Plurigaussian simulation of non-stationary categorical variables and its application to ore body modeling

Abstract

The conditional simulation of geological domains, coded through categorical regionalized variables, allows constructing outcomes (realizations) of the layout of these domains that reproduce their spatial continuity and dependence relationships. These realizations can be further processed to quantify geological uncertainty and to determine the probability that a given domain prevails at any unsampled location or jointly over several locations. This information is essential to geological control in order to take proper decisions when mining an ore deposit. Among the existing approaches for simulating geological domains, the plurigaussian model has become popular in the petroleum and mining industries. In this model, the domains are obtained by truncating one or more Gaussian random fields. Even so, the model is well-established only in the stationary case, when the spatial distribution of the domains is homogeneous in space, and suffers from theoretical and practical impediments in the non-stationary case. To overcome these limitations, this thesis proposes several improvements in plurigaussian modeling. The main one is the extension of the model to the truncation of intrinsic random fields of order k with Gaussian generalized increments, instead of stationary Gaussian random fields, which allows reproducing spatial trends and zonal patterns in the distribution of the geological domains, a feature commonly met in practice with lithological, mineralogical and alteration domains. To this end, methodological proposals are made in relation to the definition of geostatistical tools and algorithms for inferring the model parameters (truncation rule based on considerations of the domain chronology and contact relationships, truncation thresholds, and generalized covariance functions of the underlying intrinsic random fields of order k) and for the construction of realizations conditioned to existing data. Also, the proposals are put in practice through synthetic case studies and a real case study (Río Blanco ore deposit) to demonstrate their applicability. The benefits of the proposed non-stationary plurigaussian model are twofold: (i) it allows reproducing trends in the spatial distribution of the geological domains, and (ii) the local proportions of the domains are not needed in the simulation process, thus the model is not affected by possible misspecifications of these proportions. Despite the very limited number of conditioning data, the Río Blanco case study shows a remarkable agreement between the simulated rock type domains and the lithological model interpreted by geologists, and proves to be much more successful than the conventional stationary plurigaussian model. The proposal thus appears as an attractive alternative for stochastic geological domaining, based on a sound theoretical background and on the incorporation of qualitative geological knowledge, such as the chronology, contact relationships or spatial trends of the domains to be simulated, which is helpful for guiding the modeling process and validating it.