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  • Author or Editor: Noémi Jakab x
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Finding the optimal number of realizations to represent the model uncertainty when applying stochastic approaches is still a relevant question in geostatistics. The essence of the method is to visualize the realizations in a suitably constructed attribute space. To construct this space, the static connectivity metrics of the realizations were used. Within this framework, the creation of new realizations can be regarded as a sampling process, in which each new stochastic image is the equivalent of a new sampling point in the attribute space. The sampling process begins with the first few realizations appearing in a dispersed manner in random parts of the attribute space. The addition of more realizations causes the gradual emergence of higher point densities, which in the end, results in a point structure where most of the points are located in areas of high point densities with areas of low point densities surrounding them. High point densities represent typical realizations showing very similar connectivity characteristics, whereas low point densities correspond to atypical realizations with stronger deviations from the bulk. In this sense, reaching the optimal number of realizations is the equivalent of reaching a state in the sampling process where high- and low point densities are present at the same time, yet high point densities do not dominate the overall structure of the attribute space, as they also reflect the redundancy of the information content. This desired structure is strongly analogous to the complete spatial randomness of spatial point processes, where the points are neither dispersed nor aggregated in space. Based on this analogy, the normalized version of Ripley’s K-function and the L-function for the spatial inhomogeneous Poisson point process was applied to find the optimal number of realizations. The method is illustrated on a computed tomography slice and on the real-life data of the Tisza-2 reservoir.

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