We consider the problem of predicting the spatial distribution of lithology/fluid classes from observed seismic data. We formulate the problem in a Bayesian setting and argue that the best choice of prior for this problem is a Markov mesh model. To obtain a flexible prior we formulate a general class of Markov mesh models and a corresponding hyper-prior for the model parameters of the Markov mesh model. We discuss three different strategies for how to combine the hierarchical Markov mesh prior, a training image and a likelihood model for the observed seismic data, to obtain predictions of the lithology/fluid classes. We present results from a case study for a seismic section from a North Sea reservoir. In particular the results show larger connectivity in the lithology/fluid classes when using our flexible Markov mesh prior, compared to what one gets with a simpler, manually specified Markov random field prior.


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