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.