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Calibrating geothermal simulations is a critical step, both in scientific and industrial contexts, with suitable model parameterizations being optimized to reduce discrepancies between simulated and measured temperatures. Here we present a methodology to identify model errors in the calibration and compensate for measurement sparsity. With an application to the Upper Rhine Graben, we demonstrate the essential need for global sensitivity studies to robustly calibrate geothermal models, showing that local studies overestimate the influence of some parameters. We ensure the feasibility of the study through a physics-based machine learning approach (reduced basis method), reducing computation time by several orders of magnitude.

We present a probabilistic machine learning approach to determine lithologies for the wireline data from the Springbok Sandstone formation in the Surat Basin. Deterministic inversions of the data a...

This paper presents a novel perspective to understanding the spatial and statistical patterns of a cone penetration dataset and identifying soil stratification using these patterns. Both local consistency in physical space (i.e., along depth) and statistical similarity in feature space (i.e., logQt–logFrspace, where Qtis the normalized tip resistance and Fris the normalized friction ratio, or the Robertson chart) between data points are considered simultaneously. The proposed approach, in essence, consists of two parts: (i) a pattern detection approach using the Bayesian inferential framework and (ii) a pattern interpretation protocol using the Robertson chart. The first part is the mathematical core of the proposed approach, which infers both spatial pattern in physical space and statistical pattern in feature space from the input dataset; the second part converts the abstract patterns into intuitive spatial configurations of multiple soil layers having different soil behavior types. The advantages of the proposed approach include probabilistic soil classification and identification of soil stratification in an automatic and fully unsupervised manner. The proposed approach has been implemented in MATLAB R2015b and Python 3.6, and tested using various datasets including both synthetic and real-world cone penetration test soundings. The results show that the proposed approach can accurately and automatically detect soil layers with quantified uncertainty and reasonable computational cost.

Remote sensing 13(14), 2694 (2021). doi:10.3390/rs13142694 special issue: "Special Issue "Remote Sensing for Natural Hazards Assessment and Control" / Special Issue Editors: Prof. Dr. Paolo Mazzanti, Guest Editor; Dr. Saverio Romeo, Guest Editor", Published by MDPI, Basel

Geosciences 11(4), 150 (2021). doi:10.3390/geosciences11040150 special issue: "Special Issue "3D Modelling/Inversion for Mineral Exploration" / Special Issue Editors: Prof. Dr. Maxim Smirnov, Guest Editor; Dr. Maria Smirnova, Guest Editor; Prof. Dr. Thorkild Maack Rasmussen, Guest Editor", Published by MDPI, Basel

Geoscientific model development discussions preprint, 1 - 50 (2018). doi:10.5194/gmd-2018-61, Published by Copernicus, Katlenburg-Lindau

Loop is a new open source 3D geological and geophysical modelling platform in full development.The new platform consists of 4 main work packages: Knowledge Management: use of AI techniques for know...

Fault zones (FZ) are major components of geothermal exploration concepts for the Southern German Upper Jurassic aquifer (UJA). Because these sections of possibly favorable hydraulic properties can be hidden in pumping test data, their explorational importance with respect to well productivity is still debated. In this work, the effect of hydraulically active FZ on the well-productivity-index (PI) is quantified in dependency of the UJA parameter space using numerical modeling and the Reduced Basis method. Results suggest that hidden FZ can increase PI significantly, while a hydraulically active FZ thickness of ≥ 100 m is unlikely for the Upper Jurassic aquifer.

We evaulate if the concept of thermal entropy production can be used as a measure to characterize hydrothermal convection in a confined porous medium as a valuable, thermodynamically-motivated addition to the standard Rayleigh number analysis. Entropy production has been used widely in the field of mechanical and chemical engineering as a way to characterise the thermodynamic state and irreversibility of an investigated system. Pinoneering studies have since adapted these concepts to natural systems, and we apply this measure here to investigate the specific case of hydrothermal convection in a “box-shaped” confined porous medium, as a simplified analogue for, e.g., hydrothermal convection in deep geothermal aquifers. We perform various detailed numerical experiments to assess the response of the convective system to changing boundary conditions or domain aspect ratios, and then determine the resulting entropy production for each experiment. In systems close to the critical Rayleigh number, we derive results that are in accordance to the analytically derived predictions. At higher Rayleigh numbers however, we observe multiple possible convection modes, and the analysis of the integrated entropy production reveals distinct curves of entropy production that provide an insight into the hydrothermal behaviour in the system, both for cases of homogeneous materials, as well as for heterogeneous spatial material distributions. We conclude that the average thermal entropy production characterizes the internal behaviour of hydrothermal systems with a meaningful thermodynamic measure, and we expect that it can be useful for the investigation of convection systems in many similar hydrogeological and geophysical settings.

Solid earth 8(5), 987 - 1002 (2017). doi:10.5194/se-8-987-2017, Published by Copernicus Publ., Göttingen

Stochastic modeling methods and uncertainty quantification are important tools for gaining insight into the geological variability of subsurface structures. Previous attempts at geologic inversion and interpretation can be broadly categorized into geostatistics and process-based modeling. The choice of a suitable modeling technique directly depends on the modeling applications and the available input data. Modern geophysical techniques provide us with regional data sets in two- or three-dimensional spaces with high resolution either directly from sensors or indirectly from geophysical inversion. Existing methods suffer certain drawbacks in producing accurate and precise (with quantified uncertainty) geological models using these data sets. In this work, a stochastic modeling framework is proposed to extract the subsurface heterogeneity from multiple and complementary types of data. Subsurface heterogeneity is considered as the “hidden link” between multiple spatial data sets. Hidden Markov random field models are employed to perform three-dimensional segmentation, which is the representation of the “hidden link”. Finite Gaussian mixture models are adopted to characterize the statistical parameters of multiple data sets. The uncertainties are simulated via a Gibbs sampling process within a Bayesian inference framework. The proposed modeling method is validated and is demonstrated using numerical examples. It is shown that the proposed stochastic modeling framework is a promising tool for three-dimensional segmentation in the field of geological modeling and geophysics.

Topology has been used to characterise and quantify the properties of complex systems in a diverse range of scientific domains. This study explores the concept and applications of topological analysis in geology. We have developed an automatic system for extracting first order 2D topological information from geological maps, and 3D topological information from models built with the Noddy kinematic modelling system, and equivalent analyses should be possible for other implicit modelling systems. A method is presented for describing the spatial and temporal topology of geological models using a set of adjacency relationships that can be expressed as a topology network, thematic adjacency matrix or hive diagram. We define three types of spatial topology (cellular, structural and lithological) that allow us to analyse different aspects of the geology, and then apply them to investigate the geology of the Hamersley Basin, Western Australia.

Uncertainty is ubiquitous in geology, and efforts to characterise and communicate it are becoming increasingly important. Recent studies have quantified differences between perturbed geological models to gain insight into uncertainty. We build on this approach by quantifying differences in topology, a property that describes geological relationships in a model, introducing the concept of topological uncertainty. Data defining implicit geological models were perturbed to simulate data uncertainties, and the amount of topological variation in the resulting model suite measured to provide probabilistic assessments of specific topological hypotheses, sources of topological uncertainty and the classification of possible model realisations based on their topology. Overall, topology was found to be highly sensitive to small variations in model construction parameters in realistic models, with almost all of the several thousand realisations defining distinct topologies. In particular, uncertainty related to faults and unconformities was found to have profound topological implications. Finally, possible uses of topology as a geodiversity metric and validation filter are discussed, and methods of incorporating topological uncertainty into physical models are suggested.

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 step — although 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.

International audience; 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 part of geological and geophysical information is actually integrated in structural geological models. 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.

Trace plots for selected parameters and plots of calculated Geweke statistics

We present a novel methodology for performing experiments with subsurface structural models using a set of flexible and extensible Python modules. We utilise the ability of kinematic modelling techniques to describe major deformational, tectonic, and magmatic events at low computational cost to develop experiments testing the interactions between multiple kinematic events, effect of uncertainty regarding event timing, and kinematic properties. These tests are simple to implement and perform, as they are automated within the Python scripting language, allowing the encapsulation of entire kinematic experiments within high-level class definitions and fully reproducible results. In addition, we provide a~link to geophysical potential-field simulations to evaluate the effect of parameter uncertainties on maps of gravity and magnetics. We provide relevant fundamental information on kinematic modelling and our implementation, and showcase the application of our novel methods to investigate the interaction of multiple tectonic events on a pre-defined stratigraphy, the effect of changing kinematic parameters on simulated geophysical potential-fields, and the distribution of uncertain areas in a full 3-D kinematic model, based on estimated uncertainties in kinematic input parameters. Additional possibilities for linking kinematic modelling to subsequent process simulations are discussed, as well as additional aspects of future research. Our modules are freely available on github, including documentation and tutorial examples, and we encourage the contribution to this project.

SEG Conference on Keystone - Building Exploration Capability for the 21st Century, Keystone, CO, SEP 27-30, 2014; International audience; Existing three-dimensional (3-D) geologic systems are well adapted to high data-density environments, such as at the mine scale where abundant drill core exists, or in basins where 3-D seismic provides stratigraphic constraints but are poorly adapted to regional geologic problems. There are three areas where improvements in the 3-D workflow need to be made: (1) the handling of uncertainty, (2) the model-building algorithms themselves, and (3) the interface with geophysical inversion. All 3-D models are underconstrained, and at the regional scale this is especially critical for choosing modeling strategies. The practice of only producing a single model ignores the huge uncertainties that underlie model-building processes, and underpins the difficulty in providing meaningful information to end-users about the inherent risk involved in applying the model to solve geologic problems. Future studies need to recognize this and focus on the characterization of model uncertainty, spatially and in terms of geologic features, and produce plausible model suites, rather than single models with unknown validity. The most promising systems for understanding uncertainty use implicit algorithms because they allow the inclusion of some geologic knowledge, for example, age relationships of faults and onlap-offlap relationships. Unfortunately, existing implicit algorithms belie their origins as basin or mine modeling systems because they lack inclusion of normal structural criteria, such as cleavages, lineations, and recognition of polydeformation, all of which are primary tools for the field geologist that is making geologic maps in structurally complex areas. One area of future research will be to establish generalized structural geologic rules that can be built into the modeling process. Finally, and this probably represents the biggest challenge, there is the need for geologic meaning to be maintained during the model-building processes. Current data flows consist of the construction of complex 3-D geologic models that incorporate geologic and geophysical data as well as the prior experience of the modeler, via their interpretation choices. These inputs are used to create a geometric model, which is then transformed into a petrophysical model prior to geophysical inversion. All of the underlying geologic rules are then ignored during the geophysical inversion process. Examples exist that demonstrate that the loss of geologic meaning between geologic and geophysical modeling can be at least partially overcome by increased use of uncertainty characteristics in the workflow.