Sequential co-simulation for resources modelling: How good is the reproduction of the joint spatial correlation structure?

Abstract

The quantification and classification of mineral resources and ore reserves is often based on an assessment of the certainty (or uncertainty) of the estimates of tonnage and grade of elements of interest (metals and impurities) contained in a mineable deposit. However, these variables are not always sufficient to characterize the factors that impact mining and mineral processing performance and hence the estimated quantity and value of recovered product. Improved understanding of geometallurgical response variables, via spatial simulation, offers one approach to predicting concentration and recovery performance, identifying improved operating parameters, and optimizing criteria that impact on costs of recovery, such as energy and reagent consumption. In this context, the spatial modelling of these responses is challenging. Geostatistical co-simulation techniques can be used to construct high-resolution models of geometallurgical responses that reproduce both the spatial variability and the multivariate relationships between co-regionalized variables. Sequential Gaussian co-simulation is such a technique, in which the variables of interest are simulated hierarchically, using cokriging to determine the distributions of values to be randomly simulated. However, because full cokriging is generally out of reach when the model contains too many locations or blocks to simulate, simplifications based on strictly collocated or multi-collocated cokriging are often adopted. In this study, the quality of such simplifications is investigated, with an application to a porphyry copper deposit. Sampling data from two cross-correlated geometallurgical variables, the iron grade and the concentrate copper grade, have been selected and sequentially co-simulated using the abovementioned cokriging strategies. The results show that both collocated and multi- collocated cokriging succeed in reproducing the spatial correlation structure of the variables to be simulated.