Spatial hidden Markov chain models for estimation of petroleum reservoir categorical variables

Indicator variograms and transition probabilities are used to measure spatial continuity of petroleum reservoir categorical variables. Variogram-based Kriging variants are symmetric geostatistical methods, which cannot completely capture the complex reservoir spatial heterogeneity structure. The asymmetric spatial Markov chain (SMC) approaches employ transition probabilities to incorporate proportion, length and juxtaposition relation information in subsurface reservoir structures. Secondary data in petroleum geology, however, cannot be reasonably aggregated. We propose a spatial hidden Markov chain (SHMC) model to tackle these issues. This method integrates well data and seismic data by using Viterbi algorithm for reservoir forecasting. The classified sonic impedance is used as auxiliary data, directly in some kind of Bayesian updating process via a hidden Markov model. The SMC embedded in SHMC has been redefined according to first-order neighborhood with different lag in three-dimensional space. Compared with traditional SMC in Markov chain random field theory, the SHMC method performs better in prediction accuracy and reflecting the geological sedimentation process by integrating auxiliary information.