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We propose and evaluate methods for the integration of automatic implicit geological modelling into the geophysical (potential field) inversion process. The objective is to enforce structural geological realism in level-set inversion, which inverts for the location of boundaries between rock units. We propose two approaches. In the first one, a geological correction term is applied at each iteration of the inversion to reduce geological inconsistencies. This is achieved by integrating an automatic implicit geological modelling scheme within the geophysical inversion process. In the second approach, we use automatic geological modelling to derive a dynamic prior model term at each iteration of the inversion to limit departures from geologically feasible outcomes. We introduce the main theoretical aspects of the inversion algorithm and perform the proof-of-concept using two synthetic studies. The analysis of results using indicators measuring geophysical, petrophysical and structural geological misfits demonstrates that our approach effectively steers inversion towards geologically consistent models and reduces the risk of geologically unrealistic outcomes. Results suggest that geological correction may be effectively applied to pre-existing models to increase their geological realism and that it can also be used to explore geophysically equivalent models.

SUMMARYThe numerical simulation of seismic wave propagation in realistic heterogeneous media, as sedimentary basins, is a key element of seismic hazard estimation. Many numerical methods in two dimensions are based on unstructured triangular meshes and explicit time schemes. However, the presence of thin layers and tangential stratigraphic contacts in sedimentary basins entails poorly shaped mesh elements: some triangle heights are extremely small compared to the edge lengths, which requires small time steps in the simulations and thus leads to prohibitive computation times. We compare manual and automatic geological model simplification techniques to modify problematic areas of the domain, so as to improve the quality of the triangulated mesh. We modify the shape and the connectivity between rock units in the basin, with the objective to reduce the computation time without significantly changing the physical response of the geological medium. These simplification techniques are applied in an investigation of site effects in the lower Var valley, a densely urbanized area located near the city of Nice (southeast of France). Numerical simulations of plane wave propagation in a heterogeneous 2-D profile are carried out with a discontinuous Galerkin finite element method. Five simplified meshes are generated and the impacts of the simplifications are analysed in comparison to the reference model. We compare the time solutions and the transfer functions obtained on the surface of the basin. The results show that the simplification procedures, in particular automatic modifications of the model, yield a significant performance gain, with a ratio higher than 55, while having a negligible impact on the ground motion response.

International audience; Underground fluid flow in hydrocarbon reservoirs (or aquifers) is difficult to predict accurately due to geological and petrophysical uncertainties. To quantify that uncertainty, several spatial statistical methods are often used to generate an ensemble of subsurface models representing and sampling these uncertainties. However, to predict the uncertainties in terms of flow responses, one needs to run a forward flow simulator (often multiphase flow in transient state) on every model of this ensemble and this generally entails intractable computational costs. Approximate solutions (flow proxies) can help addressing this challenge but introduce physical simplifications whose impact on the uncertainty quantification is difficult to characterize. This paper proposes a workflow to assess the dynamic reservoir behavior uncertainties from an input ensemble of realizations sampling geological and geophysical uncertainties. Analytical reservoir production curves are estimated from proxy distances computed between all ensemble members and from a few accurate flow responses computed on a subset of the ensemble. A randomization process accounting for proxy quality and for model selection is used to assess confidence intervals about reservoir production quantile curves. The process can use both static and dynamic proxies and also permits to compare their efficiency. A case study on a real turbiditic reservoir shows the applicability of the method, and highlights the value of even a simple proxy to increase the confidence about future reservoir production

Without properly accounting for both fault kinematics and faulted surface observations, it is challenging to create 3D geological models of faulted geological units that are seen in all tectonic settings. Geometries where multiple faults interact, where the faulted surface geometry significantly deviate from a flat plane and where the geological interfaces are poorly characterised by sparse data sets are particular challenges. There are two existing approaches for incorporating faults into geological surface modelling: one approach incorporates the fault displacement into the surface description but does not incorporate fault kinematics and in most cases will produce geologically unexpected results such as shrinking intrusions, fold hinges without offset and layer thickness growth in flat oblique faults. Another approach builds a continuous surface without faulting and then applies a kinematic fault operator to the continuous surface to create the displacement. Both approaches have their strengths, however neither approach can capture the interaction of faults within complicated fault networks e.g fault duplexes, flower structures and listric faults because they either \\begin{inparaenum}[(1)] \\item impose an incorrect (not defined by data) fault slip direction; or \\item require an over sampled data set that describes the faulted surface location\\end{inparaenum}. In this study we integrate the fault kinematics into the implicit surface by using the fault kinematic model to restore observations and the model domain prior to interpolating the faulted surface. This approach can build models that are consistent with observations of the faulted surface and fault kinematics. Integrating fault kinematics directly into the implicit surface description allows for complex fault stratigraphy and fault-fault interactions to be modelled. Our approaches show significant improvement in capturing faulted surface geometries especially where the intersection angle between the faulted surface geometry and the fault surface varies (e.g. intrusions, fold series) and when modelling interacting faults (fault duplex).

Preprint submitted to Journal of Geophysical Research - Solid Earth; International audience; 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 proves 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 a possibility graph, whose edges represent the independent association of any two pieces of fault evidence. Each edge carries a likelihood that the endpoints belong to the same fault surface is computed, expressing 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 tedious 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 uncertainty studies and (2)~ quantify subsurface uncertainty while preserving structural consistency.

Without properly accounting for both fault kinematics and observations of a faulted surface, it is challenging to create 3D geological models of faulted geological units. Geometries where multiple faults interact, where the faulted surface geometry significantly deviate from a flat plane and where the geological interfaces are poorly characterised by sparse datasets are particular challenges. There are two existing approaches for incorporating faults into geological surface modelling. One approach incorporates the fault displacement into the surface description but does not incorporate fault kinematics and in most cases will produce geologically unexpected results such as shrinking intrusions, fold hinges without offset and layer thickness growth in flat oblique faults. The second approach builds a continuous surface without faulting and then applies a kinematic fault operator to the continuous surface to create the displacement. Both approaches have their strengths; however, neither approach can capture the interaction of faults within complicated fault networks, e.g. fault duplexes, flower structures and listric faults because they either (1) impose an incorrect (not defined by data) fault slip direction or (2) require an over-sampled dataset that describes the faulted surface location. In this study, we integrate the fault kinematics into the implicit surface, by using the fault kinematics to restore observations, and the model domain prior to interpolating the faulted surface. This new approach can build models that are consistent with observations of the faulted surface and fault kinematics. Integrating fault kinematics directly into the implicit surface description allows for complexly faulted stratigraphy and fault–fault interactions to be modelled. Our approach shows significant improvement in capturing faulted surface geometries, especially where the intersection angle between the faulted surface and the fault surface varies (e.g. intrusions, fold series) and when modelling interacting faults (fault duplex).

International audience; We introduce a new method for implicit structural modeling. The main developments in this paper are the new regularization operators we propose by extending inherent properties of the classic one-dimensional discrete second derivative operator to higher dimensions. The proposed regularization operators dis-cretize naturally on the Cartesian grid using finite differences, owing to the highly symmetric nature of the Cartesian grid. Furthermore, the proposed regulariza-tion operators do not require any special treatment on boundary nodes, and their generalization to higher dimensions is straightforward. As a result, the proposed method has the advantage of being simple to implement. Numerical examples show that the proposed method is robust and numerically efficient.

In this work, we consider a relatively simple case of fluid monitoring in a subsurface gas reservoir. Seismic wave velocities for porous rocks vary depending on fluid saturation, and our objective is to quantitatively evaluate the impact of the water/gas contact depth on elastic wave propagation. To efficiently test different contact depth scenarios and assess their impact on wave propagation, we propose to locally modify a 2D geological model and run time-dependent elastic simulations. The input model is a triangulated surface conforming to geological structures and representing physical properties. The 2D meshed model is locally updated, meaning that only a given region is modified and that the other parts of the mesh remain identical. To create several models by modifying only the reservoir layer, we insert a water/gas contact defined by a level-set at several depths with MMG. During the insertion, specific care is taken to maintain the conformity of the output mesh. As compared to global remeshing, the local modification reduces the cost of recomputing physical properties over the updated mesh. We run the numerical simulations by using Hou10ni2D code, which is based on a Discontinuous Galerkin method. Our results on a gas reservoir show a consistent behavior: we observe a correlation between the depth difference and L2-norm, the larger the distance from the reference depth contact, the higher the L2-norm. This approach could therefore be integrated into an inversion loop to determine the position of the fluid contact and reduce uncertainties in the reservoir model.

International audience; Uncertainties related to permeability heterogeneity can be estimated using geostatistical simulation methods. Usually, these methods are applied on regular grids with cells of constant size, whereas unstructured grids are more flexible to honor geological structures and offer local refinements for fluid-flow simulations. However, cells of different sizes require to account for the support dependency of permeability statistics (support effect).This paper presents a novel workflow based on the power averaging technique. The averaging exponent ω is estimated using a response surface calibrated from numerical upscaling experiments. Using spectral turning bands, permeability is simulated on points in each unstructured cell, and later averaged with a local value of ω that depends on the cell size and shape.The method is illustrated on a synthetic case. The simulation of a tracer experiment is used to compare this novel geostatistical simulation method with a conventional approach based on a fine scale Cartesian grid. The results show the consistency of both the simulated permeability fields and the tracer breakthrough curves. The computational cost is much lower than the conventional approach based on a pressure-solver upscaling.

International audience; The sedimentary record of meandering rivers contains a diverse and complex set of lithological heterogeneities, which impact natural resource management. Different methods exist to model such accumulated successions present in the subsurface by integrating knowledge of system evolutionary behaviour and geometries visible on seismic time or stratal slices. With reference to case-study examples, we review, discuss and employ two of these methods: (i) ChaRMigS generates possible scenarios for channel evolution and meander cutoffs by a reverse migration process; (ii) PB-SAND is a forward stratigraphic model which simulates fluvial point-bar geometry and facies distributions from known palaeo-channel geometries. We introduce a workflow to demonstrate how these two methods can be applied in combination to predict fluvial meander-belt facies distributions, using a subsurface dataset on a Pleistocene succession from the Gulf of Thailand where abandoned channels are visible on seismic time slices, but for which bar-accretion geometries and the exact timing of channel abandonment are unclear. Results show the value of a combined modelling approach to automate the stochastic generation of facies distributions constrained by seismic interpretations.

In the petroleum industry, time-lapse (4D) studies are commonly used for reservoir monitoring, but they are also useful to perform risk assessment for potential overburden deformations (e.g., well shearing, cap-rock integrity). Although complex anisotropic velocity changes are predicted in the overburden by geomechanical studies, conventional time-lapse inversion workflows only deal with vertical velocity changes. To retrieve the geomechanically induced anisotropy, we have adopted a reflection traveltime tomography method coupled with a time-shift estimation algorithm of prestack data of the baseline and monitor simultaneously. For the 2D approach, we parameterize the anisotropy using five coefficients, enough to cover any type of anisotropy. Before applying the workflow to a real data set, we first study a synthetic data set based on the real data set and include velocity variations between baseline and monitor found in the literature (vertical P-wave velocity decrease in the cap rock and isotropic P-wave velocity change in the reservoir). On the synthetics, we measure the angular ray coverage necessary to retrieve the target anisotropy and observe that the retrieved anisotropies depend on the offset range. Based on a synthetic experiment, we believe that the acquisition of the real case study is suitable for performing tomographic inversion. The anisotropic velocity changes obtained on three inlines separated by 375 m are consistent and show a strong positive anomaly in the cap rock along the 45° direction (the [Formula: see text] parameter in Thomsen notation), whereas the vertical velocity change is surprisingly almost negligible. We adopt a rock-physics explanation compatible with these observations and geologic considerations: a reactivation of water-filled subvertical cracks.

Geomechanical restoration methods are dependent on boundary conditions to ensure geological consistency of the restored model in terms of geometry and strain. Classical restoration boundary conditions, such as flattening a datum horizon, may lead to inconsistent displacement and strain fields. We restore a laboratory structural sandbox model with known deformation history to develop guidelines for definition of boundary conditions that produce improved results from geomechanical restorations. The sandbox model has a basal silicone layer, includes synkinematic deposition, and is characterized by structures analogous to those found in suprasalt extensional environments. The deformed geometry is interpreted from three-dimensional tomography imaging, and a time series of cross section tomography images provides a benchmark to quantify restoration error and inform boundary conditions. We confirm that imposing a lateral displacement equal and opposite to far-field tectonic shortening or extension provides a more accurate restoration. However, the amount of displacement may not be known in real cases. We therefore test several established methods, using only the unrestored geometries, to assess the amount of shortening that should be used to guide geomechanical restorations. An accurate estimation is provided by the area–depth method and potentially by a dilatation analysis. Additionally, novel fault-compliance boundary conditions produce improved results in the vicinity of crossing and branching faults. Application of similar methods should produce improved restoration of natural geologic structures.

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...

International audience; Structural interpretation of seismic images can be highly subjective, especially in complex geological settings. A single seismic image will often support multiple geologically valid interpretations. However, it is usually difficult to determine which of those interpretations are more likely than others. We refer to this problem as structural model appraisal herein. We propose the use of misfit functions to rank and appraise multiple interpretations of a given seismic image. Given a set of possible interpretations, we compute synthetic data for each structural interpretation, then compare these synthetic data against observed seismic data; this allows us to assign a data-misfit value to each structural interpretation. Our aim is to find data-misfit functions which enable a ranking of interpretations. To do so, we formalize the problem of appraising structural interpretations using seismic data and derive a set of conditions to be satisfied by the data-misfit function for a successful appraisal. We investigate both vertical seismic profiling and surface seismic configurations. An application of the proposed method to a realistic synthetic model shows promising results for appraising structural interpretations using vertical seismic profiling data, provided the target region is well illuminated. However, we find appraising structural interpretations using surface seismic data to be more challenging, mainly due to the difficulty of computing phase-shift data-misfits.

International audience; Well-seismic ties allow rock properties measured at well locations to be compared with seismic data and are therefore useful for seismic interpretation. Numerous methods have been proposed to compute well-seismic ties by correlating real seismograms with synthetic seismograms computed from velocity and density logs. However, most methods tie multiple wells to seismic data one by one; hence, they do not guarantee lateral consistency among multiple well ties. We therefore propose a method to simultaneously tie multiple wells to seismic data. In this method, we first flatten synthetic and corresponding real seismograms so that all seismic reflectors are horizontally aligned. By doing this, we turn multiple well-seismic tying into a 1D correlation problem. We then compute only vertically variant but laterally constant shifts to correlate these horizontally aligned (flattened) synthetic and real seis-mograms. This two-step correlation method maintains lateral consistency among multiple well ties by computing a laterally and vertically optimized correlation of all synthetic and real seismograms. We applied our method to a 3D real seismic image with multiple wells and obtained laterally consistent well-seismic ties.

International audience; We assess stratigraphic correlation uncertainties by stochastically generating several possible correlations lines between a set of stratigraphic logs. We motivate the use of automatic correlation methods to sample this uncertainty and introduce a stochastic version of Dynamic Time Warping (DTW) that correlates two logs. This method is extended to a larger number of logs using a sequential application of DTW. When available, low-frequency stratigraphic events are correlated first, and then used to constrain the correlation of higher-order events. All DTW variants use elementary correlation costs corresponding to the likelihood of each possible horizon. The method is demonstrated on a carbonate ramp of the Cretaceous southern Provence Basin, SE France, using costs that measure the consistency between the computed platform slope angle and a theoretical depositional profile. We show that these correlation uncertainties significantly impact facies proportions in stratigraphic layers. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS.

Stochastic discrete fracture networks (DFNs) are classically simulated using stochastic point processes which neglect mechanical interactions between fractures and yield a low spatial correlation in a network. We propose a sequential parent-daughter Poisson point process that organizes fracture objects according to mechanical interactions while honoring statistical characterization data. The hierarchical organization of the resulting DFNs has been investigated in 3-D by computing their correlation dimension. Sensitivity analysis on the input simulation parameters shows that various degrees of spatial correlation emerge from this process. A large number of realizations have been performed in order to statistically validate the method. The connectivity of these correlated fracture networks has been investigated at several scales and compared to those described in the literature. Our study quantitatively confirms that spatial correlations can affect the percolation threshold and the connectivity at a particular scale.

We have developed an implicit method to automatically generate several possible models of salt top surfaces with varying geometries and topologies. This method can be conditioned to available data such as well markers and seismic picks. Because seismic imaging of salt is prone to velocity uncertainty and Fresnel zone effects, the input of the method is a seismic image that is segmented into three regions: salt, sediments, and uncertain. The uncertain region contains the salt boundary, and all further computations focus within this zone. A monotonic scalar field, ranging from zero on the edge of the certain salt body to one on the maximal possible salt boundary, defines the cumulated probability for a point to be outside the salt body. A random scalar field, also bounded between zero and one, is then used as a threshold for the first scalar field. The salt boundary is implicitly defined by the zero isovalue of the difference between the two fields, and it can be further extracted using marching cubes. The random field parameters have a geometric and topological impact on the simulated salt volumes. They can be adapted to reproduce specific geological features, but their inference remains difficult. The application of the method for the reconstruction of diapir boundaries from a set of partly interpreted sections indicates that it is well-suited to honor numerous constraining data while proposing different possible structural scenarios in the uninterpreted parts.

International audience; Incorporating prior geological knowledge in geophysical process models often meetspractical meshing challenges and raises the question of how much detail is to be includedin the geometric model. We introduce a strategy to automatically repair and simplifygeological maps, geological cross-sections and the associated meshes while preservingelementary consistency rules. To identify features breaking validity and/or the thinfeatures potentially problematic when generating a mesh, we associate an exclusion zonewith each model feature (horizon, fault). When these zones overlap, both the connectivityand the geometry of the geological layers are automatically modified. The output modelenforces specific practical quality criteria on the model topology and geometry thatfacilitates the generation of a mesh with lower bounds on minimum angles and minimumlocal entity sizes. Our strategy is demonstrated on an invalid geological cross-section froma real-case study in the Lorraine coal basin. We further explore the impacts of the modelmodifications on wave propagation simulation. We show that the differences on theseismograms due to model simplifications are relatively small if the magnitude ofsimplifications is adapted to the physical problem parameters.C 2018 Published by Elsevier Masson SAS on behalf of Acade´mie des sciences. This is anopen access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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.

International audience; In geology, implicit structural modelling constructs the geometry of geological structures (e.g. layers) by interpolating between sparse field data. A model is represented by a volumetric scalar field which is discontinuous on structural discontinuities such as faults or stratigraphic unconformities. The management of such discontinuities may involve boolean operations on several scalar fields or the creation of conformal meshes. Instead, we propose a ghost cell technique for the cartesian grid together with a set of relations between the ghost points, the regular nodes, and the discontinuities. Consequently, poor quality meshes are avoided and only the resolution of the grid has an impact on the solution. The modelling problem is posed as a least square’s minimization of a bending energy penalization on data mismatch functions and approximated by finite difference. As all relationships in the grid are implicitly defined, except close to the discontinuities, this algorithm is computationally efficient. We provide some benchmarks of the method on two-dimensional examples with folds, faults, and erosions.

International audience; RINGMesh is an open-source platform proposing a data model to support Shared Earth Modeling with unstructured meshes. This initiative is complementary to ontologic-based syntax and standard file formats. We provide features not only to share data and interpretation but also a concrete implementation framework to convert and manipulate models with the requirements needed by geomodelers, solvers and simulators. We advocate that this opens new perspectives for more efficient subsurface modeling workflows that harness uncertainties by confronting data, models and interpretations.

International audience; We introduce a method to process boundary defined geological models and ease their meshing. Our method detects and fixes geological model invalid features, (e.g. small gaps breaking model watertightness) and complex features (e.g. thin layers, unconformities and small fault throws) which constrain mesh element resolutions and angles making mesh generation challenging. These features are modeled by a graph that provides a formal framework to operate and correct the input model. The possible operations to fix the geometrical and topological issues are equivalent to graph elementary operations. Our method then first operates on the graph aiming at removing all the edges representing invalid features. The second step is to account for these topological changes in the geometrical model. The procedure is illustrated on an invalid 2D subsurface cross-section characterized by many small gaps and several intersections between the faults and the horizons.

International audience; Interpreting salt is a complex and time consuming task in seismic interpretation. Considerable progresses have been made recently by automatic methods which detect deterministic salt tops from the seismic image. However, uncertainties about salt exist, owing to intrinsic physical limitations of seismic imaging. Therefore, we propose a new workflow to generate several possible models of salt top surfaces with varying geometries and topologies. The method we propose is divided into three steps. We first segment the seismic volume into three regions: salt, sediments and uncertain, depending on the reliability of the automatic interpretation. We then compute a monotonic scalar field in the uncertain region, ranging from zero at the contact with salt to one at the contact with sediments. We finally generate a random field bounded between zero and one. The salt boundary is implicitly defined by the zero isovalue of the scalar field defined as the difference between the distance and the random fields. Applications of this workflow on a 2D seismic image and a 3D synthetic data set illustrate the potential of the method to efficiently address salt interpretation uncertainties.

International audience; Limited resolution and quality of seismic data and time requirements for seismic interpretation can prevent a precise description of the connections between faults. We have focused on the impact of the uncertainties related to the connectivity of en echelon fault arrays on fluid flow simulations. We used a set of 100 different stochastic models of the same en echelon fault array. These fault array models varied in the number of relay zones, relative position of fault segments, size of overlap zones, and number of relay faults. We automatically generated a flow model from each fault array model in four main steps: (1) stochastic computation of relay fault throw, (2) horizon building, (3) generation of a flow simulation grid, and (4) definition of the static and dynamic parameters. Flow simulations performed on these stochastic fault models with deterministic petrophysical parameters entailed significant variability of reservoir behavior, which cannot always discriminate between the types of fault segmentation. We observed that the simplest interpretation consisting of one fault yielded significantly biased water cut forecasts at production wells. This highlighted the importance of integrating fault connectivity uncertainty in reservoir behavior studies.

International audience; In this paper we demonstrate how recent geomodelling techniques can be combined and used to build a 3D geological model on a real case study: the former coal mine of Merlebach (France), that is targeted to be exploited for low-temperature geothermal energy production. From geological maps, cross-sections, borehole and mine exploitation data, we build a 3D model in which are identified the rocks and infrastructures having significantly different permeabilities. First, a structural model of the main geological interfaces in our area of interest (2 horizons and 13 faults) is built with classical geomodelling techniques. Then, we propose to model by surfaces the 71 irregularly stacked, very close and very thin, subvertical coal beds. To ease their construction, we use an implicit method which represents 3D surfaces as isovalues of a scalar field defined in a 3D tetrahedral grid of the area. The corresponding triangulated surfaces are remeshed with a recently proposed method based on Voronoi diagrams so that the exploited parts of the coal beds, now filled by sand, can be computed. The 3D surface-based geological model, in which infrastructures can be inserted as piecewise lines, can be volumetrically meshed. It is available for download as supplemental material, as well as a volumetric grid.

International audience; Geologists and geophysicists often approach the study of the Earth using different and complementary perspectives. To simplify, geologists like to define and study objects and make hypotheses about their origin, whereas geo-physicists often see the earth as a large, mostly unknown multivariate parameter field controlling complex physical processes. This paper discusses about some strategies to combine both approaches. In particular, I review some practical and theoretical frameworks associating petrophysical heterogeneities to the geometry and the history of geological objects. These frameworks open interesting perspectives to define prior parameter space in geophysical inverse problems, which can be consequential in under-constrained cases.

International audience; Fault-related displacements impact oil and gas flow predictions at reservoir scales. In this contribution, we integrate a quantitative description of fault-related deformation directly embedded into the structural mod-eling workflow. Consistent fault displacements are produced by using numerical fault operators that deform horizons in accordance with theoretical isolated fault displacement models to generate kinematically consistent structural models. We compare structural modeling approaches based on such fault operators with those relying on interpolation. Several synthetic cross-sections are generated from a reference high-resolution structural model of the Santos Basin, Brazil. Models are reconstructed from this 2D synthetic sparse dataset using both methods. Their ability to produce consistent structural models is assessed by comparing reconstructed and reference models. On this example, kinematic modeling improves the quality of automatically generated models when only few and poor quality observations are available, thus reducing the time needed for structural validation.

International audience; We discuss the sampling and the volumetric impact of stratigraphic correlation uncertainties in basins and reservoirs. From an input set of wells, we evaluate the probability for two stratigraphic units to be associated using an analog stratigraphic model. In the presence of multiple wells, this method sequentially updates a stratigraphic column defining the stratigraphic layering for each possible set of realizations. The resulting correlations are then used to create stratigraphic grids in three dimensions. We apply this method on a set of synthetic wells sampling a forward stratigraphic model built with Dionisos. To perform cross-validation of the method, we introduce a distance comparing the relative geological time of two models for each geographic position, and we compare the models in terms of volumes. Results show the ability of the method to automatically generate stratigraphic correlation scenarios, and also highlight some challenges when sampling stratigraphic uncertainties from multiple wells.

International audience; The logic of sedimentary channelized systems is only partly preserved in the depositional record. We propose a new method to reconstruct 3D channelized systems from incomplete observations made on surface or subsurface images that integrates the uncertainty on meander abandonment chronology. Starting with the youngest channel path observed and the abandoned loops in the meander belt, the method generates local relative chronologies using cross-cutting analysis. It thus proposes a possible global chronology of channel meander abandonments by going back in time while updating the system configuration. This global chronology is obtained through a stochastic procedure that orders the youngest abandoned meanders with regard to their position and orientation relative to the current channel path. Ordered abandoned meanders are then integrated in the main channel path during the reverse migration process so that the global stochastic ordering is made at each time step of the migration algorithm consistently with the updated channel belt. The proposed approach is parameterized by the spatio-temporal density of meander cutoff along the channel belt, which can be inferred from analog databases. The application of our tool on a seismic stratal slice of the Mc-Murray Formation in Canada provides various possible global chronologies of the abandoned meanders. We analyze the variability of these chronologies and highlight its impact on the various possible subsurface 3D global archi-tectures of the paleo-system and on the associated subsurface heterogeneity.

Remote sensing data provide significant information to constrain the geometry of geological structures at depth. However, the use of intraformational geomorphologic features such as flatirons and incised valleys often calls for tedious user interaction during 3-D model building. We propose a new method to generate 3-D models of stratigraphic formations, based primarily on remote sensing images and digital elevation models. This method is based on interpretations of the main relief markers and interpolation of a stratigraphic property on a tetahedral mesh covering the domain of study. The tetrahedral mesh provides a convenient way to integrate available data during the interpolation while accounting for discontinuities such as faults. Interpretive expert input may be provided through constrained interactive editing on arbitrary cross-sections, and additional surface or subsurface data may also be integrated in the modeling. We demonstrate this global workflow on a structurally complex basin in the Sierra Madre Oriental, Northeastern Mexico.

International audience; A recent method for modeling folds uses a fold frame with coordinates based on the structural geology of folds: fold axis direction, fold axial surface and extension direction. The fold geometry can be characterised by rotating the fold frame by the pitch of the fold axis in the axial surface and the angle between the folded foliation and the axial surface. These rotation angles can be expressed as 1D functions of the fold frame coordinates. In this contribution we present methods for extracting and automatically modeling the fold geometries from structural data. The fold rotation angles used for characterising the fold geometry can be calculated locally from structural observations. The fold rotation angles incorporate the structural geology of the fold and allow for individual structural measurements to be viewed in the context of the folded structure. To filter out the effects of later folding the fold rotation angles are plotted against the coordinates of the fold frame. Using these plots the geometry of the folds can be interpolated directly from structural data where we use a combination of radial basis function and harmonic analysis to interpolate and extrapolate the fold geometry. This contribution addresses a major limitation in existing methods where the fold geometry was not constrained from structural data. We present two case studies: a proof of concept synthetic model of a non-cylindrical fold and an outcrop of an asymmetrical fold within the Lachlan Fold belt at Cape Conran, Victoria, Australia.

We have developed a 3D modeling strategy of the encased minibasin of Inceyol in Sivas (Turkey). The challenge lies in the combination of sparse outcrop data and the complex interpretive geometry of geologic structures that come from salt tectonics. We have succeeded in modeling the convoluted salt surface using an explicit indirect surface patch construction method followed by a manual mesh improvement. Then, we modeled the minibasin sediments with an implicit approach. The result highlighted the remarkable geometry of the convoluted salt horizon and its associated minibasin by extending in 3D the geologist’s interpretive 2D sections. This case study proved that building complex geometries is feasible with the existing tools and a good expertise in the various geomodeling techniques. Our work also underlined the need for new methods to ease the modeling of such tectonic features from sparse data. We have developed a 3D view of the model thanks to WebGL technology, as well as downloadable data to constitute a reference case study.

International audience; This paper focuses on fault-related uncertainties in the subsurface, which can significantly affect the numerical simulation of physical processes. Our goal is to use dynamic data and process-based simulation to update structural uncertainty in a Bayesian inverse approach. We propose a stochastic fault model where the number and features of faults are made variable. In particular, this model samples uncertainties about connectivity between the faults. The stochastic three dimensional fault model is integrated within a stochastic inversion scheme in order to reduce uncertainties about fault characteristics and fault zone layout, by minimizing the mismatch between observed and simulated data.The stochastic fault model uses a priori information such as fault orientation, location, size and sinuosity, to sample both geometrical and topological uncertainties with realistic fault descriptions. Each fault object is parameterized by the random vector used to simulate fault features. Then, during inversion, the random vector of the current model is stochastically perturbed, producing a new parameter vector used as input by the stochastic fault model to produce a new model. Even if the topology varies from one model to another, the algorithm produces correlated models so that their flow responses evolve quite smoothly.The methodology is applicable in general and illustrated on a synthetic two-phase flow example. A first set of models is generated to sample the prior uncertainty space. Then models minimizing reference water-saturation data misfit are used as seeds to generate continuous Monte Carlo Markov Chains (MCMC) of models with discrete states. Posterior models reduce uncertainties about fault position, while the topology varies from one model to another. A second example highlights the interest of the parameterization when interpreted data are available, by perturbing geological scenarios and falsifying those that do not match two-phase flow observations.

International audience; 3D Structural modeling is a major instrument in geosciences, e.g. for the assessment of groundwater and energy resources or nuclear waste underground storage. Fault net- work modeling is a particularly crucial step during this task, for faults compartmentalize rock units and play a key role in subsurface flow, whether faults are sealing barriers or drains. Whereas most structural uncertainty modeling techniques only allow for geometrical changes and keep the topology fixed, we propose a new method for creating realistic stochastic fault networks with different topologies. The idea is to combine an implicit representation of geological surfaces which provides new perspectives for handling topological changes with a stochastic binary tree to represent the spatial regions. Each node of the tree is a fault, separating the space in two fault blocks. Changes in this binary tree modify the fault relations and therefore the topology of the model.

International audience; Building a 3D geological model from field and subsurface data is a typical task in geological studies involving natural resource evaluation and hazard assessment. However, there is quite often a gap between research papers presenting case studies or specific innovations in 3D modeling and the objectives of a typical class in 3D structural modeling, as more and more is implemented at universities. In this paper, we present general procedures and guidelines to effectively build a structural model made of faults and horizons from typical sparse data. Then we describe a typical 3D structural modeling workflow based on triangulated surfaces. Our goal is not to replace software user guides, but to provide key concepts, principles, and procedures to be applied during geomodeling tasks, with a specific focus on quality control.

International audience; In this paper, we aim at providing a flexible and compact volumetric object model capable of representing many sedimentary structures at different scales. Geo-bodies are defined by a boundary representation; each bounding surface is constructed as a parametric deformable surface. We propose a three-dimensional sedimentary object with a compact parametrization which allows for representing various geometries and provides a curvilinear framework for modeling internal heterogeneities. This representation is based on Non Uniform Rational B-Splines (NURBS) smoothly interpolate between a set of points. The three-dimensional models of geobodies are generated using a small number of parameters, and hence can be easily modified. This can be done by a point and click user interactions for manual editing or by a Monte-Carlo sampling for stochastic simulation. Each elementary shape is controlled by deformation rules and has connection constraints with associated objects, in order to maintain the geometry and the consistency through editing. The boundary representations of the different sedimentary structures are used to construct hexahedral conformal grids in order to perform petrophysical property simulations following the particular three-dimensional parametric space of each object. Finally these properties can be upscaled, according to erosion rules, to a global grid that represents the global depositional environment.

International audience; Three-dimensional structural modeling is gaining importance for a broad range of quantitative geoscientific applications. However, existing approaches are still limited by the type of structural data they are able to use and by their lack of structural meaning. Most techniques heavily rely on spatial data for modeling folded layers, but are unable to completely use cleavage and lineation information for constraining the shape of modeled folds. This lack of structural control is generally compensated by expert knowledge introduced in the form of additional interpretive data such as cross-sections and maps. With this approach, folds are explicitly designed by the user instead of being derived from data. This makes the resulting structures subjective and deterministic. This paper introduces a numerical framework for modeling folds and associated foliations from typical field data. In this framework, a parametric description of fold geometry is incorporated into the interpolation algorithm. This way the folded geometry is implicitly derived from observed data, while being controlled through structural parameters such as fold wavelength, amplitude and tightness. A fold coordinate system is used to support the numerical description of fold geometry and to modify the behavior of classical structural interpolators. This fold frame is constructed from fold-related structural elements such as axial foliations, intersection lineations, and vergence. Poly-deformed terranes are progressively modeled by successively modeling each folding event going backward through time. The proposed framework introduces a new modeling paradigm, which enables the building of three-dimensional geological models of complex poly-deformed terranes. It follows a process based on the structural geologist approach and is able to produce geomodels that honor both structural data and geological knowledge.

International audience; This paper introduces a stochastic structural modelling method that honours interpretations of both faults and stratigraphic horizons on maps and cross-sections in conjunction with prior information, such as fault orientation and statistical size-displacement relationships. The generated stochastic models sample not only geometric uncertainty but also topological uncertainty about the fault network. Faults are simulated sequentially; at each step, fault traces are randomly chosen to constrain a fault surface in order to obtain consistent fault geometry and displacement profile. For each simulated fault network, stratigraphic modelling is performed to honour interpreted horizons using an implicit approach. Geometrical uncertainty on stratigraphic horizons can then be simulated by adding a correlated random noise to the stratigraphic scalar field. This strategy automatically maintains the continuity between faults and horizons. The method is applied to a Middle East field where stochastic structural models are generated from interpreted two-dimensional (2D) seismic lines, first by representing only stratigraphic uncertainty and then by adding uncertainty about the fault network. These two scenarios are compared in terms of gross rock volume (GRV) uncertainty and show a significant increase in GRV uncertainty when fault uncertainties are considered. This underlines the key role of faults in resource estimation uncertainties and advocates a more systematic fault uncertainty consideration in subsurface studies, especially in settings in which the data are sparse.

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. HighlightsWe describe complicated geometrical configurations in structural models.Nine benchmark 3D structural models for geomodeling methods are proposed.We propose four measures to compare geometry and connectivity of structural models.Several classifications of the proposed benchmark models are given.

Numerical models of geological structures are generally built with a geometrical approach, which lacks an explicit representation of the deformation history and may lead to incompatible structures. We advocate that the deformation history should be investigated and represented from the very first steps of the modelling process, provided that a series of rapid, interactive or automated, deformation tools are available for local editing, forward modelling and restoration. In this paper, we define the specifications of such tools and emphasise the need for rapidity and robustness. We briefly review the different applications of deformation tools in geomodelling and the existing deformation algorithms. We select a deformation algorithm based on rigid elements, first presented in the Computer Graphics community, which we refer to as Reed. It is able to rapidly deform any kind of geometrical object, including points, lines or volumes, with an approximated mechanical behaviour. The objects to be deformed are embedded in rigid cells whose displacement is optimised by minimising a global cost function with respect to displacement boundary conditions. This cost function measures the difference in displacement between neighbouring elements. The embedded objects are then deformed based on their original position with respect to the rigid elements. We present the basis of our implementation of this algorithm and highlight its ability to fulfil the specifications we defined. Its application to geomodelling specific problems is illustrated through the construction of a synthetic structural model of multiply deformed layers with a forward modelling approach. A special boundary condition adapted to restore large folds is also presented and applied to the large anticline of Han-sur-Lesse, Belgium, which demonstrates the ability of this method to efficiently perform a volumetric restoration without global projections. Graphical abstract(A) Initial structural model (Annot, France) adapted from Salles 2010, (b) Rigid Element based deformation tool defining a large folding event and (c) Applied deformation.Display Omitted HighlightsWe propose specifications for deformation tools for 3D geological structure modelling.We select a deformation algorithm based on rigid elements and deformation energy.We propose a process for modelling structures with several folding events.We implement boundary conditions for geological structure restoration.We implement anisotropy and local volume conservation rules.

Three-dimensional (3D) structural models are generalizations of geological maps and cross-sections used by geologists for the last 200 years. They describe the geometry and layout of rock units in 3D space by honoring available observations, measurements and geological concepts. They are used on a daily basis in industry and academia to improve one’s understanding of an area, to quantify geological processes and to address natural resource management problems (oil and gas, mining, geothermal energy, ground water). This area of research raises interesting questions concerning the ways to build these models and to appropriately describe, analyze and reduce the associated uncertainty. For these ends, new conceptual models relating to geological processes and geometric parameters are needed. This issue gathers contributions regarding all of these aspects. In preparing this special issue, we have received a total of 25 paper proposals and 13 full papers, of which 5 are published in the present issue and 2 are still in revision. We would like to thank all the authors for their contributions and the reviewers for both their help and remarks, which have been essential to the editorial process. 3D structural modeling emerged in the 1970s by generating computerized depth maps with contouring techniques. These methods are very effective and are still in use today for the processing and analysis of topographic surfaces and depth maps. However, they raise problems when it comes to fault management, or when dealing with complex surfaces having several Z-values for the same geographic coordinate (e.g., recumbent folds, salt tops). This limitation motivated the development of techniques

We propose a method to remesh the surfaces of 3D sealed geological structural models for subsequent volumetric meshing. The input of the method is a set of triangulated surfaces that are in contact along given lines and at given points. The output is a set of surfaces meshed with triangles as equilateral as possible. The method relies on a global Centroidal Voronoi optimization to place the vertices of the final surfaces combined with combinatorial considerations to either recover or simplify the surfaces, lines and points of the input model. When the final resolution is sufficient, the input contact lines and points are also contact lines and points of the final model. However, when dealing with models with complex contacts, resolution may be insufficient and instead of a refinement strategy that may lead to too many points, we propose to locally merge some features of the input model. This ability to simplify the input model is particularly interesting when the model is to be volumetrically meshed. The method is demonstrated on twelve structural models, including seven models built with an implicit modeling method, and one folded layer model affected by a discrete fracture network. HighlightsA surface remeshing method for 3D sealed geological structural models.This method is fully automatic, handles contacts properly and coherently.It generates a mesh at specified resolution and with high quality elements.Results on twelve models are evaluated and shown.

International audience; In this paper we propose a method to generate mixed-element meshes (tetrahedra, triangular prisms, square pyramids) for B-Rep models. The vertices, edges, facets, and cells of the final volumetric mesh are determined from the combinatorial analysis of the intersections between the model components and the Voronoi diagram of sites distributed to sample the model. Inside the volumetric regions, Delaunay tetrahedra dual of the Voronoi diagram are built. Where the intersections of the Voronoi cells with the model surfaces have a unique connected component, tetrahedra are modified to fit the input triangulated surfaces. Where these intersections are more complicated, a correspondence between the elements of the Voronoi diagram and the elements of the mixed- element mesh is used to build the final volumetric mesh. The method which was motivated by meshing challenges encountered in geological modeling is demonstrated on several 3D synthetic models of subsurface rock volumes.

International audience; This paper presents a 3D parametric fault representation for modeling the displacement field associated with faults in accordance with their geometry. The displacements are modeled in a canonical fault space where the near-field displacement is defined by a small set of parameters consisting of the maximum displacement amplitude and the profiles of attenuation in the surrounding space. The particular geometry and the orientation of the slip of each fault are then taken into account by mapping the actual fault onto its canonical representation. This mapping is obtained with the help of a curvilinear frame aligned both on the fault surface and slip direction. This formulation helps us to include more geological concepts in quantitative subsurface models during 3D structural modeling tasks. Its applicability is demonstrated in the framework of forward modeling and stochastic sequential fault simulations, and the results of our model are compared to observations of natural objects described in the literature.

International audience; Earth scientists have always created spatial models of the subsurface. Before the dawn of computer-based modeling, earth models were simply drawn by hand on a piece of paper as cross section or plan views, sometimes utilizing the techniques of descriptive geometry. These hand-draw models are quick and easy to create; this is why we are still doing them on white boards, note books and sometimes even on napkins. They communicate ideas very well, but they are subjective and rarely constrained by data in a measurable way. As the number of observations grew with the advancement of data collections technologies, the possibility to use mathematical algorithms to do the modeling became a reality. These processes, first applied in 2D then in 3D, removed some of the subjectivity from the modeling. These processes work very well when the data density is high enough, meaning that models built with different mathematical methods are both realistic and similar one to another.