Full Waveform Inversion (FWI) delivers high-resolution quantitative images and is a promising technique to obtain macro-scale physical properties model of the subsurface. In most geophysical applications, prior information, as those collected in wells, is available and should be used to increase the image reliability. For this, we propose to introduce three

Structural uncertainties have a direct impact in exploration, development, and production, and in drilling decisions. In this paper, we present an approach for determining and handling structural uncertainties. We first examine the magnitude of the different sources of uncertainty, and explain how to estimate their direction and correlation length. This task requires a huge geophysical input. This information is then used in a general scheme to generate multiple realizations of the structural model consistent with structural uncertainties. The technique is based on geostatistical concepts. Finally, we illustrate the application of this scheme in examples relevant for exploration, development and production, and drilling. The structural model is described as a set of horizons represented by triangulated surfaces cut by faults. The relationships between horizons and faults are expressed as a set of constraints. On a horizon, each source of uncertainty (typically migration, picking, and time‐to‐depth conversion) is described as a field of vectors with its magnitude, direction, and correlation length expressed in terms of a variogram. A special fault object has been developed to aid in discribing the faults as probabilistic objects in a very simple way. Once all sources of uncertainty have been quantified many equiprobable realizations of the structural model are generated. For this, we use a special implementation of the probability field technique adapted to triangulated surfaces that handles correlation between horizons. At each realization, faults and horizons are moved in three dimensions according to uncertainties. Links between faults and horizons are maintained. Such complex 3‐D modeling can only be achieved in the frame of a geomodeler. Finally, we propose three types of applications requiring structural uncertainty determination:rock volume distribution, well trajectory optimization and risk analysis, and the use of structural uncertainty as a parameter for history matching. Our scheme generates many equiprobable realizations of the structural model provided that each source of uncertainty has been described in terms of magnitude direction and correlation length. These realizations may then be used to quantify risk in exploration development and drilling.

Full‐waveform inversion is an appealing technique for time‐lapse imaging, especially when prior model information is included into the inversion workflow. Once the baseline reconstruction is achieved, several strategies can be used to assess the physical parameter changes, such as parallel difference (two separate inversions of baseline and monitor data sets), sequential difference (inversion of the monitor data set starting from the recovered baseline model) and double‐difference (inversion of the difference data starting from the recovered baseline model) strategies. Using synthetic Marmousi data sets, we investigate which strategy should be adopted to obtain more robust and more accurate time‐lapse velocity changes in noise‐free and noisy environments. This synthetic application demonstrates that the double‐difference strategy provides the more robust time‐lapse result. In addition, we propose a target‐oriented time‐lapse imaging using regularized full‐waveform inversion including a prior model and model weighting, if the prior information exists on the location of expected variations. This scheme applies strong prior model constraints outside of the expected areas of time‐lapse changes and relatively less prior constraints in the time‐lapse target zones. In application of this process to the Marmousi model data set, the local resolution analysis performed with spike tests shows that the target‐oriented inversion prevents the occurrence of artefacts outside the target areas, which could contaminate and compromise the reconstruction of the effective time‐lapse changes, especially when using the sequential difference strategy. In a strongly noisy case, the target‐oriented prior model weighting ensures the same behaviour for both time‐lapse strategies, the double‐difference and the sequential difference strategies and leads to a more robust reconstruction of the weak time‐lapse changes. The double‐difference strategy can deliver more accurate time‐lapse variation since it can focus to invert the difference data. However, the double‐difference strategy requires a preprocessing step on data sets such as time‐lapse binning to have a similar source/receiver location between two surveys, while the sequential difference needs less this requirement. If we have prior information about the area of changes, the target‐oriented sequential difference strategy can be an alternative and can provide the same robust result as the double‐difference strategy.

The complete solution to an inverse problem, including information on accuracy and resolution, is given by the a posterJori probability density in the model space. By running a modified simulated annealing, samples from the model space can be drawn in such a way that their frequencies of occurrence approximate their a posteriori likelihoods. Using this method, maximum likelihood estimation and uncertainty analysis of seismic background velocity models are performed on multioffset seismic data. The misfit between observed and synthetic waveforms within the time windows along computed multioffset travel times, is used as an objective function for the simulated annealing approach. The real medium is modeled as a series of layers separated by curved interfaces. Lateral velocity variations within the layers are determined by interpolation from specified values at a number of sampling points. The input data consists of multioffset seismic data. Additionally, zerooffset times are used to migrate the reflectors in time to the depth domain. The multioffset times are calculated by an efficient ray-tracing algorithm .which allows inversion of a large number of seismograms. The a posteriori probability density for this problem is highly multidimensional and highly multimodal. Therefore, the information contained in this distribution cannot be adequately represented by standard deviations and covariances. However, by sequentially displaying a large number of images, computed from the a posterjori background velocity samples and the data, it is possible to convey to the spectator a better understanding of what information we really have on the subsurface.

Modelling faults from seismic data for a 3D depth model is a difficult task because of the multiple sources of uncertainty. The uncertainty may be attributed to migration velocities, picking of faults and organization of the fault network in 3D. Faults are generally not migrated from time to depth domain like horizons are, but modelled in the depth domain from the depth migrated horizons. For this reason, a new data structure has been designed that is targeted for fault modelling. Taking uncertainties into account, this structure allows for rapid modelling of faults from depth migrated horizons. The input data and the parameterization of the new data structure will be described. Following this, a way to incorporate uncertainties during the interpretation process is proposed and a description of different stochastic methods used to compute new shapes and locations inside a given uncertainty volume will be made. Finally, the method and the results obtained will be described while studying uncertainties on more complex fault networks. The influence of fault uncertainties on the reservoir volumetric estimates will be shown as one possible result of the simulation process.

A B S T R A C TWe study a new curvilinear scheme for wave propagation modelling in presence of topography. The discrete scheme takes advantage of recent developments in areoacoustics. Our new scheme relies on the conventional grid coupled with optimized filters to remove numerical noise in case of strong material heterogeneity. We used non-centred stencils for free surface implementation and optimized the explicit RungeKutta scheme for the time differencing. We performed a complete theoretical stability and dispersion analysis of the discrete scheme. Finally, we illustrate the numerical accuracy of the new scheme by intensive experiments.

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Summary The main technical contribution of the study presented in this paper was, by an integrated assessment of uncertainties in geophysics, geology and reservoir engineering, to provide a rational basis with risk analysis for the management of uncertainties in the development of the field and therefore better decision making. The objective of the study was to integrate the uncertainties identified on the Lambda Lower & Upper reservoirs and to quantify their impact on Gross Rock Volume (GRV), Oil Originally in Place (OOIP), recoverable reserves and produc-tion profiles. The work was carried out in five main steps:Determination of the distribution of the GRV.Building of a representative cloud of geological full field models (1000 equiprobable models) integrating geophysical, sedimentary and petrophysical uncer-tainties. Determination of the distribution of OOIP.Sorting and selection of a representative subset of reservoir models to quantify dynamic uncertainties.Modelisation by means of experimental design of the impact of dynamic uncertainties on the representative subset of geological models.Integration of static and dynamic uncertainties to assess statistical distributions of recoverable reserves, production profiles and plateau duration using experimental design technique coupled with multi-variable regression and Monte-Carlo simulations. The following results were obtained:probability distributions of GRVprobability distributions of OOIP for each reservoir (Lower & Upper) and for each zone of the Upper reservoirprobability distributions of recoverable reserves and production profilesprobability distribution of production plateau durationprobability estimation of different models, associated with quantiles 10, 50 and 90 of the OOIP and Np distributionsmeasure of the weight of the main uncertainties on the OOIP and reserves. Introduction Throughout the life of a hydrocarbon reservoir, from discovery to abandonment, a great number of decisions (which development with which recovery mechanism? the sizing for surface installations? …) depend on incomplete and uncertain information. Indeed, the only certain information comes from the cuttings and cores extracted from wells. This information represents only a tiny percentage of the rock volume involved and may itself be compromised by the way samples have been extracted. Any other knowledge of the reservoir comes from indirect measurements, either seismic surveys, logs or dynamic information gathered from well tests or production histories. Thus, because it comes from an interpretation process, any parameter that characterises the reservoir is uncertain. Finally, these uncertainties are case dependent (the reservoir and its heterogeneities, the production mechanism involved or even the type of surface installation…) and, for a given field, they depend on its stage of development (initial appraisal, initial development, complementary development). Therefore major uncertainties affect the decisions. Uncertainties in reservoir characterization The process that leads from the definition of structural maps to the estimation of reserves and production profiles for a given recovery mechanism and a given development scheme can be summed up in a few main stages:Definition of the reservoir envelope: maps and faults.Definition of contacts and nature of fluids.