Non-multi-Gaussian Multivariate Simulations With Guaranteed Reproduction of Inter-variable Correlations

Stochastic modeling of interdependent continuous spatial attributes is now routinely carried out in the minerals industry through multi-Gaussian conditional simulation algorithms. However, transformed conditioning data frequently violate multi-Gaussian assumptions in practice, resulting in poor reproduction of correlation between variables in the resultant simulations. Furthermore, the maximum entropy property that is imposed on the multi-Gaussian simulations is not universally appropriate. A new Direct Sequential Cosimulation algorithm is proposed here. In the proposed approach, pair-wise simulated point values are drawn directly from the discrete multivariate conditional distribution under an assumption of intrinsic correlation with local Ordinary Kriging weights used to inform the draw probability. This generates multivariate simulations with two potential advantages over multi-Gaussian methods: (1) inter-variable correlations are assured because the pair-wise inter-variable dependencies within the untransformed conditioning data are embedded directly into each realization; and (2) the resultant stochastic models are not constrained by the maximum entropy properties of multi-Gaussian geostatistical simulation tools.