Uncertainty quantification in seismic facies inversion

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. Our method is demonstrated on synthetic and real seismic data sets, and it has high relevance in exploration studies due to the limited number of well data and in geologic environments with rapid lateral variations of the facies vertical distribution. © 2020 Society of Exploration Geophysicists.