A multidimensional, generalized coupled Markov chain model for surface and subsurface characterization

This paper develops a Markov chain-based geostatistical model for multidimensional field predictions of the categorical attributes. An efficient conditional probability equation that considers directional asymmetry was derived, and a computational algorithm was devised with numerical code. The developed model was applied to two-dimensional case studies and compared with the representative conventional sequential indicator simulation (SIS) model. On the basis of engaged comparisons with the SIS model, it was concluded that this new model performs as well as or better than the SIS model, especially for lithologic predictions and structural estimations for the case studies with sparse sampled data, which is more or less realistic. The model was also applied to a three-dimensional case and validated by its plausible results. It is expected that the developed Markov chain-based geostatistical model will become a sound option for multidimensional subsurface predictions in cases when the heterogeneities and uncertainties in the media properties are an important issue.