Semi-Markov random fields

Semi-Markov random fields


by Håkon Tjelmeland (Norwegian University of Science and Technology, Norway) and Lars Holden (Norwegian Computing Center), in Soares, A. (ed.) Geostatistics Troia '92, Proceedings of the Fourth International Geostatistical Congress, Troia, Portugal, September 13-18, 1992, Kluwer Academic Publishers, 479-492.
The spatial distribution of sedimentary facies in petroleum reservoirs is of major concern due to its influence on the flow regime in the reservoir, and thereby the production of oil and gas. A class of stochastic models, called semi-Markov Random Fields, for the facies distribution in petroleum reservoirs is presented. Semi-Markov Random Fields are a sub-class of Markov Random Field models. The model parameters in semi-Markov Random Fields have, in contrast to the usual Markov Random Fields with local neighborhood, a clear physical interpretation as size distributions of homogeneous volumes and border relations. Semi-Markov Random Fields can be regarded as a three dimensional generalization of the well known semi-Markov chain in one dimension. Simulation results both from semi-Markov Random Fields and Markov Random Fields with local neighborhood are presented.