Scaling Multiple Point Statistics for Non-Stationary Geostatistical Modeling

Multiple-point statistics are used in geostatistical simulation to improve forecasting of responses that are highly dependent on the reproduction of complex features of the phenomenon that cannot be captured by conventional two-point simulation methods. Inference of multiple-point statistics is often based on a training image that depicts the features that provide the character to the geological event being modelled. One limitation of this approach is that the univariate distribution of categories (facies or rock types) in the training image may not match the target statistics of the final model. The question of scaling multiple-point statistics arises, the idea being to take the statistics from the training image and scale them in a repeatable manner and honouring the target univariate proportions of categories.