A multidimensional scaling approach to enforce reproduction of transition probabilities in truncated plurigaussian simulation

Truncated plurigaussian (TPG) simulation is a flexible method for simulating rock types in deposits with complicated ordering structures. The truncation of a multivariate Gaussian distribution controls the proportions and ordering of rock types in the simulation while the variogram for each Gaussian variable controls rock type continuity. The determination of a truncation procedure for complicated geological environments is not trivial. A method for determining the truncation and fitting variograms applicable to any number of rock types and multivariate Gaussian distribution is developed here to address this problem. Multidimensional scaling is applied to place dissimilar categories far apart and similar categories close together. The multivariate space is then mapped using a Voronoi decomposition and rotated to optimize variogram reproduction. A case study simulating geologic layers at a large mineral deposit demonstrates the potential of this method and compares the results with sequential indicator simulation (SIS). Input proportion and transition probability reproduction with TPG is demonstrated to be better than SIS. Variogram reproduction is comparable for both techniques.