Abstract

The determination of geological units (such as lithology, alterations and mineral zones) has a huge value in different fields of application. In the specific case of ore deposit modelling, it allows the optimisation of different mining operations, for instance, the efficient purchase of mining explosives, which depends on the rock type. The spatial prediction of the layout of geological units faces issues related to the smoothing effect of interpolation methods. On the other hand, stochastic simulation approaches provide an accurate reproduction of the spatial continuity and contacts between geological units. There are many models for simulating geological units, but two of them (the truncated Gaussian and the plurigaussian) stand out in this work, both based on the Gaussian random field model. To carry out the simulation in both models, an iterative algorithm known as the Gibbs sampler has to be used to transform the input data (on the occurrence of geological units) into Gaussian data, conditioned to the geological and/or spatial structures inferred from the drill hole data of the ore deposit. To this end, the traditional implementation of the Gibbs sampler uses simple kriging with a unique neighbourhood to obtain the successive values of the Gaussian vector to simulate. This requires the inversion of a variance-covariance matrix, which often implies prohibitive computer resources. In consequence, the industry uses a moving neighbourhood in order to use a subset of the data at each iteration. Nevertheless, the Gaussian random vectors obtained with this methodology do no longer converge in distribution as the number of iterations increases. This is why the study of a new algorithm, called the dual Gibbs sampler, is proposed, which avoids the inversion of this matrix using all the available information for its application. This work examines the convergence results for the conditional simulation of geological units. Two ore deposits, a synthetic one for which all the parameters are known and a real iron deposit, are considered. In both cases, it is checked that the traditional Gibbs sampler does not converge to the desired distribution as the number of iterations increases, whereas the dual Gibbs sampler shows a consistent improvement of the outputs as the number of iterations increases giving accurate outcomes, although at a higher computer cost.