Uncertainty quantification for basin-scale geothermal conduction models

Geothermal energy plays an important role in the energy transition by providing a renewable energy source with a low CO2 footprint. For this reason, this paper uses state-of-the-art simulations for geothermal applications, enabling predictions for a responsible usage of this earth’s resource. Especially in complex simulations, it is still common practice to provide a single deterministic outcome although it is widely recognized that the characterization of the subsurface is associated with partly high uncertainties. Therefore, often a probabilistic approach would be preferable, as a way to quantify and communicate uncertainties, but is infeasible due to long simulation times. We present here a method to generate full state predictions based on a reduced basis method that significantly reduces simulation time, thus enabling studies that require a large number of simulations, such as probabilistic simulations and inverse approaches. We implemented this approach in an existing simulation framework and showcase the application in a geothermal study, where we generate 2D and 3D predictive uncertainty maps. These maps allow a detailed model insight, identifying regions with both high temperatures and low uncertainties. Due to the flexible implementation, the methods are transferable to other geophysical simulations, where both the state and the uncertainty are important.</p

GemPy 1.0 : open-source stochastic geological modeling and inversion

Peer reviewedPublisher PD

Combining low-temperature thermochronology with 3-D probabilistic kinematic modeling including uncertainties in the Eastern Alps

To understand the exhumation history of the Alps and its foreland, it is important to accurately reconstruct its time-temperature evolution. This is often done employing thermokinematic models. However, one problem of many current approaches is that they rely on prescribed geometric structures at depth without considering their uncertainty. Therefore, the aim of this work is to compare low-temperature thermochronological data with a 3-D probabilistic kinematic model. To this end, we combine 3-D kinematic forward modeling with a systematic random sampling approach to automatically generate an ensemble of kinematic models in the range of assigned uncertainties. These can later be used to obtain a 3-D probabilistic exhumation map, from which exhumation values for the sample positions of thermochronological data can be interpolated, and compared to estimates made solely from thermochronology. In a next step, the uncertainties assigned to the kinematic model can be updated with the thermochronological data, to obtain an even more robust model. We apply this approach to the Bavarian Subalpine Molasse, which is particularly suited as a test case, as it connects the Alpine orogen with its foreland, and should shed light on the strain distributions during the latest stages of Alpine mountain building. Preliminary results using previously published data show that the estimated exhumation from the modeling can serve as a constraint to thermochronological interpretations, leading to an uncertainty reduction. In a next step, we will use our own (U-Th)/He measurements to obtain an integrated picture of foreland evolution and associated uncertainties over space and time

Subdivide and Conquer: Adapting Non-Manifold Subdivision Surfaces to Surface-Based Representation and Reconstruction of Complex Geological Structures

Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure

Foreland dynamics as a measure of mountain building processes

Forelands record the uplift and exhumation history of mountain belts. The alpine foreland basin is particularly exciting, as is shows late-orogenic exhumation, possibly as a reaction to mantle-driven, plate convergence, or climatic forcings. However, inferring the contribution of the individual drivers to exhumation from stratigraphic or thermochronological data is challenging. The reason for this are along strike variability basin of stratigraphy, different degree of exhumation, as well as structural style of the Subalpine Molasse (i.e., the fold-thrust belt at the southern fringe of the basin). Furthermore, the influence of fluid flow on the thermochronological ages is unknown. Exhumation estimates in the central part of the basin are mostly based on stratigraphic arguments. Thermochronological data is scarce and limited to local studies. As the Molasse has also been uplifted in the central part of the basin since the Miocene, it is probable that it also responds to deep-seated processes, but to a lesser extent than the western part of the basin. This may be a result of different slab dynamics along strike the orogen. To test this, we used detrital and in situ low-temperature thermochronological age dating to shed light on the surface expression of the underlying geodynamic process (Figure 1). Data shows that most ages in the central part of the basin are unreset, while resetting occurs in the southernmost tectonic slices of the Subalpine Molasse. Generally, Miocene shortening in the Subalpine Molasse progressively decreases from west to east. The pattern coincides with slab geometries at depth (Mock et al., 2020). A general trend of lesser erosion from west to east is also visible in the flat lying Molasse based on vitrinite reflectance data. This suggests that a geodynamic driver is required for explaining basin exhumation on basin scale. Locally, the pattern is more complex. Particularly in the Subalpine Molasse, exhumation may be associated with plate convergence. To test the influence of faulting on exhumation, we constrained the geometries of the fold-thrust belt. Using a new compilation of stratigraphy and structures along the entire Alpine deformation front (Ortner et al., 2023), we identified two key regions: the Bregenzerach south of the eastward termination of the Jura Mountains, and the Hausham Syncline southeast of Munich. The Bregenzerach region lies at the surface boundary between Eastern and Western Alps. Furthermore, previously published thermochronological data indicate thrust activity in the mid-Miocene. Structures at depth are reasonably well-constrained due to good outcrop conditions and seismic data. The Hausham Syncline represents the region where structures at depth are less well constrained, and additionally the frontal triangle zone of the Subalpine Molasse tapers out. Structural modeling shows that it is possible to quantify the uncertainty of structures at depth, paving towards thermo-kinematic modeling including structural uncertainty (Brisson et al., 2023; Frings et al., 2023). The extensive thermochronological dataset offers the opportunity to identify local particularities not in line with the general trends observed in the data. Using thermal springs as proxy for heat flow (Luijendijk et al., 2020), we show that fluid flow may at least locally influence the cooling pattern. This is important for translating cooling into exhumation, particularly in regions where less data is available and thus outliers may be overlooked

Bayesian unsupervised machine learning approach to segment arctic sea ice using SMOS data

Microwave radiometry at L-band is sensitive to sea ice thickness (SIT) up to ~ 60 cm. Current methods to infer SIT depend on ice-physical properties and data provided by the ESA’s Soil Moisture and Ocean Salinity (SMOS) mission. However, retrieval accuracy is limited due to seasonally and regionally variable surface conditions during the formation and melting of sea ice. In this work, Arctic sea ice is segmented using a Bayesian unsupervised learning algorithm aiming to recognize spatial patterns by harnessing multi-incidence angle brightness temperature observations. The approach considers both statistical characteristics and spatial correlations of the observations. The temporal stability and separability of classes are analyzed to distinguish ambiguous from well-determined regions. Model uncertainty is quantified from class membership probabilities using information entropy. The presented approach opens up a new scope to improve current SIT retrieval algorithms, and can be particularly beneficial to investigate merged satellite products.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.713673. It was also funded through the award “Unidad de Excelencia María de Maeztu” MDM-2016-0600, by the Spanish Ministry of Science and Innovation through the project “L-band” ESP2017-89463-C3-2-R, and the project “Sensing with Pioneering Opportunistic Techniques (SPOT)” RTI2018-099008-B-C21/AEI/10.13039/501100011033.Peer ReviewedPostprint (published version

Histogram via entropy reduction (HER): an information-theoretic alternative for geostatistics

Interpolation of spatial data has been regarded in many different forms, varying from deterministic to stochastic, parametric to nonparametric, and purely data-driven to geostatistical methods. In this study, we propose a nonparametric interpolator, which combines information theory with probability aggregation methods in a geostatistical framework for the stochastic estimation of unsampled points. Histogram via entropy reduction (HER) predicts conditional distributions based on empirical probabilities, relaxing parameterizations and, therefore, avoiding the risk of adding information not present in data. By construction, it provides a proper framework for uncertainty estimation since it accounts for both spatial configuration and data values, while allowing one to introduce or infer properties of the field through the aggregation method. We investigate the framework using synthetically generated data sets and demonstrate its efficacy in ascertaining the underlying field with varying sample densities and data properties. HER shows a comparable performance to popular benchmark models, with the additional advantage of higher generality. The novel method brings a new perspective of spatial interpolation and uncertainty analysis to geostatistics and statistical learning, using the lens of information theory

Thrombocytopenia and end stage renal disease are key predictors of survival in patients with cardiac implantable electronic device infections

Introduction Cardiac implantable electronic device (CIED) infections are associated with a high mortality. Our aim was to identify key predictors of survival in patients with CIED infections as to be able to detect high‐risk patients and possibly affect modifiable factors. Methods and Results In this observational study, we collected data from 277 patients with CIED infections treated in our department between 2001 and 2017; predictors of survival were evaluated. The median time since the last CIED procedure was 0.83 years (interquartile range [IQR]: 0.25‐3.01), median time since initial CIED implant was 4.79 years (IQR: 0.90‐11.0 years). Survival at 30 days was 94.9% (95% confidence interval [CI]: 92.3‐97.5) and survival at 1 year was 80.9% (CI: 76.4‐85.7). Age (odds ratio [OR]: 1.05, CI: 1.01‐1.09; P = .009), end stage renal disease (ESRD) with dialysis (OR: 5.14, CI: 1.87‐14.11; P = .001), positive blood cultures (OR: 2.19, CI: 1.08‐4.45; P = .030), and thrombocytopenia (OR: 2.3, CI, 1.03‐5.15; P = .042) were identified as predictors of death within 1 year of treatment of CIED infection. Conclusion Patients with CIED infection with prior ESRD with dialysis or preoperative thrombocytopenia are at an increased risk of 1‐year mortality. We suggest that these patients be evaluated critically and resources be allocated to these patients more liberally. A greater understanding of the role of platelets in immunity may improve treatment of advanced infection in the future