Geostatistical modeling of heterogeneous geo-clusters in a copper deposit integrated with multinomial logistic regression: An exercise on resource estimation

Resource estimation is the main and primary step in the development of a mining project. Principally, it is necessary to first identify the geological domains through boreholes, model them at unsampled locations, and then evaluate the grade(s) of interest inside each built domain. The traditional determination of these categorical domains over the sampling points is suboptimal as it considers mostly-one or two variables from core logging. This leads to the neglect of the influence of other significant variables. To circumvent the problem of estimation domain identification, spatially dependent clustering machine learning algorithms can be of great help in detecting such domains. However, one problem that may appear when using these techniques is that the resulting geo-domains (geo-clusters) obtained by the clustering technique might be heterogeneous and show a non-stationary property. The reason is that the aim of these spatially dependent techniques is to produce compact and spatially contiguous clusters, which are well suited to establishing non-stationary geo-domains. This makes the procedure of modelling challenging as it necessitates the use of advanced geostatistical techniques to propagate the heterogeneous geo-clusters at unsampled locations. An algorithm is presented in this study that employs a non-stationary sequential indicator simulation paradigm to model such complex variability of heterogeneous geo-clusters. Since the spatial trends of underlying geo-clusters are required in this simulation method, in this study, we propose the use of multinomial logistic regression to infer these trends. The algorithm was tested using an actual case study from a porphyry copper deposit in Iran, where Cu, Mo, Au, Rock Quality Designation (RQD), mineralization zones, alteration types, and rock types were employed to identify and spatially model the heterogeneous geo-domains in the entire deposit. The results were compared with a conventional sequential indicator simulation where no trend was used. An examination of the resulting maps using several evaluation criteria including visual inspection of the realizations, probability maps, reproduction of proportion of each geo-cluster, connectivity measures, and trend analysis, showed that the findings of the proposed algorithm were superior in modelling heterogeneous geo-domains.