Content uploaded by Sam Thiele
Author content
All content in this area was uploaded by Sam Thiele on Jun 28, 2018
Content may be subject to copyright.
A preview of the PDF is not available
The topology of geology 2: Topological uncertainty
Figures
Figures - uploaded by Sam Thiele
Author content
All figure content in this area was uploaded by Sam Thiele
Content may be subject to copyright.
... The uncertainty of geological models is widely recognized as an important issue [1][2][3][4][5][6][7][8][9][10][11][12][13]. Due to the lack of mathematical systematization of uncertainty theory, it is difficult to quantitatively describe and universally interpret the uncertainty in geological models. ...
... The data point is perturbed in the range. Previous studies [8,9] used dip and slip to describe the geological features of faults. The uncertainty of fault is shown as the uncertainty of dip and slip. ...
... Up to now, there is no research on the problem of uncertainty of the spatial diffusion. The perturbation of geological model is used widely in the research on the uncertainty of geological model [18] and the uncertainty of topology [9]. The process of uncertainty diffusion is too simplified, which leads to the fact that uncertainty distribution of geological model is not reasonable. ...
The geological model plays an important role in geophysics and engineering geology. The data source of geological modeling comes from interpretation data, borehole data, and outcrop data. Due to economic and technical limitations, it is impossible to obtain highly accurate and high-density data sources. The sparsity and inaccuracy of data sources lead to the uncertainty in geological models. Unlike the problem of probability, there is not enough samples for a geological model. Spatial diffusion model and merging model are introduced, which are more satisfied with the cognition of uncertainty than the existing methods. And then, using conditional information entropy, a quantification method of geological uncertainty, is proposed. Compared with the approaches of information entropy, this method took full account of the constraints of geological laws. Based on the uncertainty models and conditional information entropy, a framework of uncertainty assessment in geological models is established. It is not necessary in our framework to create multiple geological models, which is a time-consuming and laborious task. The application of Hashan survey located at north of China shows that the method and framework of this study are reasonable and effective.
... When generating multiple stochastic models, it becomes highly unpractical to check the models one by one to see if these are geologically feasible. Thiele et al. (2016a) and Thiele et al. (2016b) have introduced the concept of geological topology, the contact relationships between discrete elements of a model, as an important constraint for many geological processes. Similarly, Schaaf et al. (2021) have shown, for geologically simple cases, that topological information can be used as a distance function in an approximate Bayesian computation framework to constrain probabilistic 3D modeling outputs. ...
... In this work, geological topology is used as a distance function in order to constrain the posterior model ensembles (as used in Schaaf et al., 2021), and eliminate models with artifacts. Topology can thus serve to reduce the overall posterior uncertainty (e.g., Thiele et al., 2016b;Schaaf et al., 2021), by allowing automatic removal of geologically unrealistic models. ...
Geological modeling commonly results in a single prescribed geometric representation of the subsurface with no consideration of uncertainties. Accounting for uncertainties is of particular importance in the triangle zone at the leading edge of deformation of the foreland fold-thrust belt of the European Alps, the Subalpine Molasse. Here, interpretations of the complex structures are limited to 2D and are based almost exclusively on subsurface data, lacking the constraint of surface data.Implicit modeling can be used to create automated 3D model realizations considering parameter uncertainty. In this sense, multiple possible models can be assessed within the uncertainty range assigned. As implicit modeling often yields artifacts or geologically unfeasible scenarios, the concept of geological topology can be used to constrain the modeling outputs, so that only models without artifacts are considered into the final model ensemble.Two experiments are designed to test out this workflow. The methodology is first tested using a very simple synthetic model, and later applied to a portion of the Subalpine Molasse, where different 2-D subsurface geometries have been proposed. For the first time, a 3D implicit model ensemble incorporating a full assessment of uncertainties is built in this area. Results show that it is feasible to use topological information for posterior model constraint, even in models of high structural complexity. To eliminate all non-meaningful models, however, it is necessary to use more than one topological constraint. A comparison of the prior and posterior model ensembles shows a correlation between model parameters and a shift in parameter probability density curves in the synthetic model experiment, and a decrease in entropy for both experiments. A topological constraint should thus be applied routinely when building a stochastic implicit model ensemble.
... In any case, deep geological formations are complex and inhomogeneous, exhibiting variations in rock types, structure, and properties [15,16,17,18,19]. Inferring their structure from geotechnical and geophysical exploration remains an interpretative task and predicting their behavior over long periods is challenging due to inherent uncertainties [20,21,22,23,24]. Factors such as the presence of fractures, fault zones, or natural pathways for fluid migration can affect the safety and stability when it comes to barrier integrity [25]. ...
... (3) There are multiple interpretations and uncertainties of geological phenomena that are subject to interpretation and uncertainty [186][187][188][189]. Although the integration of multisource data can enhance model accuracy [190], it faces challenges related to data integration and transformation. ...
This study examines the development trajectory and current trends of three-dimensional (3D) geological modelling. In recent years, due to the rising global energy demand and the increasing frequency of regional geological disasters, significant progress has been made in this field. The purpose of this study is to clarify the potential complexity of 3D geological modelling, identify persistent challenges, and propose potential avenues for improvement. The main objectives include simplifying the modelling process, improving model accuracy, integrating different data sources, and quantitatively evaluating model parameters. This study integrates global research in this field, focusing on the latest breakthroughs and applications in mineral exploration, engineering geology, geological disaster assessment, and military geosciences. For example, unmanned aerial vehicle (UAV) tilt photography technology, multisource data fusion, 3D geological modelling method based on machine learning, etc. By identifying areas for improvement and making recommendations, this work aims to provide valuable insights to guide the future development of geological modelling toward a more comprehensive and accurate “Transparent Earth”. This review underscores the global applications of 3D geological modelling, highlighting its crucial role across various sectors such as mineral exploration, the oil and gas industry, urban planning, geological hazard assessment, and geoscientific research. The review emphasizes the sector-specific importance of this technology in enhancing modelling accuracy and efficiency, optimizing resource management, driving technological innovation, and improving disaster response capabilities. These insights provide a comprehensive understanding of how 3D geological modelling can significantly impact and benefit multiple industries worldwide.
... To develop a geologic concept model efficiently, the differences and similarities between map patterns needed to be presented clearly. Although not in common practice, methods have been proposed to communicate these relationships as encoded geological topology information (Burns, 1975;Thiele et al., 2016). In areas with complex deformation histories, it is difficult to discern key relationships in the map pattern. ...
3D geological modelling is becoming an effective tool for communication and development of geological understanding. This is due to increased computer performance and availability of improved geological modelling software. 3D geological modelling technology has reached the stage where it can be implemented in regionally extensive and geologically complex settings, with the ability to achieve geological insight beyond what could otherwise have been gained through 2D investigations alone. Insight includes better constrained fault and horizon topologies, refined fold geometries, improved understanding of tectonic processes, and characterization of deformational events. By integrating field observations, aeromagnetic maps, and 3D modelling techniques in the northern Labrador Trough, a regionally extensive and structurally complex geological environment, regional faults geometries and topological relationships were refined. Additionally, a new fault, the Ujaralialuk Fault, and two shear zones were interpreted. During modelling, several challenges were identified, including higher computational costs for regionally extensive models, sparse 3D constraints, algorithmic limitations related to complex geometries, and the large investment of time and effort required to produce a single model solution. A benefit of this investigation is that new insight was also gained for a greenfields region which may assist future exploration efforts. Developing 3D models in challenging environments allows for better definition of future workflow requirements, algorithm enhancements, and knowledge integration. These are needed to achieve a geologically reasonable modelling standard and gain insight for poorly constrained geological settings. iv
... infrastructure built on the surface. One way to quantify this uncertainty is by calculating the probability of every possible configuration of the geological structures (Tacher et al., 2006;Thiele et al., 2016;Pakyuz-Charrier et al., 2018). Sampling procedures for UQ are helpful in this undertaking. ...
We analyse some of the challenges in quantifying uncertainty when using geohazard models. Despite the availability of recently developed, sophisticated ways to parameterise models, a major remaining challenge is constraining the many model parameters involved. Additionally, there are challenges related to the credibility of predictions required in the assessments, the uncertainty of input quantities, and the conditional nature of the quantification, making it dependent on the choices and assumptions analysts make. Addressing these challenges calls for more insightful approaches yet to be developed. However, as discussed in this paper, clarifications and reinterpretations of some fundamental concepts and practical simplifications may be required first. The research thus aims to strengthen the foundation and practice of geohazard risk assessments.
... Such uncertainty means significant engineering and environmental risk to, e.g., infrastructure built on the surface. One way to quantify this uncertainty is calculating the probability of every possible configuration of the geological structures (Tacher et al. 2006;Thiele et al. 2016;Pakyuz-Charrier et al. 2019). Sampling procedures ...
By describing critical tasks in quantifying uncertainty using geohazard models, we analyse some of the challenges involved. Under the often-seen condition of very limited data and despite the availability of recently developed sophistications to parameterise models, a major challenge that remains is the constraining of the many model parameters involved. However, challenges also lie in the credibility of predictions required in the assessments, the uncertainty of input quantities, and the conditional nature of the quantification on the choices and assumptions made by analysts. Addressing these challenges calls for more insightful approaches that are yet to be developed; however, clarifications and reinterpretations of some fundamental concepts together with practical simplifications may be required first, and these are discussed in this paper. The research aims at strengthening both the foundation of geohazard risk assessments and its practice.
To understand the exhumation history of the Alpine foreland, it is important to accurately reconstruct its time-temperature evolution. This is often done employing thermokinematic models. One problem of many current approaches is that they are limited to 2-D and do not consider structural or kinematic uncertainties. In this work, 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 geometric uncertainties. Using Markov chain Monte Carlo, each randomly generated model will be assessed in regards to how well they fit the available thermochronology data. This is done to obtain an updated set of modeling parameters with reduced uncertainty. The resulting, more robust model can then be used to re-interpret the thermochronological data and find alternative drivers of cooling for certain samples.We apply this approach to a simple synthetic model to test the methodology, and then to the Eastern Alps triangle zone in the Bavarian Subalpine Molasse. Results show that it is possible to translate low-temperature thermochronology data into a likelihood function to obtain a 3-D kinematic model with updated, more probable parameters. The thermochronological data by itself, however, may not be informative enough to reduce the parameter uncertainty. The method is useful, however, to study alternative mechanisms of exhumation for the thermochronological samples that are not respected by the modeling, even when uncertainty is considered.
We present a novel methodology for performing experiments with subsurface structural models using a set of flexible and extensible Python modules. We utilize 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.
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.
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 con-straints 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.
Download full paper as PDF for free until April 24, 2015:
http://authors.elsevier.com/a/1QeYTcTGxnimv
We introduce a novel approach to analyse and assess the structural framework of ore deposits that fully integrates 3D implicit modelling in data-rich environments with field observations. We apply this approach to the early Palaeozoic Navachab gold deposit which is located in the Damara orogenic belt, Namibia. Compared to traditional modelling methods, 3D implicit modelling reduces user-based modelling bias by generating open or closed surfaces from geochemical, lithological or structural data without manual digitisation and linkage of sections or level plans. Instead, a mathematically defined spatial interpolation is used to generate 3D models that show trends and patterns that are embedded in large drillhole datasets. In our 3D implicit model of the Navachab gold deposit, distinctive high-grade mineralisation trends were identified and directly related to structures observed in the field. The 3D implicit model and field data suggest that auriferous semi-massive sulphide ore shoots formed near the inflection line of the steep limb of a regional scale dome, where shear strain reached peak values during fold amplification. This setting generated efficient conduits and traps for hydrothermal fluids and associated mineralisation that led to the formation of the main ore shoots in the deposit. Both bedding-parallel and highly discordant sets of auriferous quartz-sulphide veins are interpreted to have formed during the later lock-up stage of the regional scale dome. Additionally, pegmatite dykes crosscut and remobilise gold mineralisation at the deposit scale and appear to be related to a younger joint set. We propose that kilometre-scale active folding is an important deformation mechanism that influences the spatial distribution and orientation of mineralisation in ore deposits by forming structures (traps and pathways for fluids) at different preferred sites and orientations. We also propose that areas that experience high shear strain, located along the inflection lines of folds can act as preferred sites for syn-deformational hydrothermal mineralisation and should be targeted for regional scale exploration in fold and thrust belts. Our research also suggests that examination of existing drillhole datasets using 3D implicit modelling is a powerful tool for spatial analysis of mineralisation patterns. When combined with fieldwork, this approach has the potential to improve structural understanding of a variety of ore deposits.
The reliable modeling of three-dimensional complex geological structures can have a major impact on forecasting and managing natural resources and on predicting seismic and geomechanical hazards. However, the qualification of a model as structurally complex is often qualitative and subjective making the comparison of the capabilities and performances of various geomodeling methods or software difficult. In this paper, we consider the notion of structural complexity from a geometrical point of view and argue that it can be characterized using general metrics computed on three-dimensional sealed structural models. We propose global and local measures of the connectivity and of the geometry of the model components and show how they permit to classify nine 3D synthetic structural models. Depending on the complexity elements favored the classification varies. The models we introduce could be used as benchmark models for geomodeling algorithms.