Advanced Geostatistical Models for Robust Mineral Resources Estimation in Complex Geological Settings

Modern mineral exploration and production increasingly rely on advanced spatial modeling techniques capable of handling complex geological settings characterized by structural discontinuities, irregular sampling, and physical barriers. Conventional covariance models based on Euclidean distance measures often fail to adequately represent such environments, limiting their effectiveness in resource estimation and uncertainty quantification. The adoption of non-Euclidean distance metrics offers a promising pathway toward more realistic geological modeling and improved decision-making in mining operations.This contribution presents recent advances in geostatistical covariance modeling based on the Linearly Damped Harmonic Oscillator, implemented through the Harmonic Covariance Estimator (HCE) and the Advanced Harmonic Covariance Estimator (AHCE). Nine case studies are used to demonstrate the applicability and robustness of these models across a broad range of mining-related scenarios, including univariate and multivariate mineral datasets, anisotropic orebody structures, unevenly distributed sampling, conditional simulations for uncertainty assessment and Gaussian anamorphosis models. Comparisons are made against established covariance models commonly used in mining geostatistics under both Euclidean and non-Euclidean distance frameworks. Model performance is evaluated using leave-one-out cross-validation and eigenvalue-based validity testing. Results show that harmonic covariance models remain mathematically valid and predictive in complex geological environments where traditional approaches often fail. These advances provide a flexible and reliable framework for next-generation mineral resource modeling, supporting more accurate exploration targeting, improved production planning, and sustainable resource management in the mining industry of tomorrow.The research project is implemented in the framework of H.F.R.I call “Basic research Financing (Horizontal support of all Sciences)” under the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union – NextGenerationEU (H.F.R.I. Project Number: 16537)M. D. Koltsidopoulou, A. Pavlides, D. T. Hristopulos,  E. Α. Varouchakis, 2025, Enhancing Geostatistical Analysis of Natural Resources Data with Complex Spatial Formations through non-Euclidean Distances, Mathematical Geosciences, in print.A. Pavlides, M. D. Koltsidopoulou, M. Chrysanthi, E. A. Varouchakis, 2025. A Kernel-Based Nonparametric Approach for Data Gaussian Anamorphosis, Mathematical Geosciences, https://doi.org/10.1007/s11004-025-10251-zE.A. Varouchakis, M. D. Koltsidopoulou and A. Pavlides, 2025, Designing Robust Covariance Models for Geostatistical Applications, Stochastic Environmental Research and Risk Assessment, https://doi.org/10.1007/s00477-025-02982-