Regionalized compositions, i.e., coregionalized variables that are non-negative and sum to a constant value, are met in the earth sciences to describe percentages or proportions. To deal with such variables, logratio transformations are commonly used in order to convert the composition into a set of unconstrained variables on which estimation or simulation techniques may be applied.
A different approach is explored in this work, based on an extension of the plurigaussian model used for representing categorical variables with mutually exclusive categories. Specifically, the regionalized composition is associated with a partition of the bigaussian space defined by two independent stationary Gaussian random fields.The proposed model depends on the choice of the partition, on the spatial correlation structure of each Gaussian random field, as well as on two other independent random fields with beta univariate distributions. In order to determine the model parameters, three steps are considered, which consist in successively fitting the expected values, univariate distributions and direct and cross variograms of the composition components. Once specified the parameters of the plurigaussian model, conditional simulation of the composition can be undertaken, based on the Gibbs sampler and on classical Gaussian simulation algorithms.
The applicability and versatility of the proposed approach are illustrated with a case study in ore body evaluation, in which the composition of interest consists of the proportions of sulfide minerals (mainly, bornite, chalcosine, chalcopyrite and pyrite) in rock samples.