none 10.1190/geo2019-0392.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 117014340 5981 2025121211272072400 10.1190 2025-12-12T16:27:29Z 2020-06-10T13:47:13Z 15 Geophysics 0016-8033 1942-2156 07 1 2020 85 4 Erick Costa e Silva Talarico Petrobras S.A. 1 , Rio de Janeiro, . E-mail: erick.talarico@petrobras.com.br (corresponding author). Brazil Dario Grana University of Wyoming 2 , Department of Geology and Geophysics, Laramie, . E-mail: dgrana@uwyo.edu . USA http://orcid.org/0000-0003-4220-053X Leandro Passos de Figueiredo LTrace Geophysical Solutions 3 , Florianópolis, Brazil and , Informatic and Statistics Department, Florianópolis, . E-mail: leandrop.fgr@gmail.com . Brazil Federal University of Santa Catarina 3 , Florianópolis, Brazil and , Informatic and Statistics Department, Florianópolis, . E-mail: leandrop.fgr@gmail.com . Brazil http://orcid.org/0000-0002-3694-3938 Sinesio Pesco Pontifical Catholic University of Rio de Janeiro 4 , Mathematics Department, Rio de Janeiro, . E-mail: sinesio@puc-rio.br . Brazil http://orcid.org/0000-0002-1864-7828 ABSTRACT In seismic reservoir characterization, facies prediction from seismic data often is formulated as an inverse problem. However, the uncertainty in the parameters that control their spatial distributions usually is not investigated. In a probabilistic setting, the vertical distribution of facies often is described by statistical models, such as Markov chains. Assuming that the transition probabilities in the vertical direction are known, the most likely facies sequence and its uncertainty can be obtained by computing the posterior distribution of a Bayesian inverse problem conditioned by seismic data. Generally, the model hyperparameters such as the transition matrix are inferred from seismic data and nearby wells using a Bayesian inference framework. It is assumed that there is a unique set of hyperparameters that optimally fit the measurements. The novelty of the proposed work is to investigate the nonuniqueness of the transition matrix and show the multimodality of their distribution. We then generalize the Bayesian inversion approach based on Markov chain models by assuming that the hyperparameters, the facies prior proportions and transition matrix, are unknown and derive the full posterior distribution. Including all of the possible transition matrices in the inversion improves the uncertainty quantification of the predicted facies conditioned by seismic data. 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