期刊
MATHEMATICAL GEOSCIENCES
卷 45, 期 4, 页码 383-409出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s11004-013-9456-3
关键词
Markov random field; Forward-backward algorithm; Multi-grid; Facies modeling; Maximum likelihood
Bayesian modeling requires the specification of prior and likelihood models. In reservoir characterization, it is common practice to estimate the prior from a training image. This paper considers a multi-grid approach for the construction of prior models for binary variables. On each grid level we adopt a Markov random field (MRF) conditioned on values in previous levels. Parameter estimation in MRFs is complicated by a computationally intractable normalizing constant. To cope with this problem, we generate a partially ordered Markov model (POMM) approximation to the MRF and use this in the model fitting procedure. Approximate unconditional simulation from the fitted model can easily be done by again adopting the POMM approximation to the fitted MRF. Approximate conditional simulation, for a given and easy to compute likelihood function, can also be performed either by the Metropolis-Hastings algorithm based on an approximation to the fitted MRF or by constructing a new POMM approximation to this approximate conditional distribution. The proposed methods are illustrated using three frequently used binary training images.
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