A Bayesian model for lithology/fluid class prediction using a Markov mesh prior fitted from a training image: Bayesian model for lithology/fluid class prediction

We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classesinfluences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first-order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluidclasses, and are compared on an offshore clastic oil reservoir in the North Sea. Wecombine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimateproperties of the resulting two posterior distributions by simulating from thesedistributions with the Metropolis-Hastingsalgorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluidclasses is clearly observable, but modest. The importance of the prior on the connectivityproperties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first-order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologicallyplausible.