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Variations in the migration velocity model directly affect the position of the imaged reflectors in the subsurface, leading to structural imaging uncertainties. These uncertainties are not explicitly addressed when trying to deterministically build an adequate velocity model. This paper presents a new stochastic geology-controlled velocity modeling method that handles the possible presence of a salt weld. This permits the generation of a large set of geologic scenarios and associated velocity models. Each model is used to remigrate the seismic data. Then, a statistical analysis of the resulting seismic images is performed to quantify the local variability of the seismic responses. The approach is applied to the imaging of salt diapirs in an iterative scheme (migrate, pick, and update). The results indicate that similar to stacking common-midpoint gathers, the statistical analysis preferentially preserves recurrent features from one image to another. In particular, this analysis permits the distinction between the connected and detached diapirs without prior knowledge about their connectivity, highlighting the potential of the method to resolve important aspects of the basin and reservoir architecture. More generally, it provides quantitative information on the parts of the seismic image most sensitive to migration velocity variations, which opens an interesting perspective to quantitative interpretation uncertainty assessment. Finally, the presented application also suggests that it is possible to significantly improve the quality of the generated seismic images by sampling many possible geologic scenarios.

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.

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).

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).

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; 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.

Modeling the subsurface is a complex task because the data scarcity leads to ambiguous interpretations. As a result, subsurface models are prone to many uncertainties, which can be accounted for by stochastically simulating a large set of possible models. These models are constrained by the data (of various resolution and types), but also by geological knowledge and concepts. Integrating the latter in simulation methods emerges as a key point to reduce uncertainties, although it adds another layer of complexity to the modeling process. In this presentation, I focus on two different geological contexts characterized by specific geobody shapes and connectivity: channelized systems and salt tectonics.Channelized systems are, indeed, characterized by elongated and sinuous structures, the channels, which evolve through time by continuous lateral and vertical migrations, and abrupt events like avulsion or meander cut-offs. The combination of erosion and deposition processes is an additional source of complexity in the sedimentary records. When considering the 3D reconstruction of channelized systems, honoring data while reproducing the complex spatial architecture of these structures - so their specific connectivity - remains challenging. The various methods we have recently developed can now be combined to achieve such a goal: (i) single channels or channel parts (for avulsion) can be simulated consistently with well-data, probability cubes, or confinement thanks to a method based on Lindenmayer systems; (ii) from a channel path, consistent 3D architectures can be generated with a reverse-time channel migration approach (ChaRMigS) handling the observed abandoned meanders; (iii) to honor well data within this reverse-time reconstruction, the stochastic simulation of abandoned meanders and avulsions offers interesting solutions. The impact of such modelling methodology on connectivity reproduction has been demonstrated using static criteria, and a flow-based evaluation constitutes an obvious next step.In the case of salt tectonics, one difficulty comes from the highly convoluted shapes taken by salt bodies, incompatible with the hypothesis of minimal surface classically used in geomodeling methods. To tackle this issue, we have developed a dedicated method to stochastically generate various salt envelopes in a pre-defined uncertainty zone. Simulations of welds, i.e. surfaces (or most often thin volumes) resulting from the removal of salt from a former layer or diapir stage, also allow us to reproduce topological singularities between salt and the surrounding sediments. Welds connect the different salt volumes, which let us recover a more geologically-consistent representation of such complex systems. The present method is still in its early days, and further improvements need to be undertaken to fully integrate the diversity of structures actually observed in the field.

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.

Computer-assisted stratigraphic correlation can help to produce several scenarios reflecting interpretation uncertainties. In this work, we propose a method which translates sedimentary concepts into a correlation cost for each possible stratigaphic correlation. All these correlation costs are used to populate a cost matrix in order to apply the Dynamic Time Warping algorithm and to compute the n-best correlation sets having the n-least cumulative costs. The proposed cost function reflects prior knowledge about sediment transport direction, and it is tested on two wells penetrating a Middle Jurassic reservoir in the North Sea. Well markers are described by two parameters: (1) the sedimentary facies corresponding to a depositional environment, and (2) the relative distality of the well computed from its position along the sediment transport direction. The main principle of correlation used in this article assumes that a well marker (described by a facies and a distality) cannot be correlated with another well marker described by a depositionally deeper facies at a more proximal position, or a depositionally shallower facies at a more distal position. This approach produces consistent stratigraphic well correlations, and highlights the sensitivity of the solution to the facies zonation and to the relative well distality. Therefore, the proposed rule offers a way to coherently consider chronostratigraphic correlation and the associated uncertainties at the parasequence scale, i.e., at a smaller scale than generally considered in deterministic correlation.

International audience; Fault damage zones can act as a preferential corridor for fluid flow in the subsurface, and for this reason the characterization of their structure, including the attributes of the associated fracture network, is fundamental. In this work, we characterize the damage zone of the Qala fault, a normal fault developed in platform carbonates of the Gozo Island (Maltese Islands). We propose a new workflow that combines scanline and scan-area analysis applied on a high resolution DOM. Linear scanlines allow to characterize fracture spatial distribution, detect stationary area and identify damage zone width. Areal sampling permits to extract the fracture parameters matching the stationary 1D domains. This new approach allows us to: (1) univocally separate the damage zone from the background fractures, (2) identify fracture corridors, (3) collect fracture parameters (length, trend, density, intensity, spacing and topology), (4) identify the REV of the fracture density, intensity and topology and (5) characterize the fracture network connectivity.

International audience; This paper addresses stratigraphic uncertainty and its impact on subsurface forecasts. For this, we introduce a new assisted automatic method which detects possible sequence boundaries from well log data. This method uses multi-scale signal analysis (discrete wavelet transform) to compute the probability density of finding maximum flooding surfaces and maximum regressive surfaces as a function of depth. It then recursively decomposes the studied stratigraphic section into sub-intervals where the analysis is repeated. We applied this method on a shallow marine wave dominated siliciclastic reservoir located in the Vienna Basin. We observe that several reservoir models with different stratigraphic layering (keeping all other parameters constant) have a different reservoir behavior. This allowed us to locally resolve the mismatch between measured and simulated tracer tests. This illustrates the significance of stratigraphic uncertainties in reservoir modeling and the role of automatic methods to help assess and reduce these uncertainties.

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.

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; 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

This work explains a procedure to predict Cu potentials in the ore-Kupferschiefer using structural surface-restoration and logistic regression (LR) analysis. The predictor in the assessments are established from the restored horizon that contains the ore-series. Applying flexural-slip to unfold/unfault the 3D model of the Fore-Sudetic Monocline, we obtained curvature for each restored time. We found that curvature represents one of the main structural features related to the Cu mineralization. Maximum curvature corresponds to high internal deformation in the restored layers, evidencing faulting and damaged areas in the 3D model. Thus, curvature may highlight fault systems that drove fluid circulation from the basement and host the early mineralization stages. In the Cu potential modeling, curvature, distance to the Fore-Sudetic Block and depth of restored Zechstein at Cretaceous time are used as predictors and proven Cu-potential areas as targets. Then, we applied LR analysis establishing the separating function between mineralized and non-mineralized locations. The LR models show positive correspondence between predicted probabilities of Cu-potentials and curvature estimated on the surface depicting the mineralized layer. Nevertheless, predicted probabilities are particularly higher using curvatures obtained from Late Paleozoic and Late Triassic restorations.

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.

International audience; Volumetric restoration can provide crucial insights into the structural evolution of three-dimensional (3-D) petroleum systems. A major limitation to its widespread application is the need to include complex architectures and realistic mechanics such as flexural slip. We apply an implicit approach that allows for, including unconformities, thin and/or pinched-out layers in the models but that cannot explicitly localize slip along horizons. To take advantage of this approach while accounting for flexural slip in 3-D restoration, we investigate new geomechanical properties. We consider flexural slip folding as a result of stacked rigid and thin weak layers, which can be modeled using transversely isotropic properties. We compare restorations of an anticline using transversely isotropic properties, isotropic properties, and a stack of rigid isotropic layers with nonfrictional slip between the layers. Our results show that transversely isotropic properties reasonably approximate flexural slip folding. We use these new tools to model the evolution of a complex system located in the Niger Delta toe. The system includes a detachment fold, a fault-bend fold, and a structural wedge formed in series. Growth stratigraphy and erosional surfaces delimit the kinematics of deformation. Regional erosive surfaces, 3-D gradients of fault slip, and vertical variations in mechanical strength motivated the use of our new restoration techniques. Restoring two growth units results not only in reinforcing the interpretation that the area is behaving as a deforming thrust sheet at critical taper, but also in highlighting coeval activity on both the hinterland structures and the toe of the thrust belt.

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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; Due to the limited resolution of seismic reflection data in imaging near vertical structures, structural models can have significant uncertainties related to fault geometries and position. These uncertainties can be reduced by performing a history matching analysis on a large number of structural models generated stochastically. This work investigates about the integration of vertical seismic profiling data as another way to constrain and reduce such uncertainties. Because travel-times are not sufficiently sensitive to fault geometry perturbations and because we cannot model amplitudes accurately, we rely on phase distortion of seismograms as they propagate through the faulted models. To extract instantaneous phase information from seismograms, we used the empirical mode decomposition algorithm. This approach offers several advantageous properties compared to computing the instantaneous phase by analytic signal transformation. An instantaneous phase misfit was then defined as the L2 norm of two instantaneous phase functions. A numerical experiment was carried out in which 60 fault networks were generated stochastically from a single 3D interpretation of multiple cross sections; the 60 models were then ranked from the most similar up to the most dissimilar from a randomly chosen reference model. Results show that the proposed misfit can successfully constrain fault geometry

International audience; Conditioning a forward stratigraphic model to seismic or well data is still a challenge. So, such model cannot usually be used to run static or dynamic reservoir studies. In common methodologies, training images are built from FSM and used with Multiple Point Statistics methods to integrate the information in static geocellular models. Similarly, we present a method that uses a FSM as training model to generate 3D stratigraphic correlations of a set of units identified along wells. The wells are correlated iteratively, each new well being correlated to the result of the previous correlation. This ensures to take the 3D disposition of the wells into account. When the probability of association of the units is computed, we use the Dynamic Time Warping algorithm to build a consistent stratigraphic correlation. First results on synthetic data are presented, using a forward model built with the Sedsim algorithm and three wells.

International audience; The stochastic stratigraphic well correlation method considers the stratigraphic correlation of well data as a set of possible models to sample and manage uncertainty in subsurface studies. This method addresses the incompleteness of typical subsurface data such as limited seismic resolution, seismic blindness due to the lack of impedance contrast between distinct stratigraphic formations, borehole preferential location. The stochastic stratigraphic well correlation method is applied to the Malampaya buildup (a well documented offshore gas field located NorthWest of the Palawan Island, Philippines), aged upper Eocene to lower Miocene, and developed on the crest of a tilt-block. Among the available data, ten wells, seven of which are cored, have been drilled and a high resolution 3D seismic survey was acquired by Shell Philippines in 2002.

This paper proposes to improve the natural fracture network characterisation by analysis microseismic data. We use a 3D Hough transform to build fracture orientation and density maps describing discontinuities that cannot be described by other measurements. The stochastic Discrete fracture simulator combines geostatistical and pseudo-genetic approaches to generate models that honour both measures from field characterisation and hierarchical organisation that result from the fracturing process itself. We suggest that using realistic fracture network characterisation and introducing mechanical concepts in the DFN simulation process affect connectivity of DFNs, hence is essential for predictivity of reservoir flow models.

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

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.

Accurate modelling of all scales of heterogeneities is necessary for a precise flow modelling inside clastic reservoir. We propose to simulate small scale heterogeneties that can be deposed at the interface between sedimentary structures (e.g. between accretion figure in channel point bars). The geometries of the considered sedimentary structures are modelled as boundary representation using the Non-Uniform Rational B-Spline (NURBS) mathematical formulation. This representation of various sedimentary objects (channel, point bar, clinoform, lobe and levee) provides a curvilinear framework for petrophysical properties simulations. The spatial distribution of petrophysical properties such as permeabilities has been simulated using unconditional Sequential Gaussian Simulations (SGS). An upscaling is then performed in order to integrate the surface properties into flow simulation grid. Nevertheless, these features are often very thin and local and cannot be upscaled to a complete reservoir grid cell. Thus, these interface small-scale disparities are considered as transmissibility multipliers applied to the faces of the grid’s cells. Moreover erosion due to the deposit of other geobodies can modify the repartition of surface heterogeneities. Thus, order of deposit and erosion between objects are taken into account through all these procedures.

International audience; The characterization of sedimentary structures is an important step in constructing quantitative models of sedimentary deposits from digital images, such as 3D seismic data, satellite images, or digital outcrops. However, the interpretation of these structures generally consists of tedious line pickings followed by surface modeling to define geobodies. Automatic geobody extraction is an alternative, but it is sensitive to image noise, and it does not account for prior sedimentary knowledge. We decided to combine minimal picking by an interpreter with object-guided image processing and optimization to achieve fast and semiautomatic geobody interpretation. Our approach used a realistic volumetric geobody representation based on nonuniform rational basis splines, which can easily be deformed by the interpreter and numerical optimization. Custom edge detection guided by some initial rough interpretations was performed to strengthen the most relevant edges in the picture. Automatic optimization was then computed to fit the initial geobody to these highlighted edges. This approach was applied on satellite pictures showing alluvial channels, and some preliminary results on 3D seismic time slices were also presented. The interpreted channels were then used in a retrodeformation process to automatically reconstruct the point bars. This semiautomatic method opens new perspectives to help interpreters rapidly come up with 3D models of sedimentary structures from subsurface and analog surface data sets.

International audience; Superposed to ductile syn-metamorphic deformations, post-foliation deformations affect metamorphic units during their exhumation. Understanding the role of such deformations in the structuration of metamorphic units is key for understanding the tectonic evolution of convergence zones. We characterize post-foliations deformations using 3D modelling which is a first-order tool to describe complex geological structures, but a challenging task where based only on surface data. We propose a modelling procedure that combines fast draft models (interpolation of orientation data), with more complex ones where the structural context is better understood (implicit modelling), allowing us to build a 3D geometrical model of Syros Island blueschists (Cyclades), based on field data. With our approach, the 3D model is able to capture the complex present-day geometry of the island, mainly controlled by the su-perposition of three types of post-metamorphic deformations affecting the original metamorphic pile: i) a top-to-South ramp-flat extensional system that dominates the overall island structure, ii) large-scale folding of the metamorphic units associated with ramp-flat extensional system, and iii) steeply-dipping normal faults trending dominantly NNW-SSE and EW. The 3D surfaces produced by this method match outcrop data, are geologically consistent, and provide reasonable estimates of geological structures in poorly constrained areas.

Corner-point gridding is widely used in reservoir and basin modeling but generally yields approximations in the representation of geological interfaces. This paper introduces an indirect method to generate a hex-dominant mesh conformal to 3D geological surfaces and well paths suitable for finite-element and control-volume finite-element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms, and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm (Meshkat and Talmor Int. J. Numer. Meth. Eng. 49(1-2), 17–30 2000) that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem (Bomze et al. 1999), known to be $\mathcal {N}\mathcal {P}$ -Complete. We propose several heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on 3D geological models including a faulted and folded model and a discrete fracture network.

3D geomodelling, a computer method for modelling and visualizing geological structures in three spatial dimensions, is a common exploration tool used in oil and gas since more than several decades. When adding time, 4D modelling allows reproducing the dynamic evolution of geological structures, and reconstructing the past deformation history of geological formations. 3D geomodelling has been applied to mineral exploration with some success since more than 15 years, but can be considered still challenging for modelling hard rock settings. If very few 4D modelling case studies have been carried out in mineral exploration, it nowadays begins to be applied in structural geology and mineral resources exploration. This paper describes the 3D and 4D geomodelling basic notions, concepts, and methodology when applied to mineral resources assessment and to modelling ore deposits. It draws on the state of the art of 3D and 4D-modelling, describing advanced techniques, limitations and recommendations. The text is illustrated by several 3D GeoModels of mineral belts across Europe, including the Fennoscandian Shield (Finland, Sweden), Hellenic (Greece), Iberian (Spain, Portugal) and Foresuedic (Poland, Germany) belts, all of those case-studies have been performed within the EU FP7 ProMine research project (Part of objectives of the 4 years ProMine project were to integrate the mapping of metal and mineral resources across the European Union, especially in WP1 and WP2). Perspectives and recommendations on applying 3 and 4 geomodelling in mineral resources appraisal are given in the conclusions.

We propose a method to manage uncertainties about the layering of 3D reservoir models, using stochastic correlations of sedimentary units identified along wells, according to the sequence stratigraphy paradigm. A stratigraphic model represents the architecture of the stratigraphic succession of an area. Sequence stratigraphy is a common paradigm in reservoir studies to interpret and correlate local high resolution observations (outcrops, well logs and core samples) and more exhaustive but lower resolution data such as 3D seismic. The incompleteness of these data, their quantity and their varying quality, added to the fact that the processes that control the geometry and the conformability of the sequences are complex and poorly known, lead to uncertainties. The proposed method aims at building stratigraphic models honoring 1D interpretations along wells together with conceptual sequence stratigraphic rules formulated quantitatively as correlation costs. The algorithm chosen is a modified version of the Dynamic Time Warping algorithm. More than finding the best correlation using a set of rules, it handles different orders of sequences, takes in account the conformability of the horizons, and its output is a set of different possible correlations, allowing for generating alternative stratigraphic layerings. This methodology is demonstrated on the Teapot Reservoir, Wyoming.

On the basis of a field study, we discuss the need of a new paradigm for the construction of structural models. Indeed, within the traditional framework, building a 3D consistent fault network model consists in: first, picking faulting evidences on 3D seismic images and then, according to a priori concept derived from tectonic history, manually extrapolate in a consistent manner these evidences. The extrapolation step is actually the interpretation task that any structural geologist performs to build a 3D model from the observed evidences. However, such interpretations should not be considered as unique for uncertainty assessment and management. Therefore, we argue for the use of a stochastic system which will perform the extrapolation task (i.e. the construction of the 3D structural model). However, this computer method needs to be fed with similar geological knowledge as used in manual interpretation, such as structural style or interaction between faults of different tectonic origins. Integrating this conceptual information within a numerical system remains a key challenge.

To study the impact of subsurface uncertainties on oil recovery, it is common to build a large set of models which cover these uncertainties. Despite increase of computational capabilities, as models become more complex, it is not possible to perform full physic flow simulation for all the generated models. This is why stochastic reservoir model sets are often decimated to assess the impact of static uncertainties on dynamic reservoir performance. This contribution will focus on the use of proxy to perform this data set reduction. A lot of different proxies have been developed, from the simplest to the more complicated so it is difficult to choose the good one according to a particular goal. We present different criteria to compare the proxy quality and their helps to assess uncertainties on oil recovery. A first criterion will be based on the relation which may exists between the model distances computed on the proxy responses and those compute on flow responses. Another criterion is the speed factor and simplification provide by the proxy compared to the full physic simulator. These two criteria are very simple and can be applied in an early time to avoid deploying time consuming proxies which won’t provide accurate information. The last criterion presented here, is the confidence intervals which can be computed around probabilistic reservoir production forecasts computed on a small representative subset of model. Even if this criterion can be used only when the entire dataset has been simulated, it provides some quantification about a possible bias created by a proxy and the remaining uncertainties on oil recovery. We present here a comparison study between widely different proxy responses applied on a real dataset of that methodology. This will give us some keys to choose a proxy which is a good compromise between accuracy and easy to handle methodology.

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; Magnetostratigraphy is a powerful tool to provide absolute dating of sediments enabling robust and detailed chronostratigraphic correlations. It is based on the correlation of a magnetic polarity column, observed and measured in a given sediment section, to a magnetic polarity reference scale where polarity changes are well dated via other independent methods. However, magnetostratigraphic correlations are loose as they are only constrained by binary magnetic chrons (i.e. normal or reversal) and their thickness, which are both defined from depth variations of the magnetic remanent directions. The thickness of a given magnetic polarity zone is a function of time and sediment accumulation rate, which may not be stationary, leading to ambiguities when performing the correlations. To address these ambiguities, a numerical method based on the Dynamic Time Warping algorithm is proposed. Magnetostratigraphic correlations are computed in order to minimise the local variation of the accumulation rate. The main advantage of the proposed method is to automatically provide a set of reasonably likely correlations. This set can then be scrutinised for further analysis and interpretation. However, the likelihood of a correlation should be handled carefully as it depends on the information content of the magnetostratigraphic section itself and remain ultimately valid by ancillary constraint. Nevertheless, the method gives consistent results on difficult synthetic cases that simulate abrupt variations of the sedimentation rate. Insights on true sections debated by previous authors are also given.

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.

In this paper, we use the second-generation wavelet transform as multi-scale smooth parameterization technique for history matching of seismic derived models using an ensemble based optimization method (batch-enRML). The construction of the second generation wavelet is presented and their advantages compared to first generation wavelets are discussed. Then, these wavelets are applied to a realistic 3D faulted reservoir model. Their ability to represent correctly this model with a large compression ratio is demonstrated. Finally, using the SGW re-parameterization, we set the basis for a new adaptive multi-scale inversion method, which aims at limiting the increase of the mismatch to seismic data of the seismic-derived realizations by selecting relevant parameters. Efficiency of the method is discussed through a 2D synthetic example.