Extensions of, and algorithms for, plurigaussian simulation

Abstract

Most mining applications of geostatistical simulation are to the simulation of quantitative variables, such as grade. In many instances the occurrence of quantitative variables and the values they take are controlled, at least partially, by qualitative, or categorical, variables. Examples include quartz-vein controlled gold orebodies and stratigraphic silver/lead/zinc deposits. In these cases a realistic simulation must include geological controls on the spatial distribution of the simulated quantitative variables. This paper describes extensions to, and algorithms for, the truncated plurigausian method of simulating categorical variables. The categorical variables are modelled as indicator random functions that represent the presence/absence of the variable at spatial locations. Stochastic images of the distributions are obtained by truncation of realisations of two Gaussian random functions simulated at the same locations. Parameters required are the thresholds for truncation of the Gaussian variables and the covariance structure of each Gaussian random function. These parameters are estimated from the experimental proportions of each variable and indicator direct and cross semi-variograms. A detailed case study is shown in order to illustrate the procedure, to discuss the results and to present the algorithms for plurigaussian simulation.