Exploration
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Joe Alexis Gonzalez-Vasquez
Abstract
Traditional geostatistical methods such as kriging exhibit limitations by assuming linear and symmetric dependencies, which can lead to smoothed estimates and the loss of local variability. To address these issues, this study applies Archimedean copulas (Clayton, Gumbel, and Frank) for the estimation ...
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Traditional geostatistical methods such as kriging exhibit limitations by assuming linear and symmetric dependencies, which can lead to smoothed estimates and the loss of local variability. To address these issues, this study applies Archimedean copulas (Clayton, Gumbel, and Frank) for the estimation of copper ore grades in a deposit located in Peru. A total of 5,654 composites, each 15 meters in length, were obtained from 185 diamond drill holes. The data were transformed to a uniform scale to allow for copula fitting. Dependence structures were modeled by lag distance, with the dependence parameter fitted using fifth-degree polynomials, and three-dimensional conditional estimation was implemented. Results indicate that ordinary kriging yielded RMSE = 0.161, MAE = 0.104, R2 = 0.692, and a correlation of 0.861. The Clayton copula slightly improved these metrics (RMSE = 0.154, MAE = 0.101, R2 = 0.717, R = 0.871), while the Gumbel copula captured higher local variability (RMSE = 0.161, MAE = 0.116, R2 = 0.692, R = 0.855). The Frank copula achieved the best performance with RMSE = 0.137, MAE = 0.090, R2 = 0.778, and R = 0.905. In conclusion, Archimedean copulas significantly enhance geostatistical estimation by better capturing spatial dependence, offering a robust alternative to classical geostatistical methods.
Exploration
Marco Antonio Cotrina Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Joe Alexis Gonzalez-Vasquez; Kevin Daniel Rondo-Jalca
Abstract
The classification of mineral resources significantly impacts mine planning, economic feasibility, and regulatory compliance. Despite its importance, such classification frequently depends on the subjective judgment of the Qualified Person (QP), owing to the absence of internationally standardized technical ...
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The classification of mineral resources significantly impacts mine planning, economic feasibility, and regulatory compliance. Despite its importance, such classification frequently depends on the subjective judgment of the Qualified Person (QP), owing to the absence of internationally standardized technical criteria for delineating resource categories. To mitigate this limitation, an innovative methodology integrating clustering based on Riemannian geometry with machine learning techniques was developed for mineral resource classification. A database of 5,654 composited samples from 185 diamond drill holes in a copper deposit in central Peru was utilized to classify 318,443 blocks. Copper grades were estimated through Ordinary Kriging (RMSE = 0.102; MAE = 0.069), generating geostatistical variables kriging variance, average distance to samples, and number of samples that served as input features for the classification. Clustering was performed using both classical KMeans and Riemannian KMeans, followed by spatial smoothing via XGBoost and Random Forest algorithms. Absolute coordinates were incorporated to address spatial discontinuities in classification outputs. The combination of the Riemannian model with Random Forest produced the highest classification performance, with a Silhouette index of 0.26 and a Davies-Bouldin index of 0.72. The resulting metal content was estimated at 4.24 Mt of copper at 0.44% grade (measured), 6.49 Mt at 0.34% Cu (indicated), and 7.68 Mt at 0.32% Cu (inferred), demonstrating close alignment with QP estimates while exhibiting improved spatial coherence. In summary, the Riemannian-based approach outperformed classical KMeans and conventional classification methods, providing a more robust, objective, and globally consistent alternative.
Exploration
Hamed Norouzi; Aliakbar Daya
Abstract
Estimating mineral reserves in exploration or extraction projects is a critical and challenging process. It must be conducted precisely, regardless of the mining scale and mineral type. With the growing significance of mineral resources in economic and industrial development, the importance of adopting ...
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Estimating mineral reserves in exploration or extraction projects is a critical and challenging process. It must be conducted precisely, regardless of the mining scale and mineral type. With the growing significance of mineral resources in economic and industrial development, the importance of adopting advanced technologies in mineral assessment has also surged. Modern spatial grade modeling techniques can play a pivotal role in decision-making processes. This study aims to compare the performance and capabilities of two popular machine learning methods, including Gaussian Process Regression (GPR) and Multilayer Perceptron Artificial Neural Network (MLP-ANN) in spatial grade modeling of copper at the Chehel Kureh Copper deposit. The dataset comprises 42 drill holes with an average copper grade of 0.18%. Each core sample data point includes seven variables: three spatial coordinates (X, Y, and Depth), lead grade, zinc grade, lithology and copper grade, which serves as the target variable. The Gaussian Process Regression (GPR) and Multilayer Perceptron (MLP-ANN) neural network were employed for copper grade estimation. To make a better assessment, the hyperparameters of both models were optimized using the Bayesian Optimization algorithm. The results showed that the Gaussian Process Regression outperformed MLP-ANN, achieving an RMSE of 0.04 and a coefficient of determination (R²) of 0.89 compared to an RMSE of 0.05 and a coefficient of determination (R²) of for MLP-ANN, suggest the superiority of the Gaussian Process Regression method in estimating copper grade spatial variability.
Exploration
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Jorge Chira-Fernandez; Cesar De la cruz-Poma; Solio Marino Arango-Retamozo
Abstract
The sustained increase in mining waste, particularly in the form of tailings, poses a significant environmental and economic challenge, especially in contexts where these deposits retain residual metal content. This study assessed the gold potential of Tailings Deposit I at La Cienega (Peru) by integrating ...
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The sustained increase in mining waste, particularly in the form of tailings, poses a significant environmental and economic challenge, especially in contexts where these deposits retain residual metal content. This study assessed the gold potential of Tailings Deposit I at La Cienega (Peru) by integrating geostatistical estimation and machine learning models optimized through metaheuristic algorithms. The methodology involved geochemical characterization, three-dimensional estimation using Ordinary Kriging (OK) as a geostatistical method, and prediction of gold grades through three models: XGBoost optimized with Particle Swarm Optimization (XGB+PSO), Support Vector Regression with Genetic Algorithm (SVR+GA), and Random Forest optimized using Ant Colony Optimization (RF+ACO). Estimates were validated using Leave-One-Out cross-validation and performance metrics including RMSE, MAE, Bias, and correlation coefficient (R). The RF+ACO model achieved an RMSE of 0.32 ppm, MAE of 0.24 ppm, Bias of 0.006, and an R value of 0.56. Average predicted grades ranged from 1.14 to 1.33 ppm, with estimated gold contents between 981.00 and 1,147.12 ounces, while OK yielded 1,028.77 ounces at an average grade of 1.19 ppm. These findings suggest that properly optimized machine learning models can provide reasonable estimates of metal content in tailings, particularly in settings characterized by high spatial heterogeneity and limited geological continuity.
Exploration
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Johnny Henrry Ccatamayo-Barrios; Joe Alexis Gonzalez-Vasquez; Teofilo Donaires-Flores; Maxgabriel Alexis Calla-Huayapa
Abstract
This work aimed to categorize mineral resources in a copper deposit in Peru, using a machine learning model, integrating the K-prototypes clustering algorithm for initial classification and Random Forest (RF) as a spatial smoother. A total of 318,443 blocks were classified using geostatistical and geometric ...
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This work aimed to categorize mineral resources in a copper deposit in Peru, using a machine learning model, integrating the K-prototypes clustering algorithm for initial classification and Random Forest (RF) as a spatial smoother. A total of 318,443 blocks were classified using geostatistical and geometric variables derived from Ordinary Kriging (OK) such as kriging variance, sample distance, number of drillholes, and geological confidence. The model was trained and validated using precision, recall, and F1-score metrics. The results indicated an overall accuracy of 97%, with the measured category achieving 98% precision and an F1-score of 0.98. The total estimated tonnage was 5,859.36 Mt, distributed as follows: 1,446.13 Mt (measured), 2,249.22 Mt (Indicated), and 2,164.01 Mt (Inferred), with average copper grades of 0.43%, 0.33%, and 0.31% Cu, respectively. Compared to the traditional geostatistical methods, this hybrid approach improves classification objectivity, spatial continuity, and reproducibility, minimizing abrupt transitions between categories. The RF model proved to be a robust tool, reducing classification inconsistencies and better capturing geological uncertainty. Future studies should explore hybrid models (K-means with RF, ANN with K-Prototypes, gradient boosting, and deep learning) and incorporate economic variables to optimize decision-making in resource estimation.
Exploration
Babak Sohrabian; Abdullah Erhan Tercan
Abstract
Mineral Resources have commonly been estimated through the kriging method that assigns weights to the samples based on variogram distance to the estimation point without considering their values. More robust estimators such as spatial copulas are promising tools because they consider both distance ...
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Mineral Resources have commonly been estimated through the kriging method that assigns weights to the samples based on variogram distance to the estimation point without considering their values. More robust estimators such as spatial copulas are promising tools because they consider both distance and sample values in determining weights. The purpose of this study is to demonstrate the effectiveness of the Gaussian copulas (GC) by estimating the copper grade values in the Sungun porphyry copper deposit located in Iran. Performance of the method was compared to ordinary kriging (OK) and indicator kriging (IK) by running the Jackknife test of cross-validation. The metrics used in measuring performance of the methods are global accuracy and precision of the distribution of the estimates, error statistics, and variability for globally accurate and precise estimates. The case study shows advantages of GC over OK and IK by producing globally accurate and precise estimates with acceptable error statistics and variability.
Exploration
Jairo Jhonatan Marquina Araujo; Marco Antonio Cotrina Teatino; José Nestor Mamani Quispe; Eduardo Manuel Noriega Vidal; Juan Antonio Vega Gonzalez; Juan Vega-Gonzalez; Juan Cruz-Galvez
Abstract
The objective of this research work to employ machine learning techniques including Multilayer Perceptron Artificial Neural Networks (ANN-MLP), Random Forests (RFs), Extreme Gradient Boosting (XGBoost), and Support Vector Regression (SVR) to predict copper ore grades in a copper deposit located in Peru. ...
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The objective of this research work to employ machine learning techniques including Multilayer Perceptron Artificial Neural Networks (ANN-MLP), Random Forests (RFs), Extreme Gradient Boosting (XGBoost), and Support Vector Regression (SVR) to predict copper ore grades in a copper deposit located in Peru. The models were developed using 5654 composites containing available geological information (rock type), as well as the locations of the samples (east, north, and altitude) and secondary ore grade (Mo) obtained from drilling wells. The data was divided into 10% (565 composites) for testing, 10% (565 composites) for validation, and 80% (4523 composites) for training. The evaluation metrics included SSE (Sum of Squared Errors), RMSE (Root Mean Squared Error), NMSE (Normalized Mean Squared Error), and R² (Coefficient of Determination). The XGBoost model could predict the ore grade with an SSE of 15.67, RMSE = 0.17, NMSE = 0.34, and R² = 0.66, the RFs model with an SSE of 16.40, RMSE = 0.17, NMSE = 0.36, and R² = 0.65, the SVR model with an SSE of 19.94, RMSE = 0.19, NMSE = 0.43, and R² = 0.57, and the ANN-MLP model with an SSE = 21.00, RMSE = 0.19, NMSE = 0.46, and R² = 0.55. In conclusion, the XGBoost model was the most effective in predicting copper ore grades.
Exploration
H. Sabeti; F. Moradpouri
Abstract
The geo-statistical simulation algorithms for continuous spatial variables have been used widely in order to generate the statistically-honored models. There are two main algorithms doing the continuous variable simulation, Sequential Gaussian Simulation (SGS) and Direct Sequential Simulation (DSS). ...
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The geo-statistical simulation algorithms for continuous spatial variables have been used widely in order to generate the statistically-honored models. There are two main algorithms doing the continuous variable simulation, Sequential Gaussian Simulation (SGS) and Direct Sequential Simulation (DSS). The main advantage of the DSS algorithm against the SGS algorithm is that in the DSS algorithm no Gaussian transformation of the original data is made. In this work, these two simulation algorithms are explained, and their applications to a 3D spatial dataset are deeply investigated. The dataset consists of the porosity values of 16 vertical wells extracted from an actual cube obtained by a seismic inversion process. One well data is excluded from the simulation process for the blind well test. Comparison between the histograms show that the histogram reproduction is slightly better for the SGS algorithm, although the population reproductions are the same for both SGS and DSS results. The DSS algorithm reproduce the mean of input data closer to the mean of well data compared to that of the SGS algorithm. Considering one realization from each simulation algorithm, the RMS error corresponding to all simulated cells against the real values is approximately equal for both algorithms. On the other hand, the error show a slightly less value when the mean of 100 realizations of the DSS result is considered.
