  We consider a Bayesian model for inversion of observed amplitude variation
with offset (AVO) data into lithology/fluid classes, and study in particular
how the choice of prior distribution for the lithology/fluid classes influences
the inversion results. Two distinct prior distributions are considered, a
simple manually specified Markov random field prior with a first order
neighborhood and a Markov mesh model with a much larger neighborhood estimated
from a training image. They are chosen to model both horisontal connectivity
and vertical thickness distribution of the lithology/fluid classes, and are
compared on an offshore clastic oil reservoir in the North Sea. We combine both
priors with the same linearised Gaussian likelihood function based on a
convolved linearised Zoeppritz relation and estimate properties of the
resulting two posterior distributions by simulating from these distributions
with the Metropolis-Hastings algorithm.
  The influence of the prior on the marginal posterior probabilities for the
lithology/fluid classes is clearly observable, but modest. The importance of
the prior on the connectivity properties in the posterior realisations,
however, is much stronger. The larger neighborhood 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 neighborhood Markov random field prior. As
a result, we conclude that the posterior realisations based on the Markov mesh
prior appear with much higher lateral connectivity, which is geologically
plausible.
