Analysis of hydrogeological structure uncertainty by estimation of hydrogeological acceptance probability of geostatistical models

The following describes a proposed approach to account for the equifinality of solutions that result from comparing observations to flow simulations when using realizations of geostatistical models. We introduce hydrogeological acceptance probability to estimate the propensity of a geostatistical model to produce acceptable realizations with respect to the consistency of their simulations with observations. The estimation of hydrogeological acceptance probability is equivalent to the calculation of the sample mean of a Bernoulli distribution. This allows the estimation of the acceptance probability to be preemptively terminated based on the current estimate and subject to the desired confidence level and interval length. We propose a composite uncertainty analysis of the hydrogeological heterogeneity utilizing acceptable realizations from multiple geostatistical models collected during the estimation of their acceptance probability. In the case of a non-fuzzy definition of realization acceptance, this produces a facies probability map. If the definition of realization acceptance is imprecise, the analysis yields upper and lower bounds on the facies probability map in the form of facies plausibility and belief maps, respectively. These maps can provide indications of the information content of the data and provide guidance for the collection of additional data.