Applications of reflection tomography for the determination of complex geologic structures calls for the generalization of this method so that it can take triplications and other multiple arrivals into account. In this way, we propose a new formulation of travel time inversion. It relies on the choice of an adequate parametric representation of travel time information: the parameters we have chosen for this representation are the receiver location and the ray parameter at the receiver, some quantities directly measured from seismic data. The forward problem involved in the solution of this new inverse problem consists in shooting rays from a receiver according to the measured values of the ray parameter at the receiver. We can thus predict for a given model the emergence point of the reflected ray (i.e., the shot location) and the associated reflection arrival time. The least squares formulation of the inverse problem consists in minimizing an objective function that measures the mismatch between predicted and actual shot locations on one side and predicted and actual reflection arrival times on the other side, for the considered receiver locations and the associated measured ray parameters. However, inversion of noise corrupted kinematic data calls for a realistic definition of the uncertainties associated with the data. In particular, those uncertainties should take into account the sensitivity of reflection arrival times and shot locations to an error in the measurement of the ray parameter at the receiver. The objective function to minimize being chosen, the solution of the inverse problem is performed by a Gauss‐Newton method, the Jacobian of the forward modeling operator being computed by the adjoint state technique. It is interesting to note that no two‐point ray tracing is required in our method which is therefore cheaper than classical reflection tomography. The effectiveness of this approach is illustrated on a difficult synthetic example with large lateral velocity variations and strongly noise corrupted data.
Many studies have shown the strong dependence of the solution of reflection tomography (or travel time inversion) in the model discretization interval: such solutions are purely numerical artifacts. The cause lies in the formulation of the reflection tomography which turns out to be an ill‐posed problem unless properly regularized. Adequate regularizations are those which make use of derivatives of the functions describing the model (velocity distributions and reflector geometries). The order of the derivatives to use depends on the space dimension (two or three dimension). Of practical interest is curvature regularization: it works both in two and three dimensions with minimum a priori knowledge on the substratum under survey. We give theoretical arguments to prove that, with such a regularization, the computed solution is unique, stable, and almost independent of model discretization, provided that it is fine enough. These theoretical results are confirmed by numerical tests on a two‐dimensional model with a velocity field varying both vertically and horizontally: they show the practical interest of the proposed regularization. However, mathematical stability is not sufficient, and a priori information has to be used in order to decrease the size of the set of possible solutions. As a consequence of our theoretical study of regularization techniques, only a priori information involving derivatives of the functions describing the model yields stability. In other words, except for some pathological examples, stability is obtained only if we try to determine a smooth model of the subsurface. These conclusions remain valid for three‐dimensional models and for transmission tomography. As a by‐product of our study, we suggest a preconditioning which makes much easier the solution of the linear systems involved in the Gauss‐Newton optimization method.
-The Southern Adriatic Sea is one of the five prospective areas for CO 2 storage being evaluated under the FP7 European Sitechar project. The potential reservoir identified in the investigated area is represented by a carbonate formation (Scaglia Formation -Late Cretaceous). This paper shows the site characterization applied to one of the structures identified in the carbonate storage system of the South Adriatic offshore. The interpretation and analysis of seismic and borehole data allowed the construction of a 3D geological static model on both regional and local scales. Dynamic modeling was applied, adopting a sensitivity approach ( i.e. fault transmissivity, petrophysical properties of the caprock and reservoir, and different stress regimes). Coupled fluid flow and geomechanical simulation was applied to investigate the potential risk of leakage induced by mechanical solicitation on the faults occurring in the investigated area.Résumé -Évaluation et caractérisation d'un site de stockage potentiel de CO 2 au sud de la Mer Adriatique -Le sud de la Mer Adriatique est l'une des cinq zones potentielles pour le stockage du CO 2 évaluées dans le cadre du projet FP7 européen SiteChar. Le réservoir potentiel identifié dans la zone étudiée est constitué d'une formation de carbonate (Formation Scaglia -Crétacé supérieur). Cet article présente la caractérisation de site de stockage de CO 2 appliquée à l'une des structures identifiées dans les formations carbonatées du sud de la Mer Adriatique. L'interprétation et l'analyse des données sismiques et des données de forage ont permis la construction d'un modèle statique géologique 3D à des échelles régionale et locale. Une modélisation dynamique a été effectuée, intégrant une analyse de sensibilité (sur la transmittivité des failles, les propriétés pétro-physiques des roches couverture et réservoir, et différents régimes de contraintes). Une simulation couplée géomécanique et d'écoulement de fluide a été menée pour étudier le risque potentiel de fuite provoqué par les contraintes mécaniques sur les failles de la zone étudiée.
Waveform inversion aims at a quantitative estimation of the subsurface model. Such a quantitative estimation is a nonlinear problem: the relation between elastic parameters and waveform data is basically nonlinear. Perturbations in the velocity give rise to severe nonlinear perturbations in the wavefield. Other severe nonlinear effects appear when the impedance profile is very irregular (i.e., rapidly oscillating). In this paper, we avoid these drastic nonlinear effects by assuming the velocity distribution is known, and we restrict our analysis to the reconstruction of “regular” impedance profiles. Even in this simple framework, deviations between a linear and a nonlinear model are cumulative as time increases, and the deviations cannot be neglected for propagation times of the order of standard seismic recordings. A nonlinear approach appears to be essential for quantitative imaging of deep targets. However a nonlinear approach requires the wavelet to be known with an accuracy that cannot be reached today. Our sensitivity analysis shows that the wavelet/model ambiguity is much more severe than the one met in linear inversion. As a consequence of the error accumulation inherent in a nonlinear wave propagation model, a small disturbance in the wavelet leads to a strong disturbance in the deep parts of the solution model. In this context, the classical approach for estimating the wavelet by minimizing the energy of the primary reflection waveform is not likely to provide the required accuracy except for very special cases. Accurate wavelet measurements thus appear to be a major challenge for a sound reconstruction of impedance profiles.
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