Geochemical Signatures and Element Interactions of Volcanic-Hosted Agates: Insights from Interpretable Machine Learning

Abstract

To unravel the link between agate geochemistry, host volcanic rocks, and ore-forming processes, this study integrated elemental correlation analysis, interaction interpretation, and interpretable machine learning (LightGBM-SHAP framework with SMOTE and 5-fold cross-validation) using 203 in-situ element datasets from 16 global deposits. The framework achieved 99.01% test accuracy and 97.4% independent prediction accuracy in discriminating host volcanic rock types. Key findings reveal divergence between statistical elemental correlations and geological interactions. Synergies reflect co-migration/co-precipitation, while antagonisms stem from source competition or precipitation inhibition, unraveling processes like stepwise crystallization. Rhyolite-hosted agates form via a “crust-derived magmatic hydrothermal fluid—medium-low salinity complexation—multi-stage precipitation” model, driven by high-silica fluids enriching Sb/Zn. Andesite-hosted agates follow a “contaminated fluid—hydrothermal alteration—precipitation window differentiation” model, controlled by crustal contamination. Basalt-hosted agates form through a “low-temperature hydrothermal fluid—basic alteration—progressive mineral decomposition” model, with meteoric water regulating Na-Zn relationships. Zn acts as a cross-lithology indicator, tracing crust-derived fluid processes in rhyolites, feldspar alteration intensity in andesites, and alteration timing in basalts. This work advances volcanic-agate genetic studies via “correlation—interaction—mineralization model” coupling, with future directions focusing on large-scale micro-area elemental analysis.

1. Introduction

Since systematic studies on agate’s chemical and mineralogical properties began in the 19th century, current research confirms that its diversity is determined by the sources and formation mechanisms of ore-forming fluids [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Although the majority of global agate deposits are associated with volcanic rocks such as basalt, andesite, and rhyolite, agates also occur in a wider variety of host rocks, including metamorphic [8], sedimentary [18], and even granitic rocks [19]. This diversity of host environments provides valuable insights into the formation settings and geochemical evolution of agates. Their genesis involves the siliceous enrichment during the cooling of post-magmatic hydrothermal fluids, while some deposits formed as alluvial placer deposits through weathering and transportation processes [4,10,20,21]. However, consensus remains elusive regarding the classification criteria for the volcanic rock types hosting agate, as well as their formation processes and mechanisms [3,4,5,7,15,16,19,22,23,24,25,26,27,28,29,30,31,32]. Element data from agates of different origins reveal comparable concentration levels for most chemical elements, suggesting similar formation conditions [1]. Deciphering the geochemical heterogeneities of agate hosted in distinct volcanic rocks illuminates the formation mechanisms of volcanic rock—agate systems.

Recent advances in micro-area in-situ techniques have yielded large major and trace element datasets for single-crystal minerals, fueling machine learning applications in mineralization type discrimination [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49]. Machine learning demonstrates remarkable capability in processing complex geochemical signatures, as evidenced by its successful applications in analyzing element contents of minerals like apatite, zircon, and sphalerite to distinguish deposit types, identify mineralized zones, and predict mineralization potential [34,38,40,44,48]. However, a critical limitation is that these studies often overlook inter-elemental interactions, which hampers geological interpretation.

Conventional statistical methods (e.g., correlation analysis, PCA) and classical machine learning tools are primary for deciphering patterns in geochemical, mineralogical, and petrological data. Though effective in identifying macroscopic trends (e.g., elemental enrichment/depletion associations) and boosting predictive accuracy, they rarely reveal the mechanisms by which specific features drive geological processes. Traditional ML feature importance metrics can flag “significant” elements for ore deposit classification or mineralization discrimination but cannot quantify context-dependent contributions such as how major and trace elements influences shift with concentration gradients to exert subtle yet critical regulatory effects on mineralization. In contrast, SHAP (SHapley Additive exPlanations) analysis [50,51] addresses these limitations by quantifying individual features’ directional and magnitude contributions to predictions, enabling refined interpretation of complex model outputs [52]. In geology, SHAP is predominantly applied to remote sensing data for dynamic prediction of geological hazards and analyzing the evolution of their driving factors [53,54,55,56]. Notably, this interpretive power—largely untapped in mineralogy—can explicitly identify elemental synergies or antagonisms, thereby elucidating dynamic geochemical patterns during mineralization.

For agates, scarce high-precision data and class imbalances challenge small-sample classification [15]. Here, we focus on major and trace elements of agates hosted in diverse volcanic rocks, comparing 11 common ML models to identify Light Gradient Boosting Machine (LightGBM) as the optimal geochemical-based classifier, with eXtreme Gradient Boosting (XGBoost) validating robustness. Critically, we pioneer the use of SHAP (an interpretable ML method) to reveal complex relationships between elemental geochemistry and agate classification, exploring inter-elemental synergies and individual element contributions to single-sample predictions.

Compared with our prior two-stage random forest-based classification [15], which effectively classified agates (accuracy = 0.9524) but lacked mechanistic explanations for why elements like U, Sb, or Sr drive outcomes, this study represents a breakthrough. SHAP analysis not only validates classification reliability but also uncovers key elemental interaction networks and their geochemical implications, establishing a “data-driven-geochemical validation” paradigm. This shift from mere classification to mechanistic interpretation overcomes the core limitation of “black-box” models, offering novel insights into agate-formation processes across volcanic environments.

2. Data Preparation and Interpretable Machine Learning Methods

2.1. Data Collection and Preparation

To ensure the reliability and validity of the dataset, agate sample data were carefully classified following published literature, with all element data derived from micro-area in-situ analyses. A total of 203 independent major and trace element datasets from 16 deposits (Figure 1 and Figure 2a; Supplementary Table S1) were compiled. The robustness of the model was tested using 77 test datasets derived from the research team’s previous studies (‘Test’ in Figure 2a,b; Supplementary Table S2). These out-of-sample data were specifically used for model testing and strictly excluded from both the training and testing sets of model development to ensure the robustness of the model analysis.

This dataset includes comprehensive element analyses of agates, incorporating 18 most frequently measured major and trace elements categorized into large ion lithophile elements (LILE) and high field strength elements (HFSE), including K, Sr, Cs, Ba, Ti, U (Figure 3a); other lithophile elements, including Na, Mg, Al, Ca, Sc (Figure 3b) and siderophile and chalcophile elements, including Cr, Mn, Fe, Co, Cu, Zn, Sb (Figure 3c). Such classification offers a unified and optimized dataset for subsequent analyses.

To guarantee the reliability of data, values beneath the detection limit (BDL) were given extremely low values, and missing data were filled in using median values. Raw dataset transformation is essential to mitigate misinterpretation and overfitting risks. To avoid compromising the interpretability of feature relationships, maintain consistency in the cross-model comparative framework, preserve inherent magnitude relationships among the elements, and facilitate direct cross-model comparisons of feature importance, Z-score normalization was ultimately selected. Z-Score standardization normalized data to a mean of 0 and standard deviation of 1, preserving inter-feature relationships, minimizing outlier impacts, and maintaining original distributions. Data preprocessing also included Synthetic Minority Over-sampling Technique (SMOTE) to address class imbalance. SMOTE enhances minority samples by alleviating data overlap, minimizing noise, and avoiding overgeneralization and high variance issues common in existing methods [65].

2.2. Machine Learning Methods

2.2.1. Liner Models

Logistic regression (LR) is a linear classification algorithm that uses a sigmoid function to constrain outputs between 0 and 1. Employing maximum likelihood estimation, it is suitable for multi-class classification tasks [66].

Linear Discriminant Analysis (LDA) is a supervised method for low-dimensional classification, reducing complexity in high-feature datasets using class mean differences. It assumes Gaussian-distributed data and accurate covariance estimation, with performance degraded by outliers or high dimensionality.

2.2.2. Tree-Based Models

The Decision Tree, a fundamental “weak classifier”, serves as the building block for ensemble algorithms such as LightGBM, XGBoost, and random forest. It builds a tree structure to output conditional outcomes and their probabilities, selecting optimal features as root nodes and recursively repeating this to form a complete decision tree [67].

Random Forest is an ensemble classifier with multiple decision trees [67], where each tree is trained on bootstrapped data and uses random feature subsets for optimal splitting, with final predictions via majority voting.

XGBoost, an advanced gradient boosting algorithm with native missing value handling, enhances traditional boosting via Newton-based loss optimization, L1/L2 regularization, and tree complexity penalties to avoid overfitting [68]. It utilizes second-order gradients, parallel processing, and adaptive regularization, iteratively optimizing a regularized objective function to aggregate tree outputs for high-accuracy predictions [69], suiting large-scale classification with balanced accuracy and efficiency.

AdaBoost (Adaptive Boosting), an ensemble algorithm integrating weak learners to build high-precision models [70,71], iteratively adjusts training sample weights. It initializes equal sample weights, increases weights for misclassified samples to focus subsequent models on error correction, and repeats until predefined learners or accuracy is reached, with final predictions via weighted aggregation [72]. It reduces bias through iterative training and variance via ensembling [73], requiring fewer hyperparameters and lower computation than XGBoost but being more sensitive to noise [74].

LightGBM is an efficient gradient boosting framework for large-scale high-dimensional datasets. It uses EFB to combine non-co-occurring features for dimensionality reduction and optimized feature selection, and Gradient-based One-Side Sampling (GOSS) to prioritize large-gradient samples (fixed top proportion) for enhanced efficiency and accuracy [55]. Compared to other ensemble tree models, it retains original features of large datasets with robust performance.

2.2.3. Other Models

Support Vector Machine (SVM), a key supervised method for regression/classification [75], performs well in high-dimensional spaces, using support vectors to construct hyperplanes for reliable predictions even with limited data [76].

Multi-Layer Perceptron (MLP) comprises input, output, and hidden layers with interconnected neurons, using weights/biases and activation functions for non-linear mapping [41]. Optimized via backpropagation, it excels in complex tasks with sufficient data but requires architecture tuning.

Naïve Bayes, a simple method based on Bayes’ theorem assuming attribute conditional independence given class labels, often achieves satisfactory classification accuracy despite its simplicity relative to complex classifiers [44].

K-Nearest Neighbors (KNN), a supervised method determining optimal K via nearest neighbor averaging [77], efficiently performs classification/regression by computing target averages from training neighbors using feature similarity, with K optimized via cross-validation [78]; inference assigns classes by similarity for dual prediction capabilities.

2.2.4. SHAP

SHAP (Shapley Additive Explanations) assigns importance scores by evaluating each feature’s contribution to model outputs, enabling global and local explanations of black-box models [56]. It uses additive feature attribution, with model output as a linear sum of input variable contributions [79], where SHAP values quantify individual feature impacts on sample predictions. Herein, SHAP ranks key elements influencing agate type prediction, providing comprehensive global and local interpretations.

2.3. Machine Learning Model Construction

Using 18 common element concentrations in agates, a machine learning workflow (Figure 4) was implemented with model construction in three sequential stages, utilizing Python v3.8.5 libraries for both models and the SMOTE algorithm.

• Stage 1: Data Preprocessing

Concentration data for 18 elements in rhyolite-, andesite-, and basalt-hosted agates were collected. Missing values were imputed with medians. Values below/above the detection limit are replaced with extremely low/high values. Feature selection used a hybrid filter method combining variance thresholding and mutual information analysis. After SMOTE augmentation, the dataset was split into training and testing sets at an 8:2 ratio.

• Stage 2: Machine Learning Model Construction and Optimization

This stage involved initial model selection with hyperparameter tuning via grid search, followed by cross-validation and performance evaluation through comparative analysis of linear, tree-based, and other architectures. To mitigate instrument measurement biases, multi-source literature datasets under varying conditions were integrated, with alignment preprocessing for missing data from diverse statistical standards and exclusion of unmatched samples to ensure dataset consistency. A stable model was selected, prioritizing lightweight, parsimonious methods with low computational cost (entire process < 1 min) and high interpretability, suitable for the dataset scale and facilitating replication. Ablation studies on main/auxiliary models and out-of-sample prediction verified robustness and reliability.

• Stage 3: Interpretability and Agate-Formation Mechanism Analysis

SHAP supported both global and local interpretations. Globally, it assessed element importance, the impacts of element combinations (via dependence plots), and inter-element interactions across agate types. Locally, force plots visualized how individual elements influenced sample predictions, aiding exploration of agate-formation mechanisms.

3. Results

3.1. Filter-Based Feature Selection

Filter-based feature selection used feature variance and mutual information (Figure 5). Treating elements as features, Figure 5a shows feature variance (horizontal axis) reflecting concentration dispersion: Na, Mn, K, Ca, Al, Fe, and Mghave high variances (significant inter-sample differences), while Sc, U, Cr, and Co have low variances (stable distributions). Figure 5b (horizontal axis) presents mutual information with agate classification—higher values indicate greater predictive importance: Sb, Sr, and U have high mutual information, whereas Al and Mn have lower values.

Feature selection integrated data dispersion, predictive importance, and geochemical significance to retain elements explaining agate classification and formation-related behaviors while removing redundancy. Mg, Ba, and Cs were retained despite low mutual information (Figure 5b) due to high variance (Figure 5a) and significant content differentiation among the agate (Figure 3a,b). Fe, with “high variance–low mutual information” but clear content differentiation (Figure 3c) and its role as a common coloring element, was retained. In contrast, Al and Mn (also “high variance–low mutual information”) were excluded for low inter-type differentiation (Figure 3b,c), numerous outliers, and redundant/noisy information interfering with learning. After screening, 16 elements were selected for subsequent model construction and interpretable analyses.

3.2. Classifier Comparison

In the agate classification study utilizing elemental features, 11 rigorously optimized classifiers were compared for performance (

Table 1. Summary of average performance scores of models based on 16 selected elements.

Classifier		Accuracy	Precision (Weighted)	Recall (Weighted)	F1 (Weighted)	F1 (Macro)	Kappa	AUC (Macro)	AUC (Micro)	AUPR	G-Mean	MAE
Logistic Regression	Mean	0.9460	0.9637	0.9460	0.9489	0.8859	0.8632	0.9811	0.9812	0.9375	0.9725	0.1081
	SD	0.0265	0.0112	0.0265	0.0218	0.0456	0.0559	0.0262	0.0168	0.0621	0.0137	0.0086
LDA	Mean	0.9068	0.9355	0.9068	0.9139	0.8151	0.7719	0.9600	0.9624	0.8583	0.9521	0.0705
	SD	0.0432	0.0402	0.0432	0.0403	0.0880	0.1003	0.0368	0.0192	0.0904	0.0225	0.0162
Decision Tree	Mean	0.9752	0.9776	0.9752	0.9748	0.9562	0.9296	0.9631	0.9850	0.9407	0.9704	0.0165
	SD	0.0177	0.0167	0.0177	0.0186	0.0345	0.0523	0.0494	0.0156	0.0644	0.0256	0.0103
Random	Mean	0.9950	0.9952	0.9950	0.9948	0.9915	0.9860	1.0000	0.9999	1.0000	0.9908	0.0349
Forest	SD	0.0112	0.0108	0.0112	0.0117	0.0189	0.0313	0.0000	0.0001	0.0000	0.0206	0.0055
XGBoost	Mean	0.9901	0.9913	0.9901	0.9901	0.9831	0.9733	1.0000	0.9996	1.0000	0.9883	0.0167
	SD	0.0135	0.0121	0.0135	0.0136	0.0232	0.0367	0.0000	0.0007	0.0000	0.0199	0.0044
AdaBoost	Mean	0.9802	0.9840	0.9802	0.9806	0.9527	0.9465	0.9972	0.9965	0.9878	0.9890	0.4077
	SD	0.0110	0.0089	0.0110	0.0109	0.0336	0.0302	0.0033	0.0053	0.0170	0.0065	0.0059
LightGBM	Mean	0.9901	0.9904	0.9901	0.9896	0.9810	0.9721	1.0000	0.9999	1.0000	0.9883	0.0068
	SD	0.0135	0.0131	0.0135	0.0143	0.0263	0.0382	0.0000	0.0002	0.0000	0.0199	0.0067
SVM	Mean	0.9756	0.9798	0.9756	0.9767	0.9461	0.9362	0.9797	0.9822	0.9313	0.9877	0.0578
	SD	0.0244	0.0211	0.0244	0.0234	0.0627	0.0639	0.0294	0.0169	0.0835	0.0123	0.0160
MLP	Mean	0.9560	0.9636	0.9560	0.9578	0.9015	0.8868	0.9831	0.9843	0.9433	0.9765	0.0469
	SD	0.0361	0.0333	0.0361	0.0348	0.0977	0.0939	0.0259	0.0144	0.0629	0.0188	0.0185
Naive Bayes	Mean	0.9459	0.9627	0.9459	0.9498	0.9084	0.8677	0.9890	0.9733	0.9145	0.9713	0.0383
	SD	0.0400	0.0207	0.0400	0.0354	0.0555	0.0851	0.0085	0.0230	0.0588	0.0232	0.0253
KNN	Mean	0.9755	0.9812	0.9755	0.9751	0.9349	0.9345	0.9995	0.9995	0.9967	0.9876	0.0147
	SD	0.0172	0.0124	0.0172	0.0188	0.0626	0.0472	0.0010	0.0005	0.0075	0.0087	0.0095

SD—means standard deviations. Bold content refers to the main machine learning models and their metrics used in this study; underlined content denotes the models and their metrics employed for validating model robustness.

). These models employed 16 elements—selected via variance and mutual information screening—from agates hosted in three major volcanic rock types.

Model performance was evaluated using 11 metrics. These included Accuracy (correct prediction ratio); for multiclass tasks, weighted precision/recall (class-wise averages weighted by sample proportion), weighted F1 (harmonic mean of these), and Macro F1 (average of per-class F1); Macro AUC (average of one-vs-all ROC AUC for class fairness), Micro AUC (global performance via binary flattened predictions), Kappa (agreement beyond chance), AUPR (true positive discrimination via precision-recall curves), and G-Mean (cube root of the geometric mean of class recall scores). All metrics were computed using sklearn.metrics (https://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics) to ensure methodological rigor, accessed on 28 June 2025.

The G-Mean, a geometric mean of class recall scores, is calculated as their cube root.

$$\mathrm{G}-\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{n}=\sqrt[3]{{\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}_1\times {\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}_2\times {\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}_3}$$

(1)

The Mean Absolute Error (MAE) maps agate types (rhyolite-hosted, andesite-hosted, basalt-hosted) to labels (0–2) and averages absolute differences between predicted and true values to gauge balanced accuracy.

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}_{\mathrm{i}}-{\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}}_{\mathrm{i}}\right|$$

(2)

where ${\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}_{\mathrm{i}}$ denotes the predicted class value and ${\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{e}}_{\mathrm{i}}$ represents the true class value.

Logistic regression achieved a mean accuracy of 0.9460 with high weighted precision (0.9637), whereas LDA showed lower overall performance (mean accuracy = 0.9068) and greater result variability (accuracy SD = 0.0432).

Among tree-based and ensemble models, random forest excelled with the highest mean accuracy (0.9950), stable performance (accuracy SD = 0.0112), and perfect Macro AUC (1.0000) and AUPR (1.0000), indicating robust classification. Decision Tree achieved 0.9752 mean accuracy, with the lowest MAE (0.0165) among single tree models but a relatively low Macro F1 (0.9562) versus ensembles. AdaBoost showed moderate performance (mean accuracy = 0.9802) but significantly higher MAE (0.4077) than other tree-based models, suggesting data distribution sensitivity.

XGBoost and LightGBM both reached 0.9901 mean accuracy with strong consistency (SD = 0.0135). LightGBM had minimal MAE (0.0068) and perfect Macro AUC/AUPR (1.0000), reflecting exceptional generalization. XGBoost, matching in accuracy, had slightly higher MAE (0.0167) but maintained perfect Macro AUC/AUPR, highlighting stability.

SVM and MLP showed moderate performance, with mean accuracies of 0.9756 and 0.9560 respectively. SVM had higher weighted precision (0.9798) but lower Macro F1 (0.9461), while MLP exhibited greater performance variability (accuracy SD = 0.0361). K-Nearest Neighbors (KNN) outperformed Naive Bayes, with higher mean accuracy (0.9755 vs. 0.9459) and low MAE (0.0147), though its Macro F1 (0.9349) was constrained by class imbalance sensitivity.

Overall, rigorously parameter-optimized ensemble models (random forest, XGBoost, LightGBM) outperformed single models, with smaller SDs indicating stronger anti-overfitting ability. LightGBM was optimal, combining the highest error control precision (MAE = 0.0068), perfect discriminative metrics (AUC, AUPR), and stable performance, well-suited to capture complex patterns in agate elemental features. XGBoost and LightGBM’s consistent accuracy, overlapping perfect AUC/AUPR, and comparable stability (similar SDs) confirmed LightGBM’s performance reliability, ensuring robust research conclusions.

3.3. Ablation Experiments and Robustness of LightGBM Model

In three-class classification with imbalanced distributions, tuned LightGBM, XGBoost, and AdaBoost were compared using F1 scores. LightGBM achieved the highest F1 (0.9974) with optimal parameters (learning_rate = 0.2, max_depth = −1, n_estimators = 50). XGBoost’s best F1 was 0.9947 (learning_rate = 0.1, max_depth = 3, n_estimators = 100), while AdaBoost reached 0.9787 (learning_rate = 1.0, n_estimators = 200). LightGBM and XGBoost outperformed AdaBoost, confirming their stronger noise resistance.

To systematically evaluate model performance across feature sets, ablation experiments were conducted using two sets—18 common element features and 16 filter-selected features—with LightGBM/XGBoost, both with and without SMOTE augmentation. Results (Figure 6; Supplementary Table S3) showed SMOTE significantly improved performance. For the 18-element set, LightGBM accuracy remained 0.9901, while XGBoost accuracy increased from 0.9801 to 0.9852; both models’ Macro AUC rose to 1.0000 (from 0.9948 and 0.9998). MAE improved, with LightGBM decreasing from 0.0089 to 0.0063 and XGBoost from 0.0244 to 0.0170. For the 16-element set, SMOTE led to perfect Macro AUC (1.0000) for both models, with MAE decreasing significantly (LightGBM: 0.0097→0.0068; XGBoost: 0.0234→0.0167), indicating excellent generalization. Overall, SMOTE combined with LightGBM/XGBoost achieved optimal performance using the 16-element feature set, providing a robust foundation for subsequent interpretability analyses.

Robustness analysis of the primary model was performed via comparison with an alternative model. In both LightGBM (Figure 7a) and XGBoost (Figure 7b), Na, Ca, Sr, U, Sb, Ba, and Sc showed consistent importance trends, with minor ranking variations. LightGBM better identified less prominent features. Na and Ca ranked eighth and fourth in XGBoost but first and second in LightGBM, indicating higher sensitivity to feature utilization.

To verify model prediction reliability, the trained LightGBM was tested on an untrained ‘Test’ dataset (Supplementary Table S2). Among 77 basalt-hosted agate samples, 75 were correctly predicted (97.4% accuracy; Supplementary Table S4), outperforming our previous two-stage random forest approach which achieved 0.813 accuracy on the same out-of-sample data [15], further validating LightGBM’s robustness.

3.4. SHAP-Derived Interpretations

3.4.1. SHAP Global Explanation

The global feature importance bar plot based on SHAP values (Figure 8) shows that among 16 common elements in agates from different volcanic rocks, Sr, U, and Zn are the most critical for classification, followed by Sc, Sb, and Ca. The remaining 10 elements play secondary roles overall but may act as key predictors for specific types. Ba and Cu strongly influence rhyolite-hosted agate classification but minimally affect andesite-hosted ones; Na and Cr significantly impact andesite-hosted agate predictions, while Cs and Fe notably affect basalt-hosted agate classifications.

3.4.2. Interaction Effect Analysis of Elements

Element interactions were visualized via dependence plots (Figure 9, Figure 10 and Figure 11). Due to small sample size potentially blurring trends, we precomputed SHAP interaction strengths (Supplementary Table S5) and Pearson correlations of SHAP values (Supplementary Table S6). For each class, samples with high absolute interaction strengths and high SHAP value correlations were prioritized for analysis.

In rhyolite-hosted agates, Ca-Sb (Figure 9a) and Zn-Sb (Figure 9b) showed pronounced synergies (concurrent increases amplified their positive classification impacts via SHAP values), while Ba-Cu (Figure 9c) and Cu-Sb (Figure 9d) exhibited antagonism (co-increases diminished such amplification).

In andesite-hosted agates, Na-Sr (Figure 10a) and U-Sr (Figure 10b) had positive interactions, whereas Cr-Sr (Figure 10c) and K-Zn (Figure 10d) showed antagonism.

In basalt-hosted agates, Sc-Zn (Figure 11a) and Na-U (Figure 11b) were characteristic positive interactions; Zn-U (Figure 11c) had the strongest antagonism, with Na-Zn (Figure 11d) showing weaker negative effects. Overall, elemental interactions were least pronounced in this class.

3.4.3. SHAP Local Explanation

The SHAP Force Plot, a widely used SHAP-based visualization tool for interpreting predictions from complex models (e.g., tree-based algorithms), vividly illustrates feature influences on predictions and clarifies the feature-driven classification decision process.

Force Plot analysis of Class 0 (rhyolite-hosted agate) showed predictions (f(x)) significantly above base value (≈−7), dominated by positive contributions (Figure 12). High-impact elements (U, Ba, K) elevated predictions; Sb (contributions: 0.0088–0.0393) acted as a Class 0 diagnostic with consistent positive effects. Despite minor negative pulls from Ca, Sr, Zn, overall predictions remained in the red region, reflecting these elements’ specific sample contributions. Positive synergies in Ca-Sb and Zn-Sb were observed in Figure 12a,b, respectively, while antagonistic interactions in Cu-Sb and Ba-Cu were revealed in Figure 12b,c and Figure 12d,e, respectively. High-contribution elements (e.g., U, Ba) dictated trends, with dynamic element balances (e.g., Ca-Sb synergy, Cu-Ba antagonism) fine-tuning outcomes, highlighting model sensitivity to multi-feature interactions.

For Class 1 (andesite-hosted agates), Sc was identified as a positive contributor despite its negative SHAP value (e.g., Sample 28: Sc = −0.4743; Figure 13a), consistent with earlier observations that feature influence direction is independent of numerical sign. Class 1 classification decisions resulted from combined multi-feature effects, with red features (positive contributions) exerting differential impacts. For instance, in Sample 42 (Figure 13b), Na, U, and Sr showed stronger positive effects than in Sample 28 (Figure 13a), weakening Cr’s relative influence—aligning with positive Na-Sr and U-Sr interactions and Cr-Sr antagonism noted in elemental synergy analysis. Notably, Cr’s contribution magnitude significantly affected the model’s prediction value (f(x)).

SHAP analysis of Class 2 (basalt-hosted agates) showed all sample predictions (f(x) = 4.23–5.84) exceeded the base value (3; Figure 14). Positive synergies were identified between Na-U (U’s positive effect amplified with Na = −0.7655 in Sample 62 vs. 68; Figure 14a,b) and Zn-Sc (Sc’s positive effect diminished as Zn turned positive in Sample 159 vs. 62; Figure 14a,c). In contrast, antagonistic interactions emerged between Zn-U and Na-Zn, evidenced by U’s amplified effect with negative Zn (Sample 159 vs. 68; Figure 14b,c) and Na’s positive value corresponding to less negative Zn (Sample 163 vs. 159; Figure 14c,d).

4. Discussion

The agates studied, hosted in rhyolites, andesites, and basalts, all occur in effusive facies volcanic rocks [1,3,4,9,12,24,57,58,59,60,61,62,63,64]. Rhyolite-hosted agates mainly formed during hydrothermal alteration post-Carboniferous-Permian volcanic activities [1,4,59,80]; andesite-hosted ones formed in the late Eocene (post-Lutetian) [9,60]; basalt-hosted agates have a broader age range (Paleoproterozoic to Cretaceous) [12,24,63]. Chemical compositions show no significant differences among different localities of agates hosted in the same type of rock.

Wall-rock alteration of rhyolite-hosted agates mainly forms clay minerals (kaolinite, montmorillonite), zeolites (clinoptilolite), iron oxides (hematite), and silica minerals (chalcedony, quartz) [1,4]; basalt alteration is dominated by chlorite, epidote, calcite, and zeolites [12,24,63]. Element release specificity during alteration is key to agate-formation mechanisms. In geological evolution, unstable volcanic glass, pyroxene, and feldspar in host rocks alter, releasing SiO₂ and alkali metals to form the basis of agate chemical composition [81,82,83,84,85]. However, variations in wall-rock composition and chemical environment induce high diversity in agate elemental composition.

4.1. Geochemical Characteristics of Agate Based on Correlation and Interaction

Traditional statistical methods often use “content correlation” to discuss elemental characteristics, calculating correlation coefficients between associated elements to reflect distribution synchrony (Figure 15). Here, “interaction” refers to elemental synergistic (co-migration, co-precipitation) or antagonistic (source competition, precipitation inhibition) effects in geological processes driven by physicochemical conditions. Correlation represents the statistical expression of elemental content, while interaction embodies its geological essence.

4.1.1. Co-Migration and Co-Precipitation Driven by Synergistic Effects

In rhyolite-hosted agates, Zn and Sb display positive correlation (0.031; Figure 15a) and interaction (Figure 9b). Their fluid inclusions have medium-low salinity (4.96–9.21 eq% NaCl [1] and 0.65–2.4 wt% (KCl) [4]), with Zn and Sb migrating as Zn-Cl⁻ and Sb-Cl⁻ complexes [86] and co-precipitating upon cooling. Fluid inclusion homogenization temperatures (80–375 °C [1,4,59,86]) reflect these complexes’ high-temperature stability and low-temperature co-precipitation tendency. Ca and Sb show negative correlation (Figure 15a) but positive synergy (Figure 9a). Ca derives from wall-rock alteration, Sb from crustal input [87]; both are transported by ore-forming fluids, inducing synergism. In relatively closed hydrothermal systems, Ca is fixed by early incorporation into calcite lattices, causing a sharp drop in Ca²⁺ activity in residual fluids [5]. Subsequently, when temperatures decrease to 150–250 °C with concurrent oxidation and pH elevation, Sb precipitates rapidly as Sb₂S₃, Sb₂O₃, or sulfosalts in agate-quartz bands [9]. Due to system closure, the two-stage precipitation shares a limited total metal pool; the preferential early crystallization of Ca directly deprives potential carrier sites for later Sb, resulting in a spatial negative correlation between Ca and Sb contents.(correlation coefficient −0.13; Figure 15a).

In andesite-hosted agates, plagioclase alteration releases Na⁺ and Sr²⁺, which co-migrate as NaCl and SrCl₂ and co-precipitate, showing positive correlation (Figure 15b) and interaction (Figure 10a). U, stable as UO₂(CO₃)₃⁴⁻ [88,89], co-migrates with Sr²⁺ (positive interaction) but enriches later than Sr²⁺ and CO₃²⁻ precipitation in oxidizing alkaline environments [90]; precipitation window dislocation induces their negative content correlation.

In basalt-hosted agates, Sc and Zn exhibit positive correlation (Figure 15c) and synergism (Figure 11a), as Sc³⁺ and Zn²⁺ released by basaltic rock chloritization and albitization co-migrate and precipitate in low-salinity fluids via hydroxyl-silicate-hydrated mixed complexes [91,92]. Na, released during basaltic mineral alteration [93], co-enriches and precipitates with U in hydrothermal fluids, showing positive content correlation and synergism.

4.1.2. Source Competition and Precipitation Inhibition Driven by Antagonistic Effects

In rhyolite-hosted agates, crust-derived Sb [94] and mantle-derived Cu [95] exhibit negative correlation (r = −0.13; Figure 15a) and antagonism (Figure 9d) due to source competition. Both Ba (from crust-derived material or meteoric water [96]) and Cu migrate/precipitate with Cl⁻ during mineralization; despite statistical positive correlation (Figure 15a), they show geological antagonism (Figure 9c) from source competition.

In andesite-hosted agates, Cr and Sr show positive correlation (Figure 15b) due to synchronous magmatic differentiation during wall-rock chloritization and albitization. Sr (incompatible) remains in fluids, while compatible Cr³⁺ forms hydroxyl complexes (e.g., Cr(OH)₂⁺, Cr(OH)₃) that migrate/precipitate preferentially, causing antagonism with Sr (Figure 10c). K-feldspar alteration releases abundant K⁺, which coexists with magmatic hydrothermal Zn in agate-forming systems [9], inducing positive content correlation (Figure 15b). However, high K⁺ reduces Zn-Cl complex stability and Zn²⁺ activity [97], leading to their antagonism (Figure 10d).

In basalt-hosted agates, Zn from wall-rock alteration precipitates preferentially during magma cooling, while U from late basaltic hydrothermal fluids adsorbs on silica gel as UO₂(SiO₃)₂·nH₂O [88,89]. Synchronous hydrothermal-alteration changes induce their positive correlation (Figure 15c), but precipitation mechanism differences cause antagonism (Figure 11c). Early albitization releases abundant Na⁺ with limited ferromagnesian mineral decomposition, forming high-Na, low-Zn fluids [98]; late chloritization drives ferromagnesian breakdown, releasing large Zn²⁺, while weakened plagioclase alteration reduces Na⁺ input sharply, yielding high-Zn, low-Na fluids [98]. This induces Na-Zn negative correlation (Figure 15c) and antagonism (Figure 11d).

4.2. Metallogenic Model of Agates in Volcanic Rocks

In the late hydrothermal stage of acidic magma, high-silica, volatile-rich environments [1,4,59] enrich residual fluids in incompatible elements (Sb, Zn). Both the positive correlation/interaction of Zn-Sb and the negative correlation/positive synergism of Ca-Sb are governed by magmatic hydrothermal evolution. Rhyolite-hosted agates follow the “crust-derived magmatic hydrothermal fluid—medium-low salinity complexation—multi-stage precipitation” model, featuring three key characteristics: (1) medium-low salinity complexation, reflected by Zn-Sb positive correlation/interaction; (2) stepwise crystallization, indicated by Ca-Sb negative correlation/positive synergism; and (3) crust-mantle source competition, revealed by Cu-Sb negative correlation/antagonism. This mechanism is further supported by relatively high crust-derived oxygen isotope signals (δ¹⁸O ≈ +18.7‰~+33.3‰) [4,5,21,99,100].

In the late hydrothermal stage of intermediate magma, oceanic crust-continental crust contamination enriches Sr and Na. The positive correlation/synergism of Na-Sr and positive correlation/antagonism of K-Zn reflect combined hydrothermal and wall-rock alteration effects in andesite-hosted agate formation. Andesite-hosted agates follow the “contaminated fluid—hydrothermal alteration—precipitation window differentiation” model, featuring four key aspects: (1) positive correlation/synergism of Na-Sr (released by feldspar alteration) as the core; (2) negative correlation/positive interaction of U-Sr (precipitation timing differences); (3) positive correlation/antagonism of Cr-Sr (preferential mineral crystallization); and (4) positive correlation/antagonism of K-Zn (complex stability competition). Oxygen isotopes δ¹⁸O (δ¹⁸O ≈ +17.5‰~+33.4‰) with mixed oceanic crust-continental crust signals [5] confirm fluid-plagioclase material exchange, supporting the genetic basis of their positive correlation and synergism.

During the long-term cooling in the late hydrothermal stage of basic magma, Sc-Zn positive correlation/synergism reflects element release from basic alteration, while Zn-U positive correlation/antagonism relates to late basic magma hydrothermal differentiation. Na-Zn negative content correlation and mutual antagonism associate with earlier feldspar decomposition versus later ferromagnesian mineral breakdown during wall-rock alteration. Basalt-hosted agates follow the “low-temperature hydrothermal fluid—basic alteration—progressive mineral decomposition” model, featuring four key characteristics: (1) Sc-Zn positive correlation/synergism (co-migration during alteration); (2) Zn-U positive correlation/antagonism (precipitation mechanism differences); (3) Na-U positive correlation/interaction (co-enrichment in hydrothermal fluids); and (4) Na-Zn negative correlation/antagonism (mineral decomposition timing). Meteoric water signals in oxygen isotopes (δ¹⁸O ≈ +10.4‰~+25.8‰) [3,5,20,101] support wall-rock progressive decomposition by hydrothermal fluids and compositional differences from temperature-dependent gradual crystallization in basalt-hosted agate formation.

It identifies Zn as a cross-lithology tracer for fluid evolution and alteration processes via its interactions with other elements. In rhyolite-hosted agates, Zn-Sb positive correlation/interaction reflects synergistic enrichment migration in crust-derived magmatic hydrothermal environments; in andesite-hosted agates, Zn-Na interaction sensitively indicates feldspar alteration intensity; in basalt-hosted agates, Zn-Sc positive correlation/synergism and Zn-Na negative correlation/antagonism reflect Sc³⁺-Zn²⁺ co-release during basic rock alteration and timing differences in progressive decomposition of feldspars and ferromagnesian minerals, thus forming a cross-lithology “indicator” for alteration intensity.

5. Conclusions

Integrating elemental correlation, interaction analysis, and interpretable machine learning, this study explores geochemical behaviors of characteristic elements in volcanic-hosted agates and their coupling with formation mechanisms.

Elemental statistical correlations and geological interactions diverge: synergies reflect co-migration/precipitation, antagonisms derive from source competition or precipitation inhibition, revealing processes like stepwise crystallization.

Rhyolite-hosted agates form via the “crust-derived magmatic hydrothermal fluid—medium-low salinity complexation—multi-stage precipitation” model, driven by high-silica, volatile-rich fluids enriching Sb/Zn, regulated by fluid-meteoric water mixing. Andesite-hosted agates follow the “contaminated fluid—hydrothermal alteration—precipitation window differentiation” model, controlled by crustal contamination and fluid-alteration coupling. Basalt-hosted agates form via the “low-temperature hydrothermal fluid—basic alteration—progressive mineral decomposition” model, with meteoric water-dominated environments restricting complexation and governing Na-Zn relationships.

Zn acts as a cross-lithology indicator: in rhyolites, Zn-Sb interaction indicates crust-derived fluid processes; in andesites, Zn-Na interaction reflects feldspar alteration intensity; in basalt, Zn-Sc synergism and Zn-Na antagonism indicate basic alteration and mineral decomposition timing.

This work, via “correlation—interaction—mineralization model” coupling, advances volcanic-agate genetic studies and mineral geochemical decipherment. Future research should prioritize large-scale micro-area elemental analysis to capture richer mineralization information.