TO BE OR NOT TO BE MULTI-GAUSSIAN - A REFLECTION ON STOCHASTIC HYDROGEOLOGY

The multivariate Gaussian random function model is commonly used in st ochastic hydrogeology to model spatial variability of log-conductivity . The multi-Gaussian model is attractive because it is fully character ized by an expected value and a covariance function or matrix, hence i ts mathematical simplicity and easy inference. Field data may support a Gaussian univariate distribution for log hydraulic conductivity, but , in general, there are not enough held data to support a multi-Gaussi an distribution. A univariate Gaussian distribution does not imply a m ulti-Gaussian model. In fact, many multivariate models can share the s ame Gaussian histogram and covariance function, yet differ by their pa tterns of spatial continuity at different threshold values. Hence the decision to use a multi-Gaussian model to represent the uncertainty as sociated with the spatial heterogeneity of log-conductivity is not dat abased. Of greatest concern is the fact that a multi-Gaussian model im plies the minimal spatial correlation of extreme values, a feature cri tical for mass transport and a feature that may be in contradiction wi th some geological settings, e.g. channeling. The possibility for high conductivity values to be spatially correlated should not be discarde d by adopting a congenial model just because data shortage prevents re futing it. In this study, three alternatives to a multi-Gaussian model , all sharing the same Gaussian histogram and the same covariance func tion, but with different continuity patterns for extreme values, were considered to model the spatial variability of log-conductivity. The t hree alternative models, plus the traditional multi-Gaussian model, ar e used to perform Monte Carlo analyses of groundwater travel times fro m a hypothetical nuclear repository to the ground surface through a sy nthetic formation similar to the Finnsjon site in Sweden. The results show that the groundwater travel times predicted by the multi-Gaussian model could be ten times slower than those predicted by the other mod els. The probabilities of very short travel times could be severely un derestimated using the multi-Gaussian model. Consequently, if held mea sured data are not sufficient to determine the higher-order moments ne cessary to validate the multi-Gaussian model - which is the usual situ ation in practice - other alternative models to the multi-Gaussian one ought to be considered. (C) 1997 Elsevier Science Ltd.