Can Geostatistical Models Represent Nature's Variability? An Analysis Using Flume Experiments

The lack of understanding in the Earth's geological and physical processes governing sediment deposition render subsurface modeling subject to large uncertainty. Geostatistics is often used to model uncertainty because of its capability to stochastically generate spatially varying realizations of the subsurface. These methods can generate a range of realizations of a given pattern - but how representative are these of the full natural variability? And how can we identify the minimum set of images that represent this natural variability? Here we use this minimum set to define the geostatistical prior model: a set of training images that represent the range of patterns generated by autogenic variability in the sedimentary environment under study. The proper definition of the prior model is essential in capturing the variability of the depositional patterns. This work starts with a set of overhead images from an experimental basin that showed ongoing autogenic variability. We use the images to analyze the essential characteristics of this suite of patterns. In particular, our goal is to define a prior model (a minimal set of selected training images) such that geostatistical algorithms, when applied to this set, can reproduce the full measured variability. A necessary prerequisite is to define a measure of variability. In this study, we measure variability using a dissimilarity distance between the images. The distance indicates whether two snapshots contain similar depositional patterns. To reproduce the variability in the images, we apply an MPS algorithm to the set of selected snapshots of the sedimentary basin that serve as training images. The training images are chosen from among the initial set by using the distance measure to ensure that only dissimilar images are chosen. Preliminary investigations show that MPS can reproduce fairly accurately the natural variability of the experimental depositional system. Furthermore, the selected training images provide process information. They fall into three basic patterns: a channelized end member, a sheet flow end member, and one intermediate case. These represent the continuum between autogenic bypass or erosion, and net deposition.