed predictor variables. The resulting biplot in Figure 2 provides a visual representation of inter-element relationships and their contribution to variance within the dataset.

The CLR-PCA biplot (Figure 2) explains approximately 75% of the total variance, with PC1 accounting for 62.8% and PC2 for 12.3%. Sulphur (S) shows a strong loading along PC1, indicating its dominant influence on compositional variability and its association with sulphide mineralization. The distribution of variables confirms the presence of meaningful compositional patterns and supports the validity of the selected predictor elements for modelling.

2.5. Machine Learning Models

A comparative modelling framework was implemented to evaluate the performance of machine learning algorithms against elementary baselines.

2.5.1. Linear Baseline Models

Linear regression models were used as baseline comparators, including: Ordinary Least Squares (OLS), Ridge regression, Lasso regression, and Huber regression. These models provide a reference for assessing whether nonlinear approaches offer improved predictive capability.

2.5.2. Nonlinear Machine Learning Models

The following nonlinear models were evaluated: Random Forest (RF), Support Vector Regression (SVR), k-Nearest Neighbours (kNN), and Multi-Layer Perceptron (MLP). These models were selected due to their ability to capture nonlinear relationships within complex geochemical systems.

2.6. Model Training and Evaluation

The dataset was randomly partitioned into training (70%), testing (15%), and validation (15%) subsets. Model performance was evaluated using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). All models were trained to predict the revised target variable ln(Au/G₁₀). Performance metrics were computed for training, testing, and validation sets, with emphasis placed on validation results to assess generalization performance.

2.7. Reconstruction of Gold Concentration

For interpretational completeness, the relationship between the predicted target variable and gold concentration can be expressed as: Au = exp(y) × G₁₀, where G₁₀ is calculated directly from the predictor-element concentrations. However, model evaluation and interpretation in this study are performed exclusively in the transformed target space ln(Au/G₁₀), ensuring methodological consistency and avoiding reliance on derived quantities for validation.

2.8. Model Interpretability Using SHAP

Model interpretability was assessed using SHapley Additive exPlanations (SHAP), applied to the best-performing model (Random Forest). SHAP values quantify the contribution of each predictor variable to the predicted output, allowing identification of key geochemical drivers of gold enrichment. In this study, SHAP analysis was conducted on the revised target variable ln(Au/G₁₀), ensuring that feature importance reflects valid predictive relationships rather than artefacts of compositional circularity [39].

3. Results

3.1. Model Performance in Revised Target Space

All models were retrained using the revised non-circular target variable ln(Au/G₁₀), where G₁₀ is the geometric mean of the predictor elements. Under this corrected formulation, nonlinear machine learning models consistently outperformed linear baselines. Random Forest (RF) achieved the best validation performance with R² = 0.505, RMSE = 1.264, and MAE = 1.001, followed closely by the Multi-Layer Perceptron (MLP) and Support Vector Regression (SVR). In contrast, linear models—including Ordinary Least Squares (OLS), Ridge, Lasso, and Huber regression—showed substantially lower performance, with validation R² values around 0.31, as shown in Table 2.

The comparative performance of the models is illustrated in Figure 3, which summarizes validation R² across all models.

3.2. Prediction Accuracy in the Revised Target Space

The relationship between observed and predicted values for the RF model is shown in Figure 4. The predictions exhibit a clear positive relationship with the observed values and are distributed close to the 1:1 line, indicating good agreement between model outputs and measured gold enrichment. Although some dispersion is present, particularly at higher enrichment values, the model captures the overall structure of the data effectively.

3.3. Residual Behaviour

Residual diagnostics in Figure 5 indicate that errors are approximately symmetrically distributed around zero, with no clear systematic bias across the prediction range. However, an increase in residual spread is observed at higher predicted values, suggesting reduced precision for extreme enrichment conditions.

3.4. Model Interpretation Using SHAP

SHapley Additive exPlanations (SHAP) were used to evaluate the contribution of predictor variables to model predictions. The SHAP summary plot in Figure 6 shows that sulphur (S) and iron (Fe) are the most influential predictors, with higher values of these elements generally associated with increased predicted gold enrichment. Secondary contributions are observed from elements such as Cu, Ni, and Mn. The global importance ranking in Figure 6a confirms the dominant role of S and Fe, with other elements contributing to a lesser extent.

4. Discussion

The results demonstrate that multielement geochemical data alone can provide meaningful predictive capability for gold enrichment within a sulphide-hosted orogenic system. The best-performing model, Random Forest, achieved a validation R² of approximately 0.51, indicating that the selected predictor elements capture key geochemical signals associated with gold mineralization. While this level of performance may be considered moderate, it is consistent with the inherent complexity of geological systems, where mineralization is controlled by multiple interacting factors including lithology, structure, hydrothermal fluid flow, and alteration processes.

The consistent outperformance of nonlinear models relative to linear baselines highlights the importance of capturing nonlinear relationships within geochemical datasets. Linear models assume additive and proportional relationships between predictor variables and the response, which are often insufficient to represent the complexity of geochemical processes. In contrast, nonlinear models such as Random Forest, MLP, and SVR are capable of modelling interactions and non-additive effects among elements, allowing them to better represent the underlying geochemical system. The observed improvement in validation performance, particularly the approximately 0.20 increase in R² of Random Forest over OLS, demonstrates the advantage of nonlinear learning approaches for mineral exploration applications.

The application of SHAP provides valuable insight into the geochemical controls on model predictions and has been widely applied in geosciences for interpretable modelling and uncertainty-aware prediction [42,43]. The dominance of sulphur (S) and iron (Fe) as primary predictors is consistent with the geological setting of sulphide-hosted orogenic gold systems, where gold is commonly associated with sulphide minerals such as pyrite and arsenopyrite. Elevated concentrations of S and Fe likely indicate zones of increased sulphide abundance, which are often correlated with gold mineralization. Secondary contributions from elements such as Cu, Ni, and Mn may reflect additional geochemical processes, including trace metal substitution within sulphide minerals, hydrothermal alteration, and variations in host-rock composition.

The proposed workflow has practical implications for mineral exploration, particularly in early-stage or data-limited environments. By relying solely on multielement geochemical data, the approach provides a cost-effective method for identifying zones of potential gold enrichment without requiring extensive geological, structural, or geophysical data. The interpretability provided by SHAP supports decision-making by linking model predictions to geologically meaningful variables.

Despite its strengths, the model exhibits several limitations. The increase in prediction dispersion at higher enrichment levels suggests reduced precision in extreme conditions, which may be influenced by data imbalance, analytical uncertainty, or localized geological variability. Furthermore, the use of random data partitioning does not explicitly account for spatial dependencies within the dataset. In practice, spatial autocorrelation can influence model performance, and future studies should consider spatially aware validation strategies, such as block cross-validation, to better reflect real-world prediction scenarios. Additionally, the current model is limited to geochemical variables and does not incorporate structural, lithological, or geophysical information, which are known to influence mineralization processes.

Future work should focus on integrating multielement geochemical data with spatial and geological information to enhance predictive accuracy and robustness. The application of spatial machine learning methods, including geostatistical learning and spatial cross-validation, may provide improved generalization in exploration contexts. Expanding the framework to other deposit types and geological settings would also provide insight into its broader applicability.

5. Conclusions

This study presents a machine learning-based framework for predicting relative gold enrichment in a sulphide-hosted orogenic system using multielement geochemical data. By integrating compositional data analysis (CoDA) with a non-circular target formulation defined as ln(Au/G₁₀), where G₁₀ represents the geometric mean of selected predictor elements, the methodology ensures statistical validity and eliminates dependency between predictor variables and the response.

The comparative evaluation of models demonstrated that nonlinear machine learning algorithms consistently outperform linear baselines in capturing the complexity of geochemical relationships. Among the models tested, Random Forest achieved the highest validation performance, confirming its suitability for modelling multivariate geochemical systems characterized by nonlinear interactions and element associations.

Interpretability analysis using SHAP revealed that sulphur (S) and iron (Fe) are the most influential predictors of gold enrichment, consistent with the well-established association of gold with sulphide minerals such as pyrite and arsenopyrite in orogenic systems. Secondary contributions from elements such as Cu, Ni, and Mn further highlight the role of additional geochemical processes, including trace metal substitution, hydrothermal alteration, and host-rock variability.

It is important to note that the compositional relationships and model outcomes are specific to the selected element subset and geological context. Future work should evaluate the robustness of model performance across alternative element subsets and compositional transformations (e.g., isometric log-ratio transformations) to further assess generalizability. Overall, this study demonstrates that machine learning models, when combined with appropriate compositional data preprocessing and a rigorously defined target variable, can provide reliable and geologically interpretable predictions of gold enrichment.