A cross-validation framework to extract data features for reducing structural uncertainty in subsurface heterogeneity

Spatial heterogeneity is a critical issue in the management of water resources. However, most studies do not consider uncertainty at different levels in the conceptualization of the subsurface patterns, for example using one single geological scenario to generate an ensemble of realizations. In this paper, we represent the spatial uncertainty by the use of hierarchical models in which higher-level parameters control the structure. Reduction of uncertainty in such higher-level structural parameters with observation data may be done by updating the complete hierarchical model, but this is, in general, computationally challenging. To address this, methods have been proposed that directly update these structural parameters by means of extracting lower dimensional representations of data called data features that are informative and applying a statistical estimation technique using these features. The difficulty of such methods, however, lies in the choice and design of data features, i.e. their extraction function and their dimensionality, which have been shown to be case-dependent. Therefore, we propose a cross-validation framework to properly assess the robustness of each designed feature and make the choice of the best feature more objective. Such framework aids also in choosing the values for the parameters of the statistical estimation technique, such as the bandwidth for kernel density estimation. We demonstrate the approach on a synthetic case with cross-hole ground penetrating radar traveltime data and two higher-level structural parameters: discrete geological scenarios and the continuous preferential orientation of channels. With the best performing features selected according to the cross-validation score, we successfully reduce the uncertainty for these structural parameters in a computationally efficient way. While doing so, we also provide guidelines to design features accounting for the level of knowledge of the studied system. © 2019