UNCERTAINTIES IN FACIES PROPORTION ESTIMATION I. THEORETICAL FRAMEWORK: THE DIRICHLET DISTRIBUTION

Abstract

To simulate geological models comprising several litho-types-or facies-we need first to estimate their proportions, which are often poorly known. The corresponding uncertainties can be modelled using a Bayesian approach for inverting the multinomial distribution. The result obtained is known as the Dirichlet distribution. It can be simulated by decomposition into independent conditional distributions. Application of the model is extended to the case of nonstationary proportions and, with some approximation, to the case of correlated spatial data. The mathematical developments presented in the appendices provide a more precise and general definition of the distribution, several decomposition formulae into independent variables, the determination of remarkable stability properties, and the resulting consequences for the conditional and marginal distributions.