In this paper, geological prior information is incorporated in the classification of reservoir lithologies after the adoption of Markov random fields (MRFs). The prediction of hidden lithologies is based on measured observations, such as seismic inversion results, which are associated with the latent categorical variables, based on the assumption of Gaussian distributions. Compared with other statistical methods, such as the Gaussian mixture model or k-Means, which do not take spatial relationships into account, the hidden MRFs approach can connect the same or similar lithologies horizontally while ensuring a geologically reasonable vertical ordering. It is, therefore, able to exclude randomly appearing lithologies caused by errors in the inversion. The prior information consists of a Gibbs distribution function and transition probability matrices. The Gibbs distribution connects the same or similar lithologies internally, which does not need a geological definition from the outside. The transition matrices provide preferential transitions between different lithologies, and an estimation of them implicitly depends on the depositional environments and juxtaposition rules between different lithologies. Analog cross sections from the subsurface or outcrop studies can contribute to the construction of these matrices by a simple counting procedure.

Hidden Markov Models (HMMs) have been applied to predict reservoir lithologies using seismic inversion results as inputs. This approach takes into account the conditional probabilities between different lithologies, i.e. the vertical transitions in sedimentary sequences. These properties are used as prior geological information. In order to relate the seismic inversion results to the true well-log data, HMMs need to be trained based on the Expectation-Maximization theory. Application of the resulting model on a synthetic example from the Book Cliffs (Utah, USA) showed that most lithologies are classified correctly, even for some thin layers. A comparison with point-wise methods in which data samples are treated independently from each other, such as k-means and fuzzy logic classifiers, leads to the conclusion that the spatial correlation in HMMs allows better lithological predictions because the prior information accounts for the geological depositional processes. A real case study with data from the Vienna Basin (Austria) is performed, in which lithologies in a 3D cube are obtained based on properties from seismic inversions, via trained HMMs. While the vertical sequences are shown to be reasonably well predicted, the horizontal continuities are not. This indicates that the future research should focus on the lateral geological relationships.