Domain Delineation Using Geological Data, Variogram Analysis, and Clustering Algorithms

Domaining is a crucial process in geostatistics, particularly when significant spatial variations are observed within a site, as these variations can significantly affect the outcomes of spatial modeling. This study investigates the application of hard and fuzzy clustering algorithms for domain delineation, using geological and geochemical data from two exploration campaigns at the eastern Kahang deposit in central Iran. The dataset includes geological layers (lithology, alteration, and mineral zones), geochemical layers (Cu, Mo, Ag, and Au grades), and borehole coordinates. Six clustering algorithms—K-means, hierarchical, affinity propagation, self-organizing map (SOM), fuzzy C-means, and Gustafson-Kessel—were applied to determine the optimal number of clusters, which ranged from 3 to 4. The fuzziness and weighting parameters were found to range from 1.1 to 1.3 and 0.1 to 0.3, respectively, based on the evaluation of various hard and fuzzy cluster validity indices. Directional variograms were computed to assess spatial anisotropy, and the anisotropy ellipsoid for each domain was defined to identify the model with the highest level of anisotropic discrimination among the domains. The SOM algorithm, which incorporated both qualitative and quantitative data, produced the best model, resulting in the identification of three distinct domains. These findings underscore the effectiveness of combining clustering techniques with variogram analysis for accurate domain delineation in geostatistical modeling.