Estimation of ore grades using Archimedean copulas in a copper deposit in Peru

Cotrina-Teatino M.A.; Marquina-Araujo J.J.; Mamani-Quispe J.N.; Arango-Retamozo S.M.; Gonzalez-Vasquez J.A. · Journal of Mining and Environment (2026) · DOI: 10.22044/jme.2025.16188.3127

Resumen

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 threedimensional 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.

Instituciones: Universidad Nacional de Trujillo; Universidad Nacional del Altiplano