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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.

International audience; Sedimentary strata are essential archives of the past conditions of the earth, and host significant natural resources in the subsurface. However, inferring the features of strata at depth (e.g., geometry, connectivity, physical or geological properties), remains a challenge prone to many uncertainties. Classically, the layers and their geometry are first interpreted from boreholes, geological outcrops and geophysical images, then layer properties can be addressed with geostatistical techniques and inverse methods. Theoretical models considering horizon depth uncertainty have been proposed decades ago, and geostatistical simulation can sample petrophysical uncertainties, but these approaches leave the number of layers fixed and are rely on conformable layering assumptions which are seldom met. We review some recent developments in well correlation in the frame of relative chronostratigraphy, which addresses the problem of locating potential gaps in the stratigraphic record. We also present some first results of the integration of the number of layers in inverse problems using a reversible jump Monte Carlo method. These two elements open interesting perspectives to jointly address topological, geometrical and petrophysical uncertainties at multiple scales in sedimentary basins. Although such uncertainties can have significant impact on quantitative geological and geophysical model forecasts, many computational challenges still lie ahead to appropriately sample uncertainties. Harnessing these challenges should open the way to finding, on a case-by-case basis, the suitable level of detail between detailed stratigraphic architectures and effective medium representations.

Three-dimensional structural modelling of complex metamorphic settings is an extremely challenging task. In these settings, rocks sequences record multiple ductile and brittle events, leading for instance to refolded fold structures, isoclinal folds and dense network of faults. In this contribution, we build a 3D structural model of a portion of the highly deformed core of the Alpine orogeny in the North-Western Italian Alps, by using field data (1:10,000 geological map and a dense database of structural stations) as unique input source. Our model area has an extension of ca. 1,300 km2 and a vertical elevation difference between the highest mountains (e.g., Cervino-Matterhorn) and the valley floors of ca. 4,000 meters, reflecting a truly three-dimensional dataset.Our workflow expects a first phase of orientation statistics study of the structural field database, followed by structural interpretation in vertical cross-sections and 3D interpolation using implicit surfaces and structural constraints. The implicit approach allows us to propagate field data and geological interpretation through mathematical constraints and to obtain structural interfaces reflecting observations.After introducing the new 3D structural model of the portion of the North-Western Alps, we discuss the difficulties related to geomodelling using input surface data only, by qualitatively addressing the uncertainty aspects of our workflow. We also focus on the range of geological and structural constraints that fieldwork allows us, reasoning on the distinction between observed and interpreted geological information.

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; Well-log interpretation and chronostratigraphic well correlation are essential steps in the basin and reservoir modeling, as they provide clues for the quantification of depositional history and flow units. At the sub-seismic scale (1 to 100 meters), correlations affect the layer geometry and the geobodies connectivity but are subject to many uncertainties because of lack of data at the relevant scale. To reduce these uncertainties, several interpretation and correlation steps may be necessary to obtain a model agreed upon by experts, but this process does not assess correlation uncertainties. To reduce correlation bias due to the interpreter and to help assessing stratigraphic uncertainties in a reproducible way, we propose a computer-assisted method which automatically generates possible well correlations based on facies interpretations and formal interpretation concepts.This method uses facies interpretations translated into a paleo-geographic variable inferred from depositional environments (e.g. the position along a proximal-to-distal transect). Assuming that wells have a global distality due to their position with respect to the overall basin geometry during the considered stratigraphic interval, we can interpolate a three-dimensional surface constrained by well-markers and the local stratigraphic dip measurement acquired along wells. These surfaces represent relative paleo-topographic surfaces at a given depositional time. In first approximation, a large paleo-depth gradient should be observed along the sediment transport direction, and a smaller slope should exist along the depositional strike.Well correlations are computed using a correlation cost between all possible marker combinations aggregated by the Dynamic Time Warping algorithm. These correlation costs are based on the shape of the relative paleo-topography. Additionally, proximal facies interpreted in a distal well cannot be associated with distal facies interpreted in a proximal well, and conversely distal facies interpreted in a distal well may be likely associated with a proximal facies interpreted in a proximal well. Along the depositional strike, the method tries to associate identical or close facies with respect to the distality.We apply the developed method to correlate North Sea Jurassic well cores where lagoon, wave-dominated deltaic and fluvial deposits have been identified. Results highlight well-sections where manual biostratigraphic correlations and generated consistent stratigraphic scenarios differ providing interpreters with a map of the most uncertain well sections.

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.

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.

Graphs are a commonly used and well-studied mathematical abstraction for the modeling of complex systems. Three-dimensional (3D) structural geology is no exception, and graphs have received significant attention in recent years to characterize the connectivity for fracture sets, faults, geological units and reservoir compartments. The basis for these analyzes is to summarize an existing structural model as a graph, and to label the nodes and edges using the geological features of interest. In this sense, structural geologists building a 3D structural model are actually creating a graph. For this, they use geological reasoning to relate the various rock units of the subsurface. As a matter of fact, the final graph corresponding to a 3D structural model also relates the input spatial data, such as field measurements or interpretive contact lines. Based on this observation, we have proposed a graph-based framework to stochastically model 3D fault networks from incomplete observations, which randomizes the assignment of fault evidence to fault objects. The geometry of these faults is then determined using existing geomodeling techniques. In this approach, each piece of data is considered as a node of a complete graph called a possibility graph. The edges of the possibility graph are valued by a likelihood that two graph nodes belong to the same fault surface, which makes it possible to quickly remove some edges corresponding the associations deemed impossible. A hierarchical simulation algorithm is then proposed, based on the observation that each fault network corresponds to a possible partitioning of the input graph into distinct cliques. This formulation allows to give upper bounds for the (very large) number of possibilities that can be generated. We give several examples of likelihoods that integrate prior geological knowledge (e.g., the fault size distribution and orientation distribution), and check the consistency of the sampling algorithm when more informative rules are used. These preliminary results show that the simulation method consistently explores the search space, but they also highlight the need to further study the mathematical and computational properties of the sampler. Nonetheless, this approach is promising to efficiently generate and cluster a large set of possible structural scenarios and the associated ensemble of structural models obtained by a combination of data-perturbation, interpolation and or model-perturbation.

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.

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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.

Summary Numerical flow models based on Discrete Fracture Methods (DFM) represent a fractured porous rock using an unstructured mesh where fractures are a subset of the elements faces. This allows for a high degree of geometric accuracy, but it also raises numerical challenges: the mesh must honor both small and large scale geometric features while keeping tractable and stable computations. For these reasons, we previously proposed a new geometric approximation method, which can be applied before meshing. The aim of this paper is to compare the flow impact of different geometric approximations of irregular and complex two-dimensional fracture networks. We present and validate a Control-Volume-Finite-Element DFM-based water flooding model and three fracture approximations strategies. The first strategy (A) projects fractures on the edges of an initial background mesh. The two others (B and C) rely on graph theory to analyze and modify a boundary representation of the fracture network according to minimal angles and mesh sizes criteria. Strategy B modifies the boundary representation using a contraction approach where flagged fracture elements (lines, extremities of intersections) are merged. Strategy C uses an expansion approach which moves the problematic fracture elements away one from another, hence preserving the model connectivity (we also present some adjustments as compared to the already published method). The approximation strategies A, B and C are applied to three reference data sets with respectively: two crossing fractures; highly connected fractures; anisotropic disconnected fractures. For each model, we compare the oil production and the saturation maps to the reference model. These tests show that the connectivity changes implied by the strategies A and B only have a small impact on the flow solution. Nonetheless, the expansion strategy C which preserves the fracture network topology provides the most accurate solution in all test cases.

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; 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.

International audience; Model updating is an important way forward to efficiently incorporate new information about the subsurface. Four local components are needed to address common needs: finding the subregion to be updated, updating the discrete model features (topology) locally or semi-globally, locally updating the feature geometry and locally updating the associated properties. We present a few existing strategies and highlight that topological and geometric editing are essential for geologically consistent and automatic or semi-automatic geomodel updates.

International audience; Time-lapse studies not only allow to monitor the reservoir but are also useful to access risk in the overburden. They usually assume that the velocity change during reservoir depletion is isotropic, but, from a geomechanical perspective, velocity changes have no reason to be isotropic. Numerous authors observe that the velocity changes in the overburden suggest rock damage such as crack opening which implies anisotropic elastic property changes. Rock damage depends on several geomechanical parameters such as the initial rock elastic properties, the in situ stress, the stress state change, the crack shapes and their orientations, etc. We show that retrieving an anisotropic time-lapse velocity change is possible using a pre-stack seismic tomographic approach. The anisotropic time-lapse velocity change is decomposed into a functions basis which respects the travel-time perturbation symmetries. The anisotropic time-lapse velocity change predicted by the rock physics models can be expressed in this general basis with some algebra. We apply the proposed tomographic inversion on a cross-section of a real reservoir and we relate the anisotropic time-lapse velocity change to horizontal crack distribution in the overburden. Results show a good qualitative consistency between the prediction of the rock physics model and the tomography results.

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; In this paper, an implicit structural modeling method using locally defined moving least squares shape functions is proposed. The continuous bending energy is minimized to interpolate between data points and approximate geological structures. This method solves a sparse problem without relying on a complex mesh. Discontinuities such as faults and unconformities are handled with minor modifications of the method using meshless optic principles. The method is illustrated on a two-dimensional model with folds, faults and an unconformity. This model is then modified to show the ability of the method to handle sparsity, noise and different reliabilities in the data. Key parameters of the shape functions and the pertinence of the bending energy for structural modeling applications are discussed. The predefined values deduced from these studies for each parameter of the method can also be used to construct other models.

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.

Summary We introduce a new method for implicit structural modeling. The method belongs to the Discrete Smooth Interpolation class of methods. We exploit the highly symmetric nature of Cartesian grids to propose new regularization operators that discretize very naturally on the Cartesian grid using finite differences: these operators do not have to be defined on boundary nodes, and their generalization to higher dimensions is straightforward. Numerical examples show that the proposed method is both robust and numerically efficient.

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.