Reservoir Lithology Determination by Hidden Markov Random Fields Based on a Gaussian Mixture Model

• Published in: IEEE transactions on geoscience and remote sensing Vol. 56; no. 11; pp. 6663 - 6673
• Main Authors: Feng, Runhai, Luthi, Stefan M., Gisolf, Dries, Angerer, Erika
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analogs; Bayes methods; Distribution; Distribution functions; Fields; Fields (mathematics); Gaussian mixture model; Geology; Hidden Markov models; Hidden Markov random fields (HMRFs); Inversion; Lithology; lithology determination; Markov analysis; Markov chains; Markov processes; Outcrops; Probabilistic models; Probability theory; Reservoirs; Rocks; Sedimentary environments; seismic inversion; Seismic surveys; Statistical analysis; Statistical methods; transition matrix
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2018.2841059

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 <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-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.