Abstract. Sealed geological models are commonly used as an input to process simulations, for example, in hydrogeological or geomechanical studies. Creating these meshes often requires tedious manual work, and it is therefore difficult to adjust a once-created model. In this work, we propose a flexible framework to create and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the control mesh and the definition of semi-sharp-crease values, which, in combination, enable the representation of complex structural settings with a low number of control points. We achieve this flexibility through the adaptation of recent algorithms from the field of computer graphics to the specific requirements of geological modeling, specifically the representation of non-manifold topologies and sharp features. We combine the method with a particle swarm optimization (PSO) approach to enable the automatic optimization of vertex position and crease sharpness values. The result of this work is implemented in an open-source software (PySubdiv) for reconstructing geological structures while resulting in a model which is (1) sealed/watertight, (2) controllable with a control mesh and (3) topologically similar to the input geological structure. Also, the reconstructed model may include a lower number of vertices compared to the input geological structure, which results in reducing the cost of modeling and simulation. In addition to enabling a manual adjustment of sealed geological models, the algorithm also provides a method for the integration of explicit surface representations in inverse frameworks and the consideration of uncertainties.

<p align="justify">Development of brittle damage around nuclear waste repository tunnels is a common phenomenon in massive rocks in highly-stressed conditions. The time-dependent brittle fracturing may lead to an interconnected fracture network (i.e. excavation damage zone; EDZ) and induced seismicity. Within the excavation damage zone (EDZ), the permeability is often enhanced and – in the framework of nuclear waste disposal – may provide preferential pathways for radionuclide migration. Therefore, a comprehensive understanding of the brittle fracturing requires multi- multidisciplinary monitoring systems to allow for spatial and temporal characterization of the EDZ. Recently, the Swiss Federal Institute of Technology (ETH) Zurich established a new Underground Research Laboratory (URL) in Southern Switzerland in the old Bedretto Gallery. Within the PRECODE experiment, we will establish a new, experimental tunnel as a branch from the existing tunnel, which will be densely instrumented with strain, pore pressure and acoustic emission sensors prior to the excavation. The main objectives of the PRECODE experiment are to understand: (1) short-term rock mass behavior and EDZ formation during tunneling; (2) long-term fracture propagation within the EDZ associated with environmental conditions (fluctuations in humidity and temperature); (3) permeability changes with time around an open excavation and (4) the impact of tunneling on the nearby fault zones. This study outlines an overview of the project objectives, details of the planned monitoring systems, and some preliminary results obtained from a baseline study of characterization of the +40-year EDZ from the existing Bedretto Tunnel.</p> <p align="justify"><em><strong>Bedretto Team:</strong></em><em> The team involves more than 30 people from ETHZ and 10 research institutes and companies involved in the Bedretto Laboratory (see http://www.bedrettolab.ethz.ch/en/home/ for more details)</em></p>

<p>Geological models, as 3-D representations of subsurface structures and property distributions, are used in many economic, scientific, and societal decision processes. These models are built on prior assumptions and imperfect information, and they often result from an integration of geological and geophysical data types with varying quality. These aspects result in uncertainties about the predicted subsurface structures and property distributions, which will affect the subsequent decision process.</p><p>We discuss approaches to evaluate uncertainties in geological models and to integrate geological and geophysical information in combined workflows. A first step is the consideration of uncertainties in prior model parameters on the basis of uncertainty propagation (forward uncertainty quantification). When applied to structural geological models with discrete classes, these methods result in a class probability for each point in space, often represented in tessellated grid cells. These results can then be visualized or forwarded to process simulations. Another option is to add risk functions for subsequent decision analyses. In recent work, these geological uncertainty fields have also been used as an input to subsequent geophysical inversions.</p><p>A logical extension to these existing approaches is the integration of geological forward operators into inverse frameworks, to enable a full flow of inference for a wider range of relevant parameters. We investigate here specifically the use of probabilistic machine learning tools in combination with geological and geophysical modeling. Challenges exist due to the hierarchical nature of the probabilistic models, but modern sampling strategies allow for efficient sampling in these complex settings. We showcase the application with examples combining geological modeling and geophysical potential field measurements in an integrated model for improved decision making.</p>

Computer graphics have gradually developed practical techniques to address models with the complex topology, in particular, by parametric surface-based modeling approach. Also, geologists have used this approach because it provides significant gains over grid-based modeling (e.g., implicit modeling) by using grid-free surfaces. However, since this approach originates from computer graphics, not all the capacities and limitations of this approach have been considered and investigated in geological modeling.With this aim in mind, this paper investigates surface-based geological modeling through both geological and computer graphics approaches. NURBS (Non-Uniform Rational B-Splines) and subdivision surfaces, as two main parametric surface-based modeling methods, are investigated, and the strengths and weaknesses of both are compared. Although NURBS surfaces have been used in geological modeling, subdivision surfaces as a standard method in the animation and gaming industries, have received little attention in geological modeling. Subdivision surfaces support arbitrary topologies and watertight modeling, which are quite useful for complex geological modeling.Investigating subdivision schemes with semi-sharp creases is an important part of this paper. Semi-sharp creases show the resistance of a mesh structure to the subdivision procedure, which provides a unique method for complex geological and reservoir modeling. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modeling, are explored, and the subdivision surfaces compatible with non-manifold topology are declared.Finally, the approximation of complex geological structures by the non-manifold subdivision surface method is investigated with two different case studies. The approximated mesh is a simplified and less complex version of the original mesh while the important details of the original mesh are preserved. It not only significantly reduces the cost of modeling and simulation (by reducing the number of vertices to less Preprint-Moulaeifard et al. (Submitted to Mathematical Geoscince) 3 than 5% of the number of vertices of the original mesh) but also, has features such as being watertight, smooth, topologically identical to the main original mesh and controllable with few control points. Keywords Surface-based modeling. Subdivision surfaces. Non-manifold topology. Approximation of geological structures. Grid free. NURBS.

<p>Uncertainties are an inherent part of geological interpretation and immersive rendering has the potential to play a key role in gaining better insights. However, most 3D geological models have a limited possibility of manual, fast and smooth modification in order to make better decisions and interpretations. Here we present examples of parametric surface representations which use control points as a possibility to bring interactivity to geological modelling in immersive frameworks.</p><p>In fact, using 2D surfaces of 3D solid objects is a typical representation of 3D models. Two of the major ways for surface representation in computer graphics are implicit representations and parametric surface representations. Parametric surface representations, unlike implicit representations, are based on control points. Manipulating these control points makes it easy and intuitive to modify geological models smoothly and fast, with a potential to more interactive decision-making.</p><p>We present two different examples of parametric surface approaches; Spline Surfaces and Subdivision Surfaces. Spline surfaces, e.g. Bezier or NURBS surfaces, are a popular and common standard for CAD (Computer-Aided Design). Also, these surfaces are on the basis of parametric- based curves and a set of weighted control points. Subdivision Surfaces define smooth surfaces after a series of refinement which can be controlled by control points. Subdivision surfaces are not only a popular method for making free form models but also a common tool in animation, computer games and entertainment industry.</p><p>Recently, research has been done based on using spline surfaces to model diverse geological structures and reservoirs. Similar to applications in computer graphics, using these methods in geological modelling can have specific considerations. Model refinement (e.g. adding new control points) and the requirement of many patches with geometrical constraints for the representation of complex geometries are some of the main difficulties of using spline surfaces. In this presentation, we will discuss several of these aspects and show two promising and controllable techniques for intuitive use of parametric surface-based representations in 3D geological and reservoir modelling.</p>