Summary
This paper considers Bayesian methods to discriminate between models depending on posterior model probability. When applying ensemble-based methods for model updating or history matching, the uncertainties in the parameters are typically assumed to be univariate Gaussian random fields. In reality, however, there often might be several alternative scenarios that are possible a priori. We take that into account by applying the concepts of model likelihood and model probability and suggest a method that uses importance sampling to estimate these quantities from the prior and posterior ensembles. In particular, we focus on the problem of conditioning a dynamic reservoir-simulation model to frequent 4D-seismic data (e.g., permanent-reservoir-monitoring data) by tuning the top reservoir surface given several alternative prior interpretations with uncertainty. However, the methodology can easily be applied to similar problems, such as fault location and reservoir compartmentalization. Although the estimated posterior model probabilities will be uncertain, the ranking of models according to estimated probabilities appears to be quite robust.
