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The Earth below ground is the subject of interest for many geophysical as well as geological investigations. Even though most practitioners would agree that all available information should be used in such an investigation, it is common practice that only a fraction of geological and geophysical information is used. We believe that some reasons for this omission are (a) an incomplete picture of available geological modeling methods, and (b) the problem of the perceived static picture of an inflexible geological representation in an image or geological model. With this work, we aim to contribute to the problem of subsurface interface detection through (a) the review of state-of-the-art geological modeling methods that allow the consideration of multiple aspects of geological realism in the form of observations, information and knowledge, cast in geometric representations of subsurface structures, and (b) concepts and methods to analyze, quantify, and communicate related uncertainties in these models. We introduce a formulation for geological model representation and interpolation and uncertainty analysis methods with the aim to clarify similarities and differences in the diverse set of approaches that developed in recent years. We hope that this chapter provides an entry point to recent developments in geological modeling methods, helps researchers in the field to better consider uncertainties, and supports the integration of geological observations and knowledge in geophysical interpretation, modeling and inverse approaches.

Structural geologic models are widely used to represent the spatial distribution of relevant geologic features. Several techniques exist to construct these models on the basis of different assumptions and different types of geologic observations. However, two problems are prevalent when constructing models: (1) observations and assumptions, and therefore also the constructed model, are subject to uncertainties and (2) additional information is often available, but it cannot be considered directly in the geologic modeling stepalthough it could be used to reduce model uncertainties. The first problem has been addressed in recent work. Here we develop a conceptual approach to consider the second aspect: We combine uncertain prior information with geologically motivated likelihood functions in a Bayesian inference framework. The result is that we not only reduce uncertainties in the ensemble of generated models, but we also gain the potential to learn additional features about the model parameters. We develop an implementation of this concept in a probabilistic programming framework, in which we extend the functionality of a 3D implicit potential-field interpolation method with geologic likelihood functions. With schematic examples, we show how this combination leads to suites of models with reduced uncertainties and how it provides a deeper insight into parameter correlations. Furthermore, the integration into a hierarchical Bayesian model provides an insight into potential extensions of the method, for example, the interpolation functional itself, and other types of information, such as gravity or magnetic potential-field data. These aspects constitute promising paths for future research.

Abstract. The representation of subsurface structures is an essential aspect of a wide variety of geoscientific investigations and applications, ranging from geofluid reservoir studies, over raw material investigations, to geosequestration, as well as many branches of geoscientific research and applications in geological surveys. A wide range of methods exist to generate geological models. However, the powerful methods are behind a paywall in expensive commercial packages. We present here a full open-source geomodeling method, based on an implicit potential-field interpolation approach. The interpolation algorithm is comparable to implementations in commercial packages and capable of constructing complex full 3-D geological models, including fault networks, fault–surface interactions, unconformities and dome structures. This algorithm is implemented in the programming language Python, making use of a highly efficient underlying library for efficient code generation (Theano) that enables a direct execution on GPUs. The functionality can be separated into the core aspects required to generate 3-D geological models and additional assets for advanced scientific investigations. These assets provide the full power behind our approach, as they enable the link to machine-learning and Bayesian inference frameworks and thus a path to stochastic geological modeling and inversions. In addition, we provide methods to analyze model topology and to compute gravity fields on the basis of the geological models and assigned density values. In summary, we provide a basis for open scientific research using geological models, with the aim to foster reproducible research in the field of geomodeling.

Fault zones in the Upper Jurassic aquifer of the North Alpine Foreland Basin are generally regions with possibly increased hydraulic properties. They are consequently often part of the geothermal exploration concepts in this area and a primary target for the drilling operation. Data from this aquifer, gathered in pump tests, however, show that only four out of 41 successful wells exhibit hydraulic proof for the presence of such a fault zone in terms of a bi-/linear flow regime. Besides technical effects, also the contrast in hydraulic properties itself, between fault zone and surrounding host rock, can prevent the detection of a fault zone in pump test data. This means a certain threshold has to be surpassed until its effects become clearly visible. A simplified realistic numerical model was constructed and calibrated with pressure data from an exploration site in the south of Munich. This model was then used to observe the presence of linear and bilinear flows in dependence on the Malm aquifers parameter space. Sampling the possible hydraulic property combinations with the help of an HPC (high-performance computing) cluster and automating the detection of the corresponding main flow type allowed to quantify the areas in parameter space where the fault zone-related flow regimes of interest are present. Through the investigation of more than 30,000 combinations between fault zone permeability, matrix permeability, fault zone storage, matrix storage and fault zone thickness, it was found that, in the parameter space of the Malm aquifer, a bilinear flow can be observed for the first time only if the matrix permeability is lower than 2.0 × 10 −13 m 2 , and a linear flow for matrix permeability values below 6.0 × 10 −14 m 2. Additionally, it was shown that fault zones, which have better hydraulic properties than the surrounding matrix, can indeed be hidden in pumping tests due to the parameter setting.

The spatial relationship between different rock types and relevant structural features is an important aspect in the characterization of ore-forming systems. Our knowledge about this geological architecture is often captured in 3D structural geological models. Multiple methods exist to generate these models, but one important problem remains: structural models often contain significant uncertainties. In recent years, several approaches have been developed to consider uncertainties in geological prior parameters that are used to create these models through the use of stochastic simulation methods. However, a disadvantage of these methods is that there is no guarantee that each simulated model is geologically reasonable – and that it forms a valid representation in the light of additional data (e.g. geophysical measurements). We address these shortcomings here with an approach for the integration of structural geological and geophysical data into a framework that explicitly considers model uncertainties. We combine existing implicit structural modelling methods with novel developments in probabilistic programming in a Bayesian framework. In an application of these concepts to a gold-bearing greenstone belt in Western Australia, we show that we are able to significantly reduce uncertainties in the final model by additional data integration. Although the final question always remains whether a predicted model suite is a suitable representation of accuracy or not, we conclude that our application of a Bayesian framework provides a novel quantitative approach to addressing uncertainty and optimization of model parameters.

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