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.

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.

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.

Title: The source process of Greek earthquakes Author: Dana K ížová Department: Department of Geophysics Supervisor of the doctoral thesis: Prof. RNDr. Ji í Zahradník DrSc., Department of Geophysics Abstract: Investigations of moment tensor (MT) and its uncertainty are topical. This thesis is focused on isotropic component of three shallow earthquakes: Event A in Cretan Sea (Mw 5.3) and two events near Santorini island, B (Mw 4.9) and C (Mw 4.7). MT is inverted from full waveforms in an assumed 1D velocity model. The inverse problem is non-linear in centroid depth and time, and linear in six MT parameters, one is the MT-trace. Uncertainty of isotropic component is studied by a new approach (K ížová et al., 2013). The trace is systematically varied, and remaining parameters are optimized. The method reveals tradeoffs between the isotropic component, depth, time, and focal mechanism. From two existing velocity models, we prefer the one with lower condition number, in which a (positive) isotropic component is indicated for event B. To rapidly assess a likely existence of isotropic component, an empirical method is proposed (K ížová et al., 2016). It is based on comparison between depth- dependences of waveform correlation in full and deviatoric modes. Based on extensive synthetic tests, the method confirms a...

The ever-expanding need for energy, including those related to fossil fuels, is behind the drive to explore more complicated regions, such as salt and subsalt provinces. This exploration quest relies heavily on recorded surface seismic data to provide precise and detailed subsurface properties. However, conventional seismic processing algorithms including the state-of-the-art full-waveform inversion (FWI) fail to recover those features in many areas of salt provinces. Even the industrial solution with substantial involvement of manual human-interpretation has faced challenges in many regions. In this thesis, I attempt to replace those manual, and somewhat erroneous, steps to the velocity building in salt provinces with a mathematically robust algorithm under the FWI machinery. I, specifically, regularize FWI by penalizing the velocity drops with depth with a new more flexible function. Although promising, FWI is computationally very expensive, especially for large 3D seismic data. It updates an initial guess of the model iteratively using the gradient of the misfit function, which requires lengthy computations and large memory space/disc storage. Based on the adjoint state method, gradient computation usually requires us to store the source wavefield, or include an additional extrapolation step to propagate the source wavefield from its temporary storage at the boundary. To mitigate this computational overburden, I propose an amplitude excitation gradient calculation based on representing the source wavefield history by a single, specifically the most energetic arrival. In this thesis, I also propose a novel-multiscale scheme based on ux-corrected transport (FCT) to reduce artifacts in the gradient direction due to the noise present in seismic data. FCT comprises of two finite difference schemes: a transport and a diffusion to compute the flux at a grid point. I observe a couple of benefits in FCT-based FWI. First, it yields a smooth gradient at the earlier iterations of FWI by promoting the lower frequency content of the seismic data. Second, it is easily compatible with the existing FWI code, and with any objective function. The multiscale strategy starts with a large smoothing parameter and relaxes it progressively to zero to achieve the final inverted model from traditional FWI.

Dans cette thèse, un algorithme d'inversion de formes d'ondes (FWI) est développé pour l'imagerie 3D des paramètres élastiques de la lithosphère à partir des enregistrements télésismiques dans le but d'accroître la résolution des images lithosphériques. La modélisation sismique est effectuée par un méthode hybride d'injection de champ d'ondes. Une première modélisation est effectuée dans une Terre globale avec le logiciel AxiSEM pour déterminer les champs d’ondes aux bords de la cible lithosphérique. Ces solutions sont ensuite propagées dans cette cible par une méthode aux éléments finis spectraux. Le problème inverse est résolu avec un algorithme d’optimisation locale de type quasi-Newton (l-BFGS). La sensibilité de la méthode à la configuration expérimentale (paramétrisation du milieu, modèle initial, géométrie et échantillonnage du dispositif de capteurs) est tout d’abord analysée avec un modèle synthétique réaliste des Alpes Occidentales. L’algorithme est finalement appliqué à neuf événements de la campagne CIFALPS dans les Alpes occidentales jusqu’à une fréquence de 0.2Hz. Les modèles de vitesses P et S et de densité révèlent les grandes structures lithosphériques de la chaîne alpine, en particulier le corps d’Ivrée et la géométrie des Moho européen et adriatique. Plus profondément, deux anomalies de vitesses lentes sont imagées dans le manteau et sont interprétées comme la signature d’une remontée asthénosphérique et la localisation du détachement du panneau plongeant européen. Ces résultats corroborent l’hypothèse d’une subduction continentale de la croûte européenne et d’une éventuelle déchirure du panneau plongeant européen lors de la phase de collision. / In this thesis, a full-waveform inversion (FWI) algorithm is developed with the aim to image the elastic properties (Vp, Vs and density) of 3D lithospheric models from teleseismic recordings with a spatial resolution of the order of the wavelength. Seismic modeling is performed with a wavefield injection hybrid approach. A first simulation is performed in a global radially symmetric Earth with the AxiSEM code to compute the wavefields on the borders of the lithospheric target. Then, these wavefields are propagated in the target with the spectral finite-element method. After linearization, the inverse problem is solved with a quasi-Newton (1-BFGS) optimization algorithm. The sensitivity of the teleseismic FWI to the experimental setup (subsurface parameterization, initial model, sampling and geometry of the station layout) is first assessed with a realistic synthetic model of the Western Alps. The method is finally applied to nine events of the CIFALPS experiment carried out in the Western Alps, up to a frequency of 0.2Hz. Reliable models of P and S wave speeds and density reveal with an unprecedented resolution the crustal and lithospheric structures of the Alpine Belt, in particular the geometry of the Ivrea body, and the European and Adriatic Mohos. Deeper, two slow velocity anomalies beneath the Western Alps are imaged in the mantle. The first, to the west of the chain, is interpreted as the signature of an asthenospheric upwelling, the second near the location of the Ivrea body indicates the European slab break-off. The study supports the hypothesis of the European continental crust subduction and confirms the possible tearing of the European slab.