Submitted by Júlio Leão Brandão (jlbrandao@ufba.br) on 2018-08-21T16:44:33Z No. of bitstreams: 1 Dissert_Victor_Koehne_final.pdf: 41205493 bytes, checksum: 697711c5d1d92aa01956bacc668308fb (MD5) / Approved for entry into archive by NUBIA OLIVEIRA (nubia.marilia@ufba.br) on 2018-08-29T14:51:51Z (GMT) No. of bitstreams: 1 Dissert_Victor_Koehne_final.pdf: 41205493 bytes, checksum: 697711c5d1d92aa01956bacc668308fb (MD5) / Made available in DSpace on 2018-08-29T14:51:51Z (GMT). No. of bitstreams: 1 Dissert_Victor_Koehne_final.pdf: 41205493 bytes, checksum: 697711c5d1d92aa01956bacc668308fb (MD5) / A inversão completa da forma de onda (FWI - do inglês full-waveform inversion) é atualmente uma das principais ferramentas para determinar modelos de velocidades da subsuperfície com alta resolução. Nessa dissertação, a FWI no domínio do tempo é introduzida e desenvolvida sob a ótica da implementação, na seguinte sequência: modelagem sísmica, migração reversa no tempo (ou reverse time migration, RTM) e FWI. É mostrado que a RTM, do ponto de vista computacional, equivale a duas modelagens sísmicas, ou três modelagens se for usada a implementação com borda efetiva. A abordagem da FWI como um problema iterativo que visa minimizar o resíduo dos dados sísmicos mostra que o gradiente de cada iteração é, pelo método adjunto, equivalente à RTM do resíduo. Dessa maneira, usando RTM com borda efetiva e um método de estimação do passo, é mostrado que uma iteração da FWI é computacionalmente equivalente a quatro modelagens sísmicas. Como se sabe, a modelagem é um processo muito intensivo computacionalmente, e dentre as formas eficientes de resolver esse problema se destaca o uso de computação paralela. Nessa dissertação, se escolheu a paralelização utilizando placas gráficas (ou graphics processing unit, GPU) que possui alta capacidade de cálculo de pontos flutuantes, porém baixa eficiência na transferência de dados. Tais características se adequam muito bem ao problema de extrapolação de campos de onda no tempo, em especial no cálculo do Laplaciano da equação da onda acústica em cada ponto do modelo, que correspondem a quase todo o tempo computacional da modelagem, custo esse que, paralelizado em GPU, mais que compensa as transferências de memória CPU-GPU inerentes ao problema. A GPU, todavia, tem uma restrição de memória, tipicamente variando entre 2, 5 e 12 GB. Nessa dissertação, então se focou em técnicas que permitem a economia de memória em troca de processamento. Dentre essas implementações, destaca-se o uso de borda efetiva na RTM e o uso do método de expansão rápida (REM), que permite extrapolação a maiores intervalos de tempo, reduzindo o número total de amostras temporais que precisam ser armazenadas e transferidas na memória do equipamento utilizado. A implementação em GPU também permitiu testar em tempo hábil alguns dos fatores mais importantes que influenciam a FWI. Foram testados, numa malha regular: quatro operadores de modelagem - diferenças finitas (DF), pseudo-espectral (PS), REM-DF e REMPS-; as condições de borda absorvedora taper e perfectly matching layer (PML); e os métodos de inversão conjugado gradiente não linear (CGNL) e L-BFGS. Os resultados desses testes permitiram selecionar os melhores critérios para execução da FWI em modelos de velocidades sintéticos, porém de geologia complexa. O uso da metodologia multiescala, essencial para evitar convergência a mínimos locais, associado a uma modelagem extra para obtenção de um passo adequado, permitiu a obtenção de resultados finais de alta resolução para os três modelos testados. / Full-waveform inversion (FWI) is nowadays one of the main tools for estimating high resolutionsubsurfacevelocitymodels. Inthisdissertation, time-domainFWIisintroducedfroman algorithmic point of view: seismic modeling, reverse time migration (RTM), and FWI. It is shown that RTM, from a computational point of view, is equivalent to two seismic modeling processes, or three if the effective boundaries implementation is used. The approach of FWI as an iterative problem (which aims to minimize the seismic data residue) shows that the gradient of each iteration, using the adjoint-state method, is equivalent to the RTM of the residue. In this manner, using RTM with effective boundaries and a step length estimation method, it is shown in this thesis that one iteration of FWI is computationally equivalent of four seismic modelling processes. Itisknownthatseismicmodelingisahighlyintensivecomputationalprocess, andamong the techniques to mitigate this cost the use of parallel computing stands out. In this dissertation we chose the parallelization using the graphics processing unit (GPU) which has high floating point computation capability, but low efficiency in data transfer. These characteristics fit very well to the problem of wave field extrapolation in time, especially in the calculation of the Laplacian of the acoustic wave equation at each point of the model, whose computational costs in GPU more than compensates the data transfers inherent to the problem. The GPU, however, has a memory constraint, typically ranging from 2, 5 and 12 GB. In this thesis, we then focused in techniques that allowed memory savings in exchange of processing. Among these implementations, we highlight the use of effective boundaries in RTM and the rapid expansion method (REM) for time extrapolation, which allows marching at longer time steps, reducing the total time samples that need to be stored and transferred. The GPU implementation also enabled to test in a timely manner some of the most important factors influencing FWI. We tested, in a regular grid: four modeling operators finite-differences (FD), pseudo-spectral (PS), REM-FD, REM-PS -; the absorbing boundary conditions taper and perfectly matching layer (PML); and the inversion methods L-BFGS and non-linear conjugate gradient (NLCG). The results of these tests allowed to select the best criteria for FWI execution in synthetic velocity models of complex geology. The use of the multiscale methodology, essential to avoid convergence to local minima, in conjunction with an extra modeling step to ensure an efficient step length, allowed achieving final results of high resolution for the three tested models.

Este trabalho realizou um estudo sobre a aplicação de algoritmos de inversão da forma de onda completa (FWI) sobre dados de sísmica de reflexão em uma escala rasa ( 0 100 m de profundidade). A FWI foi estudada com o fim de melhorar as velocidades estimadas através do processamento de reflexão PP e PS convencional. Para um melhor entendimento da resposta obtida por este tipo de problema, a inversão foi avaliada sobre dados sintéticos por métodos de busca global e local. Na busca global foi utilizado o algoritmo de Evolução Diferencial que é uma variante de um algoritmo genético. O intuito da busca global foi avaliar a sensibilidade da função objetivo para cada parâmetro do modelo em diferentes janelas de afastamentos em relação à fonte. Na busca local foi utilizado um algoritmo de gradiente conjugado para a estimativa 2D dos parâmetros do meio. Dentre os principais resultados têm-se que a função objetivo é mais sensível aos parâmetros em janelas de afastamentos próximas da fonte. Em tais janelas, dominadas por ondas superficiais, a velocidade da onda S é facilmente estimada. Entretanto, mesmo em janelas mais afastadas a velocidade da onda S é o parâmetro do modelo que se destaca em relação aos demais. Já a busca por todos os parâmetros concomitantemente mostrou-se difícil e implicaria na necessidade de mais iterações do algoritmo de inversão. O método também foi aplicado em dados reais adquiridos no terreno do Instituto de Física da USP. A FWI foi aplicada nestes dados buscando apenas pelos valores de Vs, mantendo os valores de Vp e densidade fixos. A aplicação do algoritmo 2D nestes dados resultaram em valores de Vs coerentes com as velocidades observadas em um ensaio downhole na área. Concluindo, os resultados apresentados na tese mostram que a FWI é aplicável para a melhoria do modelo de velocidade da onda S obtido através do processamento de eventos de reflexão PP e PS. / This work carried out a study on the application of full waveform inversion algorithms (FWI) on reflection seismic data on a shallow scale (0 - 100 m depth). FWI has been studied in order to improve estimated velocities through conventional PP and PS reflection processing. For a better understanding of the response obtained by this type of problem the inversion was evaluated by global and local search methods. In the global search the algorithm employed was the Differential Evolution which is a variant of a genetic algorithm. The aim of the global search was to evaluate the sensitivity of the objective function for each parameter of the model in different windows of distance from the source. In the local search a conjugate gradient algorithm was used for a 2D estimate of the medium parameters. Among the main results is the fact that in a suitable window, for a reflection data acquisition the sensitivity is reduced in relation to a window with geophones closer to the source. However, even in more distant windows the velocity of the S wave is the parameter of the model that stands out in relation to the others. The concomitant search for all parameters at the same time is still difficult and implies the need for more iterations of the inversion algorithm. The method was also applied in a data acquired in the field of the Institute of Physics of USP. The results of the application of the 2D algorithm for this data showed modifications of the provided initial model for a velocity of the S wave coherent with the observed velocities in downhole and lithological informations from this area. In conclusion, the results found that FWI is applicable to improve the S-wave velocity model obtained by processing PP and PS reflection events.

Este trabalho realizou um estudo sobre a aplicação de algoritmos de inversão da forma de onda completa (FWI) sobre dados de sísmica de reflexão em uma escala rasa ( 0 100 m de profundidade). A FWI foi estudada com o fim de melhorar as velocidades estimadas através do processamento de reflexão PP e PS convencional. Para um melhor entendimento da resposta obtida por este tipo de problema, a inversão foi avaliada sobre dados sintéticos por métodos de busca global e local. Na busca global foi utilizado o algoritmo de Evolução Diferencial que é uma variante de um algoritmo genético. O intuito da busca global foi avaliar a sensibilidade da função objetivo para cada parâmetro do modelo em diferentes janelas de afastamentos em relação à fonte. Na busca local foi utilizado um algoritmo de gradiente conjugado para a estimativa 2D dos parâmetros do meio. Dentre os principais resultados têm-se que a função objetivo é mais sensível aos parâmetros em janelas de afastamentos próximas da fonte. Em tais janelas, dominadas por ondas superficiais, a velocidade da onda S é facilmente estimada. Entretanto, mesmo em janelas mais afastadas a velocidade da onda S é o parâmetro do modelo que se destaca em relação aos demais. Já a busca por todos os parâmetros concomitantemente mostrou-se difícil e implicaria na necessidade de mais iterações do algoritmo de inversão. O método também foi aplicado em dados reais adquiridos no terreno do Instituto de Física da USP. A FWI foi aplicada nestes dados buscando apenas pelos valores de Vs, mantendo os valores de Vp e densidade fixos. A aplicação do algoritmo 2D nestes dados resultaram em valores de Vs coerentes com as velocidades observadas em um ensaio downhole na área. Concluindo, os resultados apresentados na tese mostram que a FWI é aplicável para a melhoria do modelo de velocidade da onda S obtido através do processamento de eventos de reflexão PP e PS. / This work carried out a study on the application of full waveform inversion algorithms (FWI) on reflection seismic data on a shallow scale (0 - 100 m depth). FWI has been studied in order to improve estimated velocities through conventional PP and PS reflection processing. For a better understanding of the response obtained by this type of problem the inversion was evaluated by global and local search methods. In the global search the algorithm employed was the Differential Evolution which is a variant of a genetic algorithm. The aim of the global search was to evaluate the sensitivity of the objective function for each parameter of the model in different windows of distance from the source. In the local search a conjugate gradient algorithm was used for a 2D estimate of the medium parameters. Among the main results is the fact that in a suitable window, for a reflection data acquisition the sensitivity is reduced in relation to a window with geophones closer to the source. However, even in more distant windows the velocity of the S wave is the parameter of the model that stands out in relation to the others. The concomitant search for all parameters at the same time is still difficult and implies the need for more iterations of the inversion algorithm. The method was also applied in a data acquired in the field of the Institute of Physics of USP. The results of the application of the 2D algorithm for this data showed modifications of the provided initial model for a velocity of the S wave coherent with the observed velocities in downhole and lithological informations from this area. In conclusion, the results found that FWI is applicable to improve the S-wave velocity model obtained by processing PP and PS reflection events.

L'inversion des formes d'ondes (FWI) est une procédure d'imagerie sismique pour imager le sous-sol de la Terre. FWI est résolue comme un problème d'optimisation. En fonction du contenu en fréquence des données, la fonction objective de FWI peut être fortement non linéaire. Pour des données associées des réflexions, ce problème empêche notamment les méthodes basées sur le gradient de retrouver les grandes longueurs d'onde du modèle de vitesse. Dans cette thèse, nous proposons une variante de FWI basée sur la séparation des champs d'ondes, typiquement en champs montants et descendants, pour atténuer la non-linéarité du problème. Il consiste à décomposer le gradient de FWI en une partie de courte longueur d'onde et une partie de grande longueur d'onde après décomposition des champs d'ondes. L'inversion est effectuée d'une manière alternée entre ces deux parties. Nous appliquons cette méthode à plusieurs études de cas et montrons que la nouvelle approche est plus robuste en particulier pour la construction du modèle de grande longueur d'onde. / Full Waveform Inversion (FWI) is a seismic imaging procedure to image the subsurface of the Earth. FWI is resolved as an optimization problem . Depending on the frequency content of the data, the objective function of FWI may be highly nonlinear. If a data set mainly contains reflections, this problem particularly prevents the gradient-based methods from recovering the long wavelengths of the velocity model.In this thesis, I propose a variant of FWI based on the wavefield separation, typically between up- and down- going waves, to mitigate the nonlinearity of the problem. The new method consists of decomposing the gradient of FWI into a short-wavelength part and a long-wavelength part after wavefield decomposition. The inversion is performed in an alternating fashion between these two parts. We apply this method to several case studies and show that the new method is more robust especially for constructing the long-wavelength model.

Full Waveform Inversion (FWI) is a non-linear optimization problem aimed to estimating subsurface parameters by minimizing the misfit between modeled and recorded seismic data using gradient descent methods, which are the only practical choice because of the size of the problem. Due to the high non-linearity of the problem, gradient methods will converge to a local minimum if the starting model is not close to the true one. The accuracy of the long-wavelength components of the initial model controls the level of non-linearity of the inversion. In order for FWI to converge to the global minimum, we have to obtain the long wavelength components of the model before inverting for the short wavelengths. Ultra-low temporal frequencies are sensitive to the smooth (long wavelength) part of the model, and can be utilized by waveform inversion to resolve that part. Unfortunately, frequencies in this range are normally missing in field data due to data acquisition limitations. The lack of low frequencies can be compensated for by utilizing wide-aperture data, as they include arrivals that are especially sensitive to the long wavelength components of the model. The higher the scattering angle of a 5 recorded event, the higher the model wavelength it can resolve. Based on this property, a scattering-angle filtering algorithm is proposed to start the inversion process with events corresponding to the highest scattering angle available in the data, and then include lower scattering angles progressively. The large scattering angles will resolve the smooth part of the model and reduce the non-linearity of the problem, then the lower ones will enhance the resolution of the model. Recorded data is first migrated using Pre-stack Exploding Reflector Migration (PERM), then the resulting pre-stack image is transformed into angle gathers to which an angle filtering process is applied to remove events below a certain cut-off angle. The filtered pre-stack image cube is then demigrated (forward modeled) to produce filtered surface data that can be used in waveform inversion. Numerical tests confirm the feasibility of the proposed filtering algorithm. However, the accuracy of the filtered section is limited by PERM’s singularity for horizontally-traveling waves, which in turn is dependent on the velocity model used for migration and demigration

L'imagerie quantitative des propriétés physiques du sous-sol est fondamentale pour de nombreuses applications impliquant des échelles d'exploration très variées: géotechnique pour l'imagerie de la proche surface, exploration à l'echelle crustale, reconstruction lithosphérique et imagerie globale pour la compréhension fondamentale des processus géodynamiques, mais aussi pour l'exploitation optimale des ressources du sous-sol.Parmi les méthode géophysiques, les méthodes sismiques ont le pouvoir de résolution le plus élevé. La densification des dispositifs d'acquisition, la mise au point de sources et de capteurs large bande et l'augmentation de la puissance de calcul ouvrent de nouvelles perspectives pour le développement et l'application de méthodes non conventionnelles d'imagerie sismique pour une extraction plus complète de l'information contenue dans les données sismiques. Parmi ces méthodes d'imagerie non conventionnelles, les méthodes d'inversion du champ d'onde complet, fondées sur la résolution complète de l'équation d'onde pour le problème direct (modélisation sismique) et la résolution d'un processus d'optimisation pour le problème inverse, font actuellement l'objet de nombreux développements méthodologiques, tant au sein des communautés industrielles qu'académiques.Le challenge numérique est la résolution du problème direct en trois dimensions pour un grand nombre de sources sismiques caractéristique des acquisitions pétrolières massives, et le challenge méthodologique est la gestion de la non-linéarité du problème inverse résultant de l'éclairage incomplet du sous-sol depuis la surface par des sources de bande-passante limitée. L'apport attendu de ces méthodes est la résolution de l'imagerie sismique de l'ordre de la demi-longueur d'onde propagée, sa capacité à imager des cibles complexes d'un point de vue structural notamment sous des écrans salifères ou basaltiques et la quantification des paramètres physiques caractérisant le sous-sol tels que la vitesse de propagation des ondes de compression à laquelle peuvent s'ajouter la densité, l'atténuation, la vitesse de propagation des ondes de cisaillement et des paramètres caractérisant l'anisotropie du milieu.L'objectif de cette thèse est de poursuivre le développement d'une méthode d'imagerie sismique acoustique 3D par l'inversion du champ d'onde complet et de l'appliquer à des données réelles pétrolières 3D de fond de mer enregistrées sur le champ pétrolier de Valhall en Mer du Nord et de fournir une des premières évaluations du potentiel des méthodes d'inversion des formes d'onde pour l'imagerie de milieux géologiques 3D L'inversion est effectuée en domaine fréquentiel où un nombre limité de fréquences est inversé suivant un protocole hiérarchique maintenant bien éprouvé procédant des basses fréquences vers les hautes fréquence: cette approche multi-échelle favorise la prise en compte de la non-linéarité du problème inverse.L'approche de modélisation en domaine temporel avec extraction du champ monochromatique par une transformée de Fourier discrète est effectuée pour calculer les champs d'onde monochromatique nécessaires à la résolution du problème inverse. L'algorithme d'optimisation du problème inverse est fondé sur une méthode de gradients conjugués préconditionés ou sur une méthode quasi-Newton. Les méthodes sont appliquées dans le cadre de l'approximation visco-acoustique isotrope où le milieu est paramétré par la vitesse de propagation des ondes de compression, l'atténuation et la densité. Seule, la composante hydrophone acquise en fond de mer est inversée. L'enjeu méthodologique de cette thèse est de fournir un modèle tri-dimensionelle du champ pétrolier de Valhall dans un cube de dimensions approximatives 18 km x 12 km x 5 km en poussant l'inversion à la fréquence la plus élevée possible. / Quantitative imaging of the subsurface physical properties is fundamental to many applications involving very various explorations, such as geotechnical imaging of the near surface, petroleum exploration, crustal lithospheric exploration. This helps us to understand the fundamental of geodynamic processes and also to exploit the resources of subsurface. Among the geophysical methods, seismic methods can give a higher resolution. The improvements of the acquisition in size and density, the multifold/multicomponent wide-aperture and wide-azimuth acquisitions, and the increased high-performance computing power open new perspectives to develop and apply non-conventional seismic imaging methods for extraction more complete and continuous information in the seismic data. Among these non-conventional methods, the full waveform inversion method based on the complete resolution of the wave equation for the direct problem (seismic modeling) and the resolution of optimization process for the inverse problem, are currently the subject of many methodological developments, in both industrial and academic communities. The numerical challenge is the resolution of the three-dimensional direct problem for a large number of seismic sources, typically few to tens of thousands in petroleum industry acquisition. The methodological challenge is the management of the non-linearity of the inverse problem resulting from the incomplete illumination of subsurface from the surface survey with a limited bandwidth source. The expected contribution of these methods is to reach a spatial resolution of half-a-wavelength. It has the ability to image complex structure targets such as saline or salt-bearing basaltic and to quantify the subsurface physical parameters such as velocity, density, attenuation, anisotropic parameters and so on. The objective of this thesis is to develop a method of three-dimensional seismic imaging by full waveform inversion and apply it to real ocean-bottom data set recorded in the Valhall oil field (in the North Sea) and to provide an early evaluation of the potentialities of full waveform inversion for imaging three-dimensional geological environments . The inversion is performed in frequency domain. A limited number of frequencies is inverted following a hierarchical protocol from low to high frequencies. This multi-scale approach helps to reduce the non-linearity of the inverse problem. The modeling approaches is performed in time domain and monochromatic wavefields are extracted by discrete Fourier transform to solve the inverse problem in frequency domain. The optimization algorithm of the inverse problem is based on conjugate gradients method or quasi-Newton method. The method is applied in the framework of the visco-acoustic isotropic approximation, where the medium is parameterized by the velocity of compressional wave propagation, attenuation, and density. The hydrophone data component located at the seabed is inverted. The methodological issue of this thesis is to develop by full waveform inversion a three-dimensional high-resolution velocity model of the Valhall oil field in a cube with a size of 18 km $\times$ 12 km $\times$ 5 km, and to push the inversion towards frequencies as high as possible.

Sogeti is an IT consulting company that’s active in large parts of the world. One of their biggest clients in Sundsvall is SCA Skog. In case of fire risk, SCA parti- cipates in consultation meetings with contractors to determine fire prevention measures. SMHI’s fire forecasts and warnings are a few of the bases that deter- mine when a consultation meeting is to begin. The problem is that the contractor today does not receive an automatic indication of fire risk. The purpose of the project was therefore to investigate SMHI’s services and find a solution to the problem and to find a limit for when a consultation meeting should be initia- ted based on the risk within an area. The solution presented is illustrated by a proof-of-concept model. The work has been carried agile in sprinting. Data has been taken from SMHI for a more detailed documentation over warnings and against MSB for the raw data that is behind fire forecasts so that those can be included in the solution. The project has resulted in an application that supports indication of risk based on a list of coordinates as well as automatic indication to the user’s position. An implementation guide was also created to facilitate a possible further development of the solution. The investigation shows that fire forecasts give a more precise indication of danger, but warnings should not be overlooked, as they indicate a risk of other warnings than fire risk. The solution is only intended to give the contractor an additional tool when making a deci- sion. The responsibility remains with the contractor, but the tool will hopefully allow the right decision to be made. / Sogeti är ett IT-konsultföretag med kontor i många länder. En av deras största klienter i Sundsvall är SCA Skog. Vid brandrisk deltar SCA tillsammans deras entreprenörer i samrådsmöten för att bestämma brandförebyggande åtgärder. SMHI:s brandprognoser och varningar är ett par av de underlag som avgör när ett samrådsmöte ska inledas. Problemet är att entreprenören idag inte får en automatisk indikation för brandrisk. Syftet med projektet blev därför att undersöka SMHI:s tjänster och finna en automatisk lösning samt att hitta en gräns för när ett samrådsmöte bör inledas baserat på brandrisken inom ett område. Den lösning som tagits fram illustreras genom en Proof-of-Concept modell. Arbetet har utförts agilt i sprintar. En datainsamling har utförts mot SMHI för en mer detaljerad dokumentation och mot MSB för den rådata som ligger bakom brandprognoser så att detta kan inkluderas i lösningen. Projektet har resulterat i en applikation som stödjer indikation av risk baserat på geografiska positioner samt automatisk indikation av risk vid en användares position. En implementationsguide togs även fram för att underlätta en möjlig vidareutveckling av lösningen. Undersökningen visar att brandprognoser ger en mer precis indikation på fara däremot bör varningar inte helt förbises då dessa kan indikera risk vid andra varningar än just brandrisk. Lösningen är enbart avsedd att ge entreprenören ett extra verktyg när denne ska ta ett beslut. Ansvaret ligger fortfarande hos entreprenören men en implementation möjliggör att beslut kan tas med gott un- derlag.

Multisource Least-Squares Migration (LSM) of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. But for the marine acquisition geometry this approach faces the challenge of erroneous misfit due to the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modeling method. To tackle this mismatch problem, I present a frequency selection strategy with LSM of supergathers. The key idea is, at each LSM iteration, to assign a unique frequency band to each shot gather, so that the spectral overlap among those shots—and therefore their crosstallk—is zero. Consequently, each receiver can unambiguously identify and then discount the superfluous sources—those that are not associated with the receiver in marine acquisition. To compare with standard migration, I apply the proposed method to 2D SEG/EAGE salt model and obtain better resolved images computed at about 1/8 the cost; results for 3D SEG/EAGE salt model, with Ocean Bottom Seismometer (OBS) survey, show a speedup of 40×. This strategy is next extended to multisource Full Waveform Inversion (FWI) of supergathers for marine streamer data, with the same advantages of computational efficiency and storage savings. In the Finite-Difference Time-Domain (FDTD) method, to mitigate spectral leakage due to delayed onsets of sine waves detected at receivers, I double the simulation time and retain only the second half of the simulated records. To compare with standard FWI, I apply the proposed method to 2D velocity model of SEG/EAGE salt and to Gulf Of Mexico (GOM) field data, and obtain a speedup of about 4× and 8×. Formulas are then derived for the resolution limits of various constituent wavepaths pertaining to FWI: diving waves, primary reflections, diffractions, and multiple reflections. They suggest that inverting multiples can provide some low and intermediate-wavenumber components of the velocity model not available in the primaries. In addition, diffractions can provide twice or better the resolution as specular reflections for comparable depths of the reflector and diffractor. The width of the diffraction-transmission wavepath is on the order of λ at the diffractor location for the diffraction-transmission wavepath.

L'imagerie quantitative des propriétés physiques du sous-sol est fondamentale pour de nombreuses applications impliquant des échelles d'exploration très variées: géotechnique pour l'imagerie de la proche surface, exploration à l'echelle crustale, reconstruction lithosphérique et imagerie globale pour la compréhension fondamentale des processus géodynamiques, mais aussi pour l'exploitation optimale des ressources du sous-sol.Parmi les méthode géophysiques, les méthodes sismiques ont le pouvoir de résolution le plus élevé. La densification des dispositifs d'acquisition, la mise au point de sources et de capteurs large bande et l'augmentation de la puissance de calcul ouvrent de nouvelles perspectives pour le développement et l'application de méthodes non conventionnelles d'imagerie sismique pour une extraction plus complète de l'information contenue dans les données sismiques. Parmi ces méthodes d'imagerie non conventionnelles, les méthodes d'inversion du champ d'onde complet, fondées sur la résolution complète de l'équation d'onde pour le problème direct (modélisation sismique) et la résolution d'un processus d'optimisation pour le problème inverse, font actuellement l'objet de nombreux développements méthodologiques, tant au sein des communautés industrielles qu'académiques.Le challenge numérique est la résolution du problème direct en trois dimensions pour un grand nombre de sources sismiques caractéristique des acquisitions pétrolières massives, et le challenge méthodologique est la gestion de la non-linéarité du problème inverse résultant de l'éclairage incomplet du sous-sol depuis la surface par des sources de bande-passante limitée. L'apport attendu de ces méthodes est la résolution de l'imagerie sismique de l'ordre de la demi-longueur d'onde propagée, sa capacité à imager des cibles complexes d'un point de vue structural notamment sous des écrans salifères ou basaltiques et la quantification des paramètres physiques caractérisant le sous-sol tels que la vitesse de propagation des ondes de compression à laquelle peuvent s'ajouter la densité, l'atténuation, la vitesse de propagation des ondes de cisaillement et des paramètres caractérisant l'anisotropie du milieu.L'objectif de cette thèse est de poursuivre le développement d'une méthode d'imagerie sismique acoustique 3D par l'inversion du champ d'onde complet et de l'appliquer à des données réelles pétrolières 3D de fond de mer enregistrées sur le champ pétrolier de Valhall en Mer du Nord et de fournir une des premières évaluations du potentiel des méthodes d'inversion des formes d'onde pour l'imagerie de milieux géologiques 3D L'inversion est effectuée en domaine fréquentiel où un nombre limité de fréquences est inversé suivant un protocole hiérarchique maintenant bien éprouvé procédant des basses fréquences vers les hautes fréquence: cette approche multi-échelle favorise la prise en compte de la non-linéarité du problème inverse.L'approche de modélisation en domaine temporel avec extraction du champ monochromatique par une transformée de Fourier discrète est effectuée pour calculer les champs d'onde monochromatique nécessaires à la résolution du problème inverse. L'algorithme d'optimisation du problème inverse est fondé sur une méthode de gradients conjugués préconditionés ou sur une méthode quasi-Newton. Les méthodes sont appliquées dans le cadre de l'approximation visco-acoustique isotrope où le milieu est paramétré par la vitesse de propagation des ondes de compression, l'atténuation et la densité. Seule, la composante hydrophone acquise en fond de mer est inversée. L'enjeu méthodologique de cette thèse est de fournir un modèle tri-dimensionelle du champ pétrolier de Valhall dans un cube de dimensions approximatives 18 km x 12 km x 5 km en poussant l'inversion à la fréquence la plus élevée possible.

Actuellement, le principal obstacle à la mise en œuvre de la FWI élastique en trois dimensions sur des cas d'étude réalistes réside dans le coût de calcul associé aux taches de modélisation sismique. Pour surmonter cette difficulté, je propose deux contributions. Tout d'abord, je propose de calculer le gradient de la fonctionnelle avec la méthode de l'état adjoint à partir d'une forme symétrisée des équations de l'élastodynamique formulées sous forme d'un système du premier ordre en vitesse-contrainte. Cette formulation auto-adjointe des équations de l'élastodynamique permet de calculer les champs incidents et adjoints intervenant dans l'expression du gradient avec un seul opérateur de modélisation numérique. Le gradient ainsi calculé facilite également l'interfaçage de plusieurs outils de modélisation avec l'algorithme d'inversion. Deuxièmement, j'explore dans cette thèse dans quelle mesure les encodages des sources avec des algorithmes d'optimisation du second-ordre de quasi-Newton et de Newton tronqué permettait de réduire encore le coût de la FWI. Finalement, le problème d'optimisation associé à la FWI est mal posé, nécessitant ainsi d'ajouter des contraintes de régularisation à la fonctionnelle à minimiser. Je montre ici comment une régularisation fondée sur la variation totale du modèle fournissait une représentation adéquate des modèles du sous-sol en préservant le caractère discontinu des interfaces lithologiques. Pour améliorer les images du sous-sol, je propose un algorithme de débruitage fondé sur une variation totale locale au sein duquel j'incorpore l'information structurale fournie par une image migrée pour préserver les structures de faible dimension. / Currently, the main limitation to perform 3D elastic full waveform inversion on a production level is the computational cost it represents. With this in mind, we provide two contributions. First, we develop a self adjoint formulation of the isotropic first order velocity-stress elastic equations that allow to implement only one forward modeling operator in the gradient computation. Second, we combine Newton and quasi-Newton optimization methods with source encoding techniques to see to what extent the computational cost could be further reduced. Finally, the optimization process associated to FWI is ill posed and requires regularization constraints. I show that the total variation of the model as a regularization term provides and adequate description of earth models, preserving the discontinuous character of the lithological layers. To improve the quality of the images, we propose a local total variation denoising algorithm based on the incorporation of the information provided by a migrated image.