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... We can also try to apply a metric, such as model topology, to analyse how well sampled the model space is. Thiele et al. (2016b) analysed the topology of stochastically generated Noddy models and found that after 100 models for small perturbations around a starting model, the number of new topologies dropped off rapidly. In our case we are not making small perturbations, so we could expect to require more models before the rate of production of new topologies decays, and topology is only one possible metric for comparing models. ...
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Unlike some other well-known challenges such as facial recognition, where machine learning and inversion algorithms are widely developed, the geosciences suffer from a lack of large, labelled data sets that can be used to validate or train robust machine learning and inversion schemes. Publicly available 3D geological models are far too restricted in both number and the range of geological scenarios to serve these purposes. With reference to inverting geophysical data this problem is further exacerbated as in most cases real geophysical observations result from unknown 3D geology, and synthetic test data sets are often not particularly geological or geologically diverse. To overcome these limitations, we have used the Noddy modelling platform to generate 1 million models, which represent the first publicly accessible massive training set for 3D geology and resulting gravity and magnetic data sets (https://doi.org/10.5281/zenodo.4589883, Jessell, 2021). This model suite can be used to train machine learning systems and to provide comprehensive test suites for geophysical inversion. We describe the methodology for producing the model suite and discuss the opportunities such a model suite affords, as well as its limitations, and how we can grow and access this resource.
... Although fundamental uncertainties in geological and environmental models and various studies around them are of great importance (Bond, 2015;Jessell et al., 2016;Refsgaard et al., 2007;Wellmann and Caumon, 2018;Wellmann and Regenauer-Lieb, 2012;White et al., 2016), uncertainty is currently not reflected in Geopropy. ...
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Geological modelling is an essential aspect of underground investigations, with cross-sections being one of the key aspects. This modelling can be done by experienced geologists or using mathematical methods. We present Geopropy, an open-source decision-making algorithm implemented in Python, that generates 3D cross-sections (the boreholes do not have to be aligned). It performs as an intelligent agent that simulates the steps taken by the geologist in the process of creating the cross-section, coupled with data-driven decisions. The algorithm detects zones with more than one possible outcome and, based on the level of complexity (or user preference), proceeds to automatic, semiautomatic or manual stages. Geopropy could be the basis of a new, simpler, more comprehensible way of looking at geological models in industry and academia while at the same time creating the potential for using novel machine learning algorithms in geological modelling.
... After constructing a fine triangulation fault surface model with the fault point data, the intersecting relationship of the fault surfaces is automatically judged and recorded by the graph model of graph theory. Graph theory has some applications in the field of geology (such as fracture modeling [28][29][30], two-dimensional (2D) geological map recognition [10], the organization of geological relations [31,32], etc.). Compared with the fault model, the fracture model has a small scale and a simple surface structure. ...
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Three-dimensional complex fault modeling is an important research topic in three-dimensional geological structure modeling. The automatic construction of complex fault models has research significance and application value for basic geological theories, as well as engineering fields such as geological engineering, resource exploration, and digital mines. Complex fault structures, especially complex fault networks with multilevel branches, still require a large amount of manual participation in the characterization of fault transfer relationships. This paper proposes an automatic construction method for a three-dimensional complex fault model, including the generation and optimization of fault surfaces, automatic determination of the contact relationship between fault surfaces, and recording of the model. This method realizes the automatic construction of a three-dimensional complex fault model, reduces the manual interaction in model construction, improves the automation of fault model construction, and saves manual modeling time.
... Indeed, all the structural details do not have the same impact on the subsurface processes [e.g., Anquez, 2019, Raguenel, 2019. In particular, topological details may play a prominent role as compared to geometric variations [e.g., Thiele et al., 2016b, Wellmann andCaumon, 2018]. Therefore, various authors have also proposed to quantify the structural uncertainties based on the results of forward physical simulations [e.g., Manzocchi et al., 2008, Lindsay et al., 2013, Julio et al., 2015 or geophysical inversion [e.g., Lindsay et al., 2014, Giraud et al., 2017. ...
Thesis
Building a numerical 3D model of the subsurface requires to integrate sparse and ambiguous data. Due to salt tectonics specificities, salt bodies have complex shapes and may present topological singularities. Modeling their geometries is, therefore, difficult, but important as they introduce large physical property contrasts in the subsurface. Seismic imaging is commonly used to map salt and get information about its geometry. Nevertheless, building a seismic image is a long and iterative process, which requires numerous interpretation phases. These interpretations are prone to uncertainties, stemming from the limits of data acquisition and resolution and the assumptions underlying their processing. These uncertainties propagate through the imaging process and impact our understanding and models of the subsurface. Taking them into account is, therefore, crucial during seismic interpretation and requires to be done automatically given the iterative nature of seismic imaging. In this thesis, I am interested in the assessment of structural uncertainties related to the interpretation of ambiguous seismic images of salt tectonics environments. The main contribution of this thesis is a numerical method for stochastically modeling variable shapes of salt bodies and their connectivity. The modeling is based on an a priori definition of the uncertainties, represented as a buffer zone encompassing the salt boundary. The boundary is defined as the combination of a reference scalar field, computed from the buffer zone, and a spatially correlated random field that is used as a perturbation. This implicit formulation allows for the simulation of both varying salt geometries and topologies while ensuring the validity of the simulated boundaries. When the simulated diapir is a bulb detached from its pedestal, a weld is simulated to connect them. The position of the weld is determined from the scalar field representing the salt boundary, to ensure its consistency with the simulated salt bodies. The method is automatic and proposes to integrate punctual information (e.g., well data or manual seismic picks) and, to some extent, prior geological knowledge. The second contribution of this thesis is an application of this method to the characterization of structural uncertainties underlying seismic imaging on a 2D synthetic data set. Starting from a rough buffer zone, I simulate a set of possible interpretations of the salt boundary. I use these interpretations to define a set of equiprobable migration velocity models, that are used in turn to generate as many seismic images. The statistical analysis of this image set, both directly and from derived seismic attributes, permits to highlight the image parts which are most sensitive to migration velocity variations, and provides insights on the nature of the imaged salt bodies. These contributions open new perspectives for uncertainty quantification in an automatic velocity model updating framework in seismic imaging.
... To date, many efforts have been made to analyze and quantify the uncertainties of geological models (Chilès et al. 2004;Caumon and Journel 2005;Bistacchi et al. 2008;Suzuki et al. 2008;Jessell et al. 2010;Wellmann and Regenauer-Lieb 2012;Thiele et al. 2016;Schneeberger et al. 2017;Edwards et al. 2017). Uncertainties in 3D geological models can be classified into three types, according to their different sources (Mann 1993;Bárdossy and Fodor 2004;Wu et al. 2005;Wellmann et al. 2010;Zhu and Zhuang 2010;Bond et al. 2011;Lindsay et al. 2012;Bond 2015). ...
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A 3D geological structural model is an approximation of an actual geological phenomenon. Various uncertainty factors in modeling reduce the accuracy of the model; hence, it is necessary to assess the uncertainty of the model. To ensure the credibility of an uncertainty assessment, the comprehensive impacts of multi-source uncertainties should be considered. We propose a method to assess the comprehensive uncertainty of a 3D geological model affected by data errors, spatial variations and cognition bias. Based on Bayesian inference, the proposed method utilizes the established model and geostatistics algorithm to construct a likelihood function of modeler’s empirical knowledge. The uncertainties of data error and spatial variation are integrated into the probability distribution of geological interface with Bayesian Maximum Entropy (BME) method and updated with the likelihood function. According to the contact relationships of the strata, the comprehensive uncertainty of the geological structural model is calculated using the probability distribution of each geological interface. Using this approach, we analyze the comprehensive uncertainty of a 3D geological model of the Huangtupo slope in Badong, Hubei, China. The change in the uncertainty of the model during the integration process and the structure of the spatial distribution of the uncertainty in the geological model are visualized. The application shows the ability of this approach to assess the comprehensive uncertainty of 3D geological models.
... The proposed sampling method may generate the same fault scenario several times. To assess whether the sampler has converged, a common strategy consists in generating models until the number of distinct scenarios stabilizes (Pakyuz-Charrier et al., 2019; Thiele et al., 2016). For this, we use the metric N diff (l, m) which counts the number of differences between any two realizations G asso l and G asso m . ...
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The characterization of geological faults from geological and geophysical data is often subject to uncertainties, owing to data ambiguity and incomplete spatial coverage. We propose a stochastic sampling algorithm which generates fault network scenarios compatible with sparse fault evidence while honoring some geological concepts. This process is useful for reducing interpretation bias, formalizing interpretation concepts, and assessing first‐order structural uncertainties. Each scenario is represented by an undirected association graph, where a fault corresponds to an isolated clique, which associates pieces of fault evidence represented as graph nodes. The simulation algorithm samples this association graph from the set of edges linking the pieces of fault evidence that may be interpreted as part of the same fault. Each edge carries a likelihood that the endpoints belong to the same fault surface, expressing some general and regional geological interpretation concepts. The algorithm is illustrated on several incomplete data sets made of three to six two‐dimensional seismic lines extracted from a three‐dimensional seismic image located in the Santos Basin, offshore Brazil. In all cases, the simulation method generates a large number of plausible fault networks, even when using restrictive interpretation rules. The case study experimentally confirms that retrieving the reference association is difficult due to the problem combinatorics. Restrictive and consistent rules increase the likelihood to recover the reference interpretation and reduce the diversity of the obtained realizations. We discuss how the proposed method fits in the quest to rigorously (1) address epistemic uncertainty during structural studies and (2) quantify subsurface uncertainty while preserving structural consistency.
... Interpolation error can also be obtained if stochastic methods such as kriging are used. The estimates do not provide insight into geometrical or topological variability (Thiele et al. 2016) in the 3D model which may be due to interactions between inconsistent input data in order to answer the question "should resource exploration an extraction strategies, volume estimates and value assessments use this model? (Quigley et al., Minerva, in review)" ...
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A structural geological model describes the structure of subsurface and plays an important role in the exploration of mineral and petroleum resources. Despite the widespread use of three-dimensional geological models, the theoretical research of informatics in the field of structural geology is still very limited. We have noticed a lack of methods for integrating explicit semantics of field observation data and geophysical data into geological models. The existing model representation methods focus on accurately representing the geometric morphological information of underground structures, ignoring the high-level semantics implied in the model. The formal representation of the semantic information is necessary to promote the development of intelligent methods in geomodeling and geophysical inversion. In this paper, we propose a new framework to formally represent the semantics of structural geological models with a clear distinction of geometric and geological semantics. For the geometric semantics, based on the extension of the 9-intersection model, we mathematically define the spatial topological relations between geometric objects that make up the geological model. For the geological semantics, we define the geological contact and compositional relations between geological bodies and geological surfaces and reveal the temporal implications of these geological relationships. We design a multilayer heterogeneous network as a computer characterization of the semantics of the geological model. A better representation of semantic information aids in the creation and validation of geological models, as well as management, queries, and analyses of geological knowledge.
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As climate changes and populations grow, a deeper understanding of deltaic surface and subsurface processes will help design sustainable management practices of delta resources. Numerical delta models are useful tools for understanding the relationship between the surface and subsurface, but quantitatively linking surface dynamics to subsurface structures remains difficult. The challenges stem from uncertainty in the numerical model parameters and the selection of informative post-processing metrics. In this work a Monte Carlo- and metric-based probabilistic framework is proposed for testing how well a numerical delta model captures the link between surface dynamics and subsurface structure. Probabilistic analysis of three graph-theoretic metrics describing morphology, morphodynamics, and subsurface structure shows that, at the laboratory scale, certain delta surface features, including channelization and channel stability, are informative of the spatial organization of sediment in the subsurface. Other surface features, such as sheet flows, are less informative. The surface dynamics metrics are also applied to data from a laboratory-scale physical experiment to show key differences in the numerical and experimental surface dynamics. The experimental morphology is more channelized than the numerical model and also undergoes more dramatic morphologic changes. These differences are likely due to a combination of numerical model resolution limitations, assumptions in the numerical model physics, and differences in flow field extraction in the numerical model and physical experiment.
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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.
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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.
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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.
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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.
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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.