Behavior of Indicator Variograms and Transition Probabilities in Relation to the Variance in Lengths of Hydrofacies

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When using indicator geostatistics to represent the distribution of hydrofacies or lithofacies, the range and curvature of the autotransition probabilities or the autovariogram are related to the variation in facies lengths. As the coefficients of variation for the length of each facies increase toward unity, the effective range increases while the indicator-correlation structure evolves from a periodic linear structure to a somewhat periodic spherical structure to an aperiodic exponential structure. Multimodal distributions of facies lengths can give rise to autotransition probabilities or autovariograms that appear to have nested structures. With the understanding of these relationships it is possible to choose a model form and model parameters for the autotransition probability or autovariogram based upon the facies proportions and the modality, mean, and variance in length of the facies. This is illustrated with data from a case study.