Modeling the volume-dependent distribution of categorical variables

Facies is an important categorical variable. In facies modeling, point data and scaled up block data must be considered. The scaled up facies proportions form a multivariate distribution that is dependent on the volume.; Back transformation of Logratio values satisfies the order relation constraints (non-negative proportions that sum to one), but the non-linear nature of the logratio transformation and the issue of dealing with zero proportions make it problematic to apply logratio in multiscale facies modeling.; Describing the volume dependent multivariate distribution of facies proportions and fitting the distribution at different volumetric supports is the major purpose of this thesis. Several parametric statistical distributions will be tested and practical recommendations will be made.; The volume dependent distribution of facies proportions can be predicted using a proper parametric distribution. Block kriging and sequential simulation algorithm are applied and tested in estimating the 3-dimensional distribution of facies proportions over different volumetric scales.