Comparing connected structures in ensemble of random fields

Very different connectivity patterns may arise from using different simulation methods or sets of parameters, and therefore different flow properties. This paper proposes a systematic method to compare ensemble of categorical simulations from a static connectivity point of view. The differences of static connectivity cannot always be distinguished using two point statistics. In addition, multiple-point histograms only provide a statistical comparison of patterns regardless of the connectivity. Thus, we propose to characterize the static connectivity from a set of 12 indicators based on the connected components of the realizations. Some indicators describe the spatial repartition of the connected components, others their global shape or their topology through the component skeletons. We also gather all the indicators into dissimilarity values to easily compare hundreds of realizations. Heat maps and multidimensional scaling then facilitate the dissimilarity analysis. The application to a synthetic case highlights the impact of the grid size on the connectivity and the indicators. Such impact disappears when comparing samples of the realizations with the same sizes. The method is then able to rank realizations from a referring model based on their static connectivity. This application also gives rise to more practical advices. The multidimensional scaling appears as a powerful visualization tool, but it also induces dissimilarity misrepresentations: it should always be interpreted cautiously with a look at the point position confidence. The heat map displays the real dissimilarities and is more appropriate for a detailed analysis. The comparison with a multiple-point histogram method shows the benefit of the connected components: the large-scale connectivity seems better characterized by our indicators, especially the skeleton indicators.