Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I utilize what I consider being an optimal parameterization. To do so, I extend the prestack time-domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practical. Results based on synthetic data of isotropic and anisotropic case examples illustrate the benefits and limitations of this method.

Accounting for azimuthal anisotropy is necessary for the processing and inversion of wide-azimuth and wide-aperture seismic data because wave speeds naturally depend on the wave propagation direction. Orthorhombic anisotropy is considered the most effective anisotropic model that approximates the azimuthal anisotropy we observe in seismic data. In the framework of full wave form inversion (FWI), the large number of parameters describing orthorhombic media exerts a considerable trade-off and increases the non-linearity of the inversion problem. Choosing a suitable parameterization for the model, and identifying which parameters in that parameterization could be well resolved, are essential to a successful inversion. In this thesis, I derive the radiation patterns for different acoustic orthorhombic parameterization. Analyzing the angular dependence of the scattering of the parameters of different parameterizations starting with the conventionally used notation, I assess the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. In order to build practical inversion strategies, I suggest new parameters (called deviation parameters) for a new parameterization style in orthorhombic media. The novel parameters denoted ∈d, ƞd and δd are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. The main feature of the deviation parameters consists of keeping the scattering of the vertical transversely isotropic (VTI) parameters stationary with azimuth. Using these scattering features, we can condition FWI to invert for the parameters which the data are sensitive to, at different stages, scales, and locations in the model. With this parameterization, the data are mainly sensitive to the scattering of 3 parameters (out of six that describe an acoustic orthorhombic medium): the horizontal velocity in the x1 direction, ∈1 which provides scattering mainly near the zero offset in the x1-x3 vertical plane, and ∈d, which is the ratio of the horizontal velocity squared in the x1 and x2 direction. Since, with this parameterization, the radiation pattern for the horizontal velocity is azimuth independent, we can perform an initial VTI inversion for two parameters (velocity and ∈1), then use ∈d to fit the azimuth variation in the data. This can be done at the reservoir level or any region of the model.

Micro-seismology is attracting more and more attention in the exploration seismology community. The main goal in micro-seismic imaging is to find the source location and the ignition time in order to track the fracture expansion, which will help engineers monitor the reservoirs. Conventional imaging methods work fine in this field but there are many limitations such as manual picking, incorrect migration velocity and low signal to noise ratio (S/N). In traditional surface survey imaging, full waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. Use the FWI technique, and overcomes the difficulties of manual pickings and incorrect velocity model for migration. However, the technique of waveform inversion of micro-seismic events faces its own problems. There is significant nonlinearity due to the unknown source location (space) and function (time). We have developed a source independent FWI of micro-seismic events to simultaneously invert for the source image, source function and velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. To examine the accuracy of the inverted source image and velocity model the extended image for source wavelet in z-axis is extracted. Also the angle gather is calculated to check the applicability of the migration velocity. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity in the synthetic experiments with both parts of the Marmousi and the SEG Overthrust model. On the other hand, a new imaging condition of natural Green’s function has been implemented to mitigate the effect of the unknown velocity model. It is based on putting receivers in a horizontal well close to the micro-seismic events so that only a small part of the velocity model is required for the imaging. In order to focus the multi scattering energy to the source location, as well as to suppress the influence of the noise in the data, we introduced a new method to compensate the energy in the receiver wavefield. It is based on reflection waveform inversion (RWI) theory. We simply migrate for the scatters (reflectors) in the medium, and set the image as a secondary source to compensate for the multi scattering energy in the receiver wavefield. By applying the same imaging condition, the energy of those scattering events can be traced to the source location. Thus the source point has higher energy in the source image. A simple two-layer medium test demonstrates the features.

The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth's subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the scattering integral method. Application to various synthetic and real data examples show accurate inversion results. I show that a good background ƞ model is required to accurately recover vh. For 3-D problems, I promote a hybrid approach, where efficient ray tracing is used to compute the sensitivity kernels. The proposed method highly reduces the computational cost.

The Chesapeake Bay impact structure is one of the largest and most well preserved impact structures on Earth. It has a unique morphology composed of an inner crater penetrating crystalline basement surrounded by a wider crater in the overlying sediments. In 2004, the U.S. Geological Survey conducted a seismic survey with the goals of constraining crater structure and in support of the drilling of a borehole into the deepest part of the crater. Travel-time and waveform inversion were applied to the data to produce a high-resolution velocity model of the crater. Low-fold reflection processing was also applied. Northeast of the crystalline crater, undeformed, eastward-sloping crystalline basement is ~1.5 km deep. The edge of the inner crater is at ~ 15 km radius and slopes gradually down to a depth of 1.5 - 1.8 km. A central peak of 4-5 km radius rises to a depth of ~0.8 km. Basement velocity in the crystalline crater is much lower than undeformed basement, which suggests ~10% fracturing of the crater floor, and up to 20% fracturing of the central uplift. A basement uplift and lateral change of velocity, interpreted as the edge of the transient crater, occurs at a radius of ~ 11 km. Assuming a 22 km diameter transient crater, scaling laws predict a ~30 km diameter crater and central peak diameter of 8-10 km. This indicates that post-impact collapse processes that created the ~ 30 km diameter crystalline crater were unaffected by the much weaker rheology of the overlying sediments. / Master of Science

L’atténuation sismique est un paramètre physique très utile pour décrire et imager les propriétés du sous-sol, et tout particulièrement les roches saturées et les nuages de gaz. Les approches classiques analysent l’amplitude du spectre des données ou bien la distorsion de ce spectre, avec des méthodes asymptotiques. L’inversion des formes d’onde (Full Waveform Inversion en anglais, FWI) est une approche alternative qui prend en compte les aspects de fréquences finies. En pratique, à la fois les vitesses et l’atténuation doivent être déterminées. Il est connu que l’inversion multi-paramètre ne conduit pas à un résultat unique.Ce travail se focalise sur la détermination des vitesses et de l’atténuation. La dispersion liée à l’atténuation produit des modèles de vitesse équivalents en termes de cinématique. Je propose une inversion hybride : la « relation cinématique » est un moyen de guider l’inversion des formes d’onde non-linéaire. Elle se décompose en deux étapes. Dans un premier temps, l’information cinématique est remise à jour, et ensuite les vitesses et l’atténuation sont modifiées, pour une cinématique donnée. Différentes approches sont proposées et discutées au travers d’applications sur des données synthétiques 2D, en particulier sur les modèles Midlle-East et Marmousi. / Seismic attenuation is a useful physical parameter to describe and to image the properties of specific geological bodies, e.g., saturated rocks and gas clouds. Classical approaches consist of analyzing seismic spectrum amplitudes or spectrum distortions based on ray methods. Full waveform inversion is an alternative approach that takes into account the finite frequency aspect of seismic waves. In practice, both seismic velocities and attenuation have to be determined. It is known that the multi-parameter inversion suffers from cross-talks.This thesis focuses on retrieving velocity and attenuation. Attenuation dispersion leads to equivalent kinematic velocity models, as different combinations of velocity and attenuation have the same kinematic effects. I propose a hybrid inversion strategy: the kinematic relationship is a way to guide the non-linear full waveform inversion. The hybrid inversion strategy includes two steps. It first updates the kinematic velocity, and then retrieves the velocity and attenuation models for a fixed kinematic velocity. The different approaches are discussed through applications on 2D synthetic data sets, including the Midlle-East and Marmousi models.

Seismic full waveform inversion (waveform tomography) is a method to reconstruct the underground velocity field in high resolution using seismic data. The method was first introduced during the 1980’s and became computationally feasible during the late 1990’s when the method was implemented in the frequency domain. This work presents three case studies and one synthetic benchmark of full waveform inversion applications. Two of the case studies are focused on time-lapse cross-well and 2D reflection seismic data sets acquired at the Ketzin CO2 geological storage site. These studies are parts of the CO2SINK and CO2MAN projects. The results show that waveform tomography is more effective than traveltime tomography for the CO2 injection monitoring at the Ketzin site for the cross-well geometry. For the surface data sets we find it is difficult to recover the true value of the velocity anomaly due to the injection using the waveform inversion method, but it is possible to qualitatively locate the distribution of the injected CO2. The results agree well with expectations based upon conventional 2D CDP processing methods and more extensive 3D CDP processing methods in the area. A further investigation was done to study the feasibility and efficiency of seismic full waveform inversion for time-lapse monitoring of onshore CO2 geological storage sites using a reflection seismic geometry with synthetic data sets. The results show that waveform inversion may be a good complement to standard CDP processing when monitoring CO2 injection. The choice of method and strategy for waveform inversion is quite dependent on the goals of the time-lapse monitoring of the CO2 injection. The last case study is an application of the full waveform inversion method to two crooked profiles at the Forsmark site in eastern central Sweden. The main goal of this study was to help determine if the observed reflections are mainly due to fluid filled fracture zones or mafic sills. One main difficulty here is that the profiles have a crooked line geometry which corresponds to 3D seismic geometry, but a 2D based inversion method is being used. This is partly handled by a 3D to 2D coordinate projection method from traveltime inversion. The results show that these reflections are primarily due to zones of lower velocity, consistent with them being generated at water filled fracture zones.

This thesis proposes a nonlinear differential semblance approach to full waveform inversion as an alternative to standard least squares inversion, which cannot guarantee a reliable solution, because of the existence of many spurious local minima of the objective function for typical data that lacks low-frequency energy. Nonlinear differential semblance optimization combines the ability of full waveform inversion to account for nonlinear physical effects, such as multiple reflections, with the tendency of differential semblance migration velocity analysis to avoid local minima. It borrows the gather-flattening concept from migration velocity analysis, and updates the velocity by flattening primaries-only gathers obtained via nonlinear inversion. I describe a general formulation of this algorithm, its main components and implementation. Numerical experiments show for simple layered models, standard least squares inversion fails, whereas nonlinear differential semblance succeeds in constructing a kinematically correct model and fitting the data rather precisely.

While shoaling from deepwater in a stratified ocean, an interfacial solitary wave (ISW) may experience waveform inversion on a continental margin. Although many oceanographers have believed that the inversion from depression to elevation may commence at the turning point where the upper and bottom layers are equal in depth, this phenomenon has not been fully verified in field observations nor in a laboratory. In this study, a series of laboratory experiments and numerical modeling were conducted on the evolution of an ISW of depression across uniform slope joining a horizontal plateau which resembles pseudo slope-shelf topography, in order to clarify this fascinating phenomenon and the variations of wave properties associated with the process. In the laboratory experiments, a depression ISW was produced by a collapse mechanism in a stratified two-layer fluid system within a steel-framed wave flume (12 m long, 0.7 m high by 0.5 m wide) at the National Sun Yat-sen University in Taiwan. The fluid density in the upper (fresh) and bottom (brine) layers was 996 and 1030 kg/m3, respectively. A series of experiments were conducted upon varying the magnitude of the most important physical factors (i.e., nominal thickness of pycnocline, depth ratio between upper and bottom layer, front gradient and shape of pseudo slope-shelf), from which the results are now discussed in four separate chapters in this thesis. Present laboratory results indicate that the process of waveform inversion took place after an ISW had experienced internal run-down, hydraulic jump, vortex motion and surge-up on the front slope, prior to its propagation onto the plateau. Moreover, the fundamental wave period of leading wave on the plateau was significantly smaller than that in the preceding sections on the front slope and the incident stage earlier, thus representing frequency downshift. Amongst the factors involved, the depth ratio between the upper and bottom layer was the most significant one for waveform inversion. Only when the upper layer was thicker than the bottom layer on the plateau of pseudo slope-shelf, waveform inversion could occur, besides the length of the plateau. On the other hand, the front gradient and shape of pseudo slope-shelf also affected the magnitude of the transmitted wave over the plateau as the wave across this specific topography. In the case of a steeper front gradient, waveform inversion became insignificant due to stronger wave reflection and intense energy dissipation caused by turbulent mixing while a depression ISW propagated over a slope-shelf; particularly against a submerged vertical cliff. As a depression ISW across pseudo slope-shelf with short plateau, intense wave breaking might occur again with vortex motion at its rear end as the newly inversed waveform reentering deep water. In this region, the upper layer was smaller than the bottom layer, hence it could not support the continuous existence of an ISW in elevation. Again, energy dissipation occurred due to turbulent mixing beyond the rear end of a short plateau. Finally, a different mode of ISW appeared within pycnocline, while its nominal thickness was larger than the amplitude of the incident wave. In addition to the laboratory investigations, numerical model was also adopted to study the variations in the flow field as an ISW propagated over a pseudo slope-shelf, in order to complement the experimental results. The results of numerical modeling revealed that the horizontal velocity in the bottom layer increased when the wave encountered the front slope, even if the depth of upper layer was thinner than that of the bottom layer on the plateau. Consequently, the velocity in the upper layer became less than that in the bottom layer when the former was thicker than that of the latter on the plateau. On the other hand, the vertical velocity within the self-generated vortex switched direction as waveform inversion commenced after the wave across the shoulder of pseudo slope-shelf where the local depth of the upper layer was larger than that of bottom part. Overall, the significance of the four pertinent factors (i.e., nominal thickness of pycnocline, water depth ratio, front slope, and plateau length) that affected a depression ISW across pseudo slope-shelf is discussed in detail in this thesis, as well as the variation of flow field calculated by the numerical mode presented.

L'inversion de forme d'onde complète (FWI) est un processus non-linéaire et mal posé d’ajustement de données, dans notre cas, issues d’acquisitions simiques. Cette technique cherche à reconstruire, à partir d’un modèle initial obtenu à faible nombre d’onde (faible résolution), des paramètres constitutifs contrôlant la propagation des ondes à grands nombres d’ondes (forte résolution). Durant ce processus itératif, certains artéfacts peuvent altérer la qualité du modèle reconstruit. Afin de diminuer ces artéfacts et d’assurer une reconstruction des paramètres qui soit cohérente d’un point de vue géologique, différentes techniques de pré-conditionnement ou de régularisation peuvent être proposées.Cette thèse se focalise sur le potentiel de nouveaux filtres multi-dimensionnels construits dans l’espace des nombres d’ondes et orientés suivant les structures géologiques. Une stratégie de pré-conditionnement a été mise au point à l’aide de ces filtres et a été appliquée avec succès à la problématique FWI. La formulation analytique 1D de l’opérateur inverse de covariance laplacienne (Tarantola, 2005) constitue la base de la formulation d’opérateurs de dimension supérieure qui sont validés ici en les comparants avec l’opérateur analytique de covariance laplacienne 1D. Nous avons utilisé cette fonction analytique inverse 1D comme la base de filtrage de dimension supérieure, via l’addition de multiples fonctions inverses orientées orthogonalement. Ces fonctions laplaciennes inverses additionnelles (AIL) sont obtenues pour des configurations 2D et 3D après discrétisation par des techniques de différences finies. Nous montrons que l’on peut calculer un filtre en nombre d’onde de manière rapide et robuste en résolvant le système linéaire associé à ces opérateurs inverses. Lorsque des pentes sont inclues à l’étape de discrétisation par différences finies, il est alors possible d’utiliser ces opérateurs comme des filtres en nombre d’ondes orientés vers les structures géologiques, ceci avec une grande efficacité.Ce filtre (AIL) montre des propriétés rapides de convergence et des performances indépendantes du vecteur à filtrer. Nous montrons notamment comment ce filtre peut être utilisé comme un opérateur utile pour le gradient associé à la FWI. Le pré-conditionnement du gradient peut atténuer les effets du problème mal-posé qui vont s’étendre dans l’espace des modèles. Deux exemples synthétiques (Valhall et Marmousi) calculés dans l’espace des fréquences sont proposés dans cette thèse. Le pré-conditionnement AIL s’avère efficace pour atténuer d’une part la signature mal-posée provenant de la présence de bruit ambient dans les données observées et d’autre part d’artéfacts liés aux effets de repliement spatial liés aux conditions d’imagerie par FWI. La possibilité d’inclure des pentes permet de filtrer de manière préférentielle en considérant des pendages géologiques. Cette stratégie de filtrage permet l’atténuation d’artéfacts, tout en préservant le contenu en nombre d’ondes de la stratigraphie orthogonale au pendage.Un cas réel d’inversion 2D FWI est finalement abordé permettant tout d’abord d’illustrer la sensibilité des résultats d’inversion au modèle initial. Celui-ci est d’importance majeure, particulièrement dans les régions profondes dépassant la pénétration maximale des ondes transmises. L’application de la technique FWI à cette acquisition sismique a permis d’améliorer de manière significative la cohérence sur une image migrée par renversement du temps (RTM). Nous montrons également que le pré-conditionneur AIL permet une décroissance significative du nombre de tirs requis à modéliser dans la boucle d’inversion, sans pour autant dégrader le contenu en nombre d’onde des structures géologiques principales dans les résultats finaux obtenus après inversion. / Full waveform inversion (FWI) is a non-linear, ill-posed, local data fitting technique. FWI looks to moves from an initial, low-wavenumber representation of the earth parameters to a broadband representation. During this iterative process a number of undesirable artifacts can map into our model parameter reconstruction. To mitigate these artifacts and to ensure a geologically consistent model parameter reconstruction, various preconditioning and/or regularization strategies have been proposed.This thesis details the construction of new, efficient, multi-dimensional, structurally-orientated wavenumber filters. A preconditioning strategy has been devised using these filters that we have successfully applied to FWI. The 1D analytical inverse Laplacian covariance operator (Tarantola, 2005) forms the basis of higher dimensional operators and is initially validated by comparing to the 1D analytical Laplacian covariance operator. We use this analytical 1D inverse function as the basis for higher dimensional filtering via the addition of multiple, orthogonally orientated inverse functions. These additive inverse laplacian functions (AIL) are shown in 2D and 3D configurations and are discretized using finite-difference techniques. We show that one can calculate, a rapid and robust wavenumber filter, by solving the linear system associated with these inverse operators. When dip is included at the finite difference discretization stage, it is possible to use these operators as highly efficient, structurally orientated wavenumber filters.The AIL filter is shown to be rapid to converge and its performance is independent of the vector to be filtered. We show, that the filter can be a useful preconditioning operator for the FWI gradient. Preconditioning the gradient can mitigate against ill-posed effects mapping into the model-space. Two synthetic (Valhall and Marmousi) frequency domain FWI example are shown in this thesis. The AIL preconditioner has success at mitigating the ill-posed imprint coming from ambient noise in the observed data and also artifacts from spatial aliasing effects in the FWI imaging condition. The ability to include dip, allows one to preferentially filter along geological dip. This filtering strategy allows the mitigation of artifacts, while simultaneously preserving the stratigraphic based wavenumber content that is orthogonal to dip.A 2D, real data FWI case-study is also shown and we highlight the sensitivity of the inversion result to the initial model. The initial model is of key importance, this especially true in the areas deeper than the maximum penetration of transmitted waves. The application of FWI on this line is able to significantly improve gather alignment on a RTM, migrated image. We also see that the AIL preconditioner can allows us to significantly decrease the number of shot records we are required to model in our inversion workflow without degrading the key geological wavenumber content in the final inversion result.