Gaussian copulas for spatial estimation of ore grade in a copper deposit

Cotrina-Teatino M.A.; Marquina-Araujo J.J.; Mamani-Quispe J.N.; Arango-Retamozo S.M.; Gonzalez-Vasquez J.A.; Ortiz-Quintanilla S. · International Journal of Mining and Geo-Engineering (2026) · DOI: 10.22059/ijmge.2025.398485.595277

Resumen

This study evaluates the effectiveness of the Gaussian copula (GC) in estimating copper grades in a Peruvian copper deposit, comparing its performance with Ordinary Kriging (OK). The methodology was implemented in Python 3.11.7 and Jupyter Notebook 4.2.5. Model accuracy was assessed through 5-fold spatial cross-validation using metrics such as Mean Squared Error (MSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), and Variance. The estimation was conducted using a database of 5,654 composites. The results demonstrate that GC outperforms OK, achieving an MSE of 0.0882, an MAE of 0.1956, an MBE of 0.0394, and a variance of 0.0369. These values indicate that GC provides more accurate and less biased estimates, capturing local grade variability more effectively than OK. Although GC shows slightly higher estimation variance (0.0369 vs. 0.027), it successfully captures the maximum copper grade observed in the real data (2.95%), unlike OK (1.62%), suggesting that GC mitigates the excessive smoothing of OK while still maintaining a centered and stable distribution. In conclusion, the GC method emerges as a robust alternative to OK, offering improved precision, better spatial representation, and enhanced reliability in mineral resource estimation. Its implementation in Python also promotes greater accessibility and reproducibility, reinforcing its value as a practical tool in geostatistics.

Instituciones: Universidad Nacional de Trujillo; Universidad Nacional del Altiplano; Universidad Nacional Jorge Basadre Grohmann