Uncertainty assessment in 3-D geological models of increasing complexity

Abstract

Abstract. The quality of a 3-D geological model strongly depends on the type of integrated geological data, their interpretation and associated uncertainties. In order to improve an existing geological model and effectively plan further site investigation, it is of paramount importance to identify existing uncertainties within the model space. Information entropy, a voxel-based measure, provides a method for assessing structural uncertainties, comparing multiple model interpretations and tracking changes across consecutively built models. The aim of this study is to evaluate the effect of data integration (i.e., update of an existing model through successive addition of different types of geological data) on model uncertainty, model geometry and overall structural understanding. Several geological 3-D models of increasing complexity, incorporating different input data categories, were built for the study site Staufen (Germany). We applied the concept of information entropy in order to visualize and quantify changes in uncertainty between these models. Furthermore, we propose two measures, the Jaccard and the city-block distance, to directly compare dissimilarities between the models. The study shows that different types of geological data have disparate effects on model uncertainty and model geometry. The presented approach using both information entropy and distance measures can be a major help in the optimization of 3-D geological models.

On the dynamic nature of hydrological similarity

“…The term "compression" was originally coined by Claude Shannon to refer to the quantification, storage and communication of information (Shannon, 1948). In environmental science, information theoretic concepts such as the Shannon entropy have found widespread use in various applications (e.g., Brunsell, 2010;Weijs et al, 2013a;Yakirevich et al, 2013), ranging from uncertainty assessment in 3-D geological models (Schweizer et al, 2017) to the delineation of water resource zones in Japan (Kawachi et al, 2001). For an introduction to, and detailed review of, information theoretic concepts we refer the reader to Cover and Thomas (2005), Singh (2013), and Weijs and van de Giesen (2013).…”

“…3.1 and 3.2) is a careful choice of the bin widths used to construct the probability density functions (pdf; Gong et al, 2014; Pechlivanidis et al, 2016). Various guidelines are available regarding how to properly estimate the bin width from the viewpoint of statistical rigor (e.g., Scott, 1979). However, Weijs and van de Giesen (2013) also point out that the bin width for a pdf should always be chosen based on considerations related to the question one wishes to answer.…”

3D Parametric Modeling of Complex Geological Structures for Geotechnical Engineering of Dam Foundation Based on T‐Splines

“…Figure b describes the intersectant location of these spatial cross‐sections and illustrates the additional geological boundaries extracted from these cross‐sections with blue continuous lines. The relatively dense geological information is necessary to update the geomodel to reduce the local geological uncertainty and help more realistically depict the fault subsurface in the critical local part where the rock mass withstands the thrust load of the arch dam (Li et al., ; Schweizer et al., ).…”

“…Figure 21b describes the intersectant location of these spatial cross-sections and illustrates the additional geological boundaries extracted from these cross-sections with blue continuous lines. The relatively dense geological information is necessary to update the geomodel to reduce the local geological uncertainty and help more realistically depict the fault subsurface in the critical local part where the rock mass withstands the thrust load of the arch dam (Li et al, 2013;Schweizer et al, 2017). In this case, T-splines technique can provide better local descriptions of the geomodel adaptive to the local refined geological data and relatively improve the local reliability of the critical areas with engineering significance.…”

On the dynamic nature of hydrological similarity

“…In environmental science, information-theoretic concepts such as the "Shannon entropy" have found widespread use in various applications (e.g. Brunsell, 2010;Weijs et al, 2013a;Yakirevich et al, 2013), ranging from uncertainty assessment in 3-D geological models (Schweizer et al, 2017) to the delineation of water 135 resource zones in Japan (Kawachi et al, 2001). For an introduction to, and detailed review of, information theoretic concepts we refer the reader to Cover and Thomas (2005), Singh (2013), and Weijs and van de Giesen (2013).…”