Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is not suitable for identification in this problem, but that with further research, the resonant frequency (imaginary part) of the complex poles shows promise as an identification feature. / February 2005

Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is not suitable for identification in this problem, but that with further research, the resonant frequency (imaginary part) of the complex poles shows promise as an identification feature.

Part I: Various image reconstruction algorithms used for subsurface targets are reviewed. It is shown how some approximate wavefield inversion techniques: Stripmap Synthetic Aperture Radar (SAR), Kirchhoff Migration (KM) and Frequency-Wavenumber (FK) migration are developed from various models for wavefield scattering. The similarities of these techniques are delineated both from a theoretical and practical perspective and it is shown that Stripmap SAR is, computationally, almost identical to FK migration. A plane wave interpretation of both Stripmap SAR and FK migration is used to show why they are so similar. The electromagnetic assumptions made in the image reconstruction algorithms are highlighted. In addition, it is shown that, theoretically, FK and KM are identical. Image reconstruction results for KM, Stripmap SAR and FK are shown for both synthetic and experimental Ground Penetrating Radar (GPR) data. Subjectively the reconstructed images show little difference, but computationally, Stripmap SAR (and therefore, FK migration) are much more efficient. Part II: A preliminary investigation into the use of the Singularity Expansion Method (SEM) for use in identifying landmines is completed using a Finite-Difference Time-Domain code to simulate a simplified GPR system. The Total Least Squares Matrix Pencil Method (TLS-MPM) is used to determine the complex poles from an arbitrary late-time signal. Both dielectric and metallic targets buried in lossless and lossy half-spaces are considered. Complex poles (resonances) of targets change significantly when the objects are buried in an external medium, and perturbation formulae for Perfect Electric Conductor (PEC) and dielectric targets are highlighted and used. These perturbation formulae are developed for homogenous surrounding media, and their utilization for the half-space (layered medium) GPR problem causes inaccuracies in their predictions. The results show that the decay rate (real part) of the complex poles is not suitable for identification in this problem, but that with further research, the resonant frequency (imaginary part) of the complex poles shows promise as an identification feature.

The ability to synthesize recordings from surface data as if they had come from subsurface sources has allowed geophysicists to estimate subsurface properties. Either in the form of classical seismic migration which creates structural maps of the subsurface, to the more recent seismic interferometry which turns seismic sources into receivers and vice-versa, this ability has provided a rich trove of methods with which to probe the Earth's interior. While powerful, both of these techniques suffer from well-known issues. Standard migration requires data without multiply-scattered waves (multiples). Seismic interferometry, on the other hand, can be applied to full recorded data (containing multiples and other wave types), but requires sources (receivers) to be physically placed at the location from (to) one wishes to estimate responses. The Marchenko method, developed recently for the seismic setting, circumvents both of these restrictions: it creates responses from virtual subsurface sources as if measured at the surface. It requires only single-sided surface data, and a smooth estimate of the subsurface velocities. Initially developed for acoustic media, this thesis contributes the first elastic formulation of the Marchenko method, providing a more suitable setting for applications for the solid Earth. In another development, this thesis shows how the obtained virtual recordings may be used for migration. With these two contributions, this thesis shows that for elastic surface seismic data, the main drawbacks of migration and interferometry can be overcome using the Marchenko method: multiples do not harm migrated images, and sources (receivers) need not be physically placed in the medium for their responses to be accessible. In addition to the above methods, generating images devoid of multiple-related artifacts can be achieved in several other different ways. Two approaches to this are the use of a post-imaging filter, and attenuation of internal multiples in the data itself. This thesis contributes one new method using each of these approaches. First, a form of Marchenko imaging is known to create spurious reflectors, as also occurs in standard reverse-time migration (RTM). However, these artifacts usually appear at different locations in RTM and this form of Marchenko imaging. Using this insight, this thesis presents a way to combine pairs of seismic images in such a way that their differences (e.g. artifacts) are attenuated, while similarities (e.g. true reflectors) are preserved. Applying this to RTM and Marchenko-derived images markedly improves image quality. Second, this thesis presents a method to estimate multiples in the data. Multiples can either be migrated on their own to aid in interpretation, or be adaptatively removed from the data to improve image quality. However, because of the nature of adaptive subtraction, this second method may harm primary energy. To avoid this problem, this thesis develops a final method to directly image using only primary energy in the recorded data using only a small number of virtual points. This method bypasses the need for multiple removal and the estimation of subsurface responses at every depth location. In addition, primaries from particular reflectors may be particularly selected such that they can be imaged individually. Overall this thesis provides several new ways to use surface seismic data in such a way that multiples do not hamper the end product of seismic data processing: the seismic image. It demonstrates this use on synthetic and real data, proving their effectiveness.

Conventionally, to speed up scientific or engineering (S&E) computation programs on general-purpose computers, one may elect to use faster CPUs, more memory, systems with more efficient (though complicated) architecture, better software compilers, or even coding with assembly languages. With the emergence of Field Programmable Gate Array (FPGA) based Reconfigurable Computing (RC) technology, numerical scientists and engineers now have another option using FPGA devices as core components to address their computational problems. The hardware-programmable, low-cost, but powerful “FPGA-enhanced computer” has now become an attractive approach for many S&E applications. A new computer architecture model for FPGA-enhanced computer systems and its detailed hardware implementation are proposed for accelerating the solutions of computationally demanding and data intensive numerical PDE problems. New FPGAoptimized algorithms/methods for rapid executions of representative numerical methods such as Finite Difference Methods (FDM) and Finite Element Methods (FEM) are designed, analyzed, and implemented on it. Linear wave equations based on seismic data processing applications are adopted as the targeting PDE problems to demonstrate the effectiveness of this new computer model. Their sustained computational performances are compared with pure software programs operating on commodity CPUbased general-purpose computers. Quantitative analysis is performed from a hierarchical set of aspects as customized/extraordinary computer arithmetic or function units, compact but flexible system architecture and memory hierarchy, and hardwareoptimized numerical algorithms or methods that may be inappropriate for conventional general-purpose computers. The preferable property of in-system hardware reconfigurability of the new system is emphasized aiming at effectively accelerating the execution of complex multi-stage numerical applications. Methodologies for accelerating the targeting PDE problems as well as other numerical PDE problems, such as heat equations and Laplace equations utilizing programmable hardware resources are concluded, which imply the broad usage of the proposed FPGA-enhanced computers.

[pt] O processamento de sinais sísmicos é peça chave na exploração petrolífera. O caminho entre aquisição de dados e interpretação sísmica é composto por uma trilha de processos interdependentes, entre eles os processos de modelagem e migração. A dissertação apresenta a composição de um algoritmo de modelagem acústica 2D no domínio da transformada wavelet a partir de ferramentas próprias e outras já existentes na literatura. São estabelecidas as aproximações necessárias à solução em meios heterogêneos e à independência entre os subdomínios de processamento. Esta independência possibilita a exploração de técnicas de processamento paralelo. Através de exemplos, seu desempenho é avaliado com comparações à solução via diferenças finitas. Estas soluções são ainda submetidas ao mesmo processo de migração baseado em um terceiro modo de solução. / [en] Seismic signal processing is a key step to oil exploration. The path between data acquisition and seismic interpretation is composed by a sequence of interdependent processes, among which are modeling and migration processes. A 2D acoustic modeling algorithm in wavelet Transform domain, based on custom tools and tools already made known in literature is presented. Approximations necessary for the solution in inhomogeneous media and for complete independence between processing subspaces are established. Such independence allows exploration of parallel processing techniques. Throughout examples, performance is evaluated in comparison to finite-difference solution. These solutions are further processed by a migration technique based in yet another solution method.

La géologie, et plus particulièrement la géophysique, repose sur l’observation, directe et indirecte, de phénomènes se produisant en surface et dans les profondeurs de la Terre. Ces observations nous permettent d’étudier et définir la structure et les dynamiques globales de la Terre. L’étude des ondes sismiques générées par les tremblements de terre les plus puissants permet, par exemple, d’entrevoir la structure des hétérogénéités dans les premières centaines de kilomètres de la Terre. Dans cette thèse, nous nous intéressons au champ d’onde diffracté, qui est composé des arrivées tardives qui suivent les ondes incidentes. Par définition, les ondes diffractés contiennent de l’information liée aux hétérogénéités diffractantes, autrement dit les structures à petite échelle de la Terre, qu’elles rencontrent le long de leur trajet. De ce fait, il est possible d’étudier les variations rapides de vitesses sismiques grâce au champ d’onde diffracté, alors que ces informations seraient perdues dans les méthodes tomographiques à cause des facteurs de régularisation. Afin d’exploiter le champ d’onde diffracté, on a recours aux fonctions récepteurs (« receiver function » en anglais, RF) et à la migration sismique en profondeur de pré-empilage. Les procédures standard de migration sismiques sont de deux types principaux. Le premier type de procédures, dont l’exemple type est la migration en point de conversion communs (« common conversion point » en anglais, CCP) est rapide mais repose sur l’hypothèse fondamentale que les discontinuités que l’on cherche à imager sont horizontales. Le second type de procédures, pour lesquelles on peut citer la « reverse time migration » (RTM), ou la « generalized radon transform » (GRT), ne font pas d’hypothèse sur la structure du sous-sol, mais demandent une forte intensité des calculs et sont de fait souvent limités à des géométries bidimensionnelles. Au cours de ce manuscrit, nous développons une migration sismique de type Kirchhoff qui se base sur des calculs de temps de trajet sismique rapides en trois dimensions et quasiment aucune hypothèse sur la structure du milieu sous-jacent. Cet algorithme efficace nous permet de nous affranchir des traditionnelles limitations à des études 1D ou 2D. Notre principe d’imagerie prend en compte les ondes diffractées transmises et réfléchies, et se place dans la suite des travaux de Cheng et al. (2016). Nous adaptons la migration de type Kirchhoff élastique aux géométries de diffraction inhérentes à la sismologie passive et prenons en compte les multiples de surface. Les temps de trajet de toutes les ondes diffractées sont calculées grâce à la « fast marching method » (FMM). Les amplitudes et la polarité des signaux des RF sont corrigées à l’aide du calcul de figures de diffraction 3D. Pour extraire l’information des conversions transmises et réfléchies de façon cohérente, les résultats pour chaque mode de diffraction sont sommés de plusieurs façons (linéaire, à filtre de phase, et à filtre d’amplitude non linéaire). Afin de démontrer l’efficacité et la précision de notre méthode de migration, nous procédons à des tests synthétiques, aussi bien dans des situations réalistes qu’artificiellement compliquées, en nous servant du logiciel Raysum. Les résultats de ces tests prouvent que cette méthode de migration permet d’obtenir une image fidèle du milieu imagé quasiment sans artéfacts. En intégrant les trois composantes des RF dans la migration, cette méthode de migration est capable d’exploiter l’information d’ondes arrivant avec n’importe quel angle d’incidence et n’importe quel azimut. Finalement, cette méthode de migration multi-mode 3D est appliquée à deux jeux de données de terrain issus de réseaux sismiques déployés au dessus de zones de subduction, en Grèce et en Alaska / In geology, and in particular in geophysics, direct and indirect observations of processes occurring both at the surface of the Earth and at depth are used to understand the structure and dynamics of the Earth. For instance, seismic waves generated by large earthquakes can be used to study the structure of heterogeneities in the first few hundred kilometers inside the Earth. In this work, we use the scattered wavefield, which corresponds to energy arriving after the incident wavefield, to image the Earth. By nature, the scattered waves are linked to the scattering heterogeneities encountered along their propagation path, i.e. the fine scale structure of the Earth. Hence, the scattered wavefield has the ability to highlight structures where rapid velocity variations would otherwise be smoothed out by tomographic regularization, such as the structure of subducting slabs. To extract the information from the scattered wavefield, we resort to receiver function (RF) analysis and pre-stack depth migration. Standard migration procedures either rely on the assumption that underlying discontinuities are horizontal, such as in Common Conversion Point stacking (CCP), or are computationally expensive and usually limited to 2D geometries, such as in Reverse Time Migration (RTM) or Generalized Radon Transform (GRT). Here, we develop a Kirchhoff-type teleseismic imaging method that uses fast 3D travel-time calculations with minimal assumptions about the underlying structure. This provides high computational efficiency without limiting the problem to 1D or 2D geometries. In our method, we apply elastic Kirchhoff migration to transmitted and reflected teleseismic waves (i.e., RF). The approach expands on the work of Cheng et al. (2016). The 3D elastic Kirchhoff migration is adapted to the passive seismology scattering geometry and to account for free surface multiples. We use an Eikonal solver based on the fast marching method (FMM) to compute travel times for all scattered phases. 3D scattering patterns are computed to correct the amplitudes and polarities of the three component input signals. We consider three different stacking methods (linear, phase weighted and 2 nd root) to enhance the structures that are most coherent across scattering modes. To showcase the efficiency and accuracy of our migration procedure, we test it by conducting a series of synthetic tests in both artificially challenging and realistic scenarios. Results from synthetic tests show that our imaging principle can recover scattering structures accurately with minimal artifacts. We show that integrating the three components of the RF into the imaging principle allows to coherently retrieve the scattering potential for arbitrarily dipping discontinuities from all back-azimuths, and are able to retrieve a typical 2.5D subduction zone structure. We apply this novel 3D multi-mode Kirchhoff migration method to two different subduction zones, in Western Greece and Southern Alaska

La partie ouest du rift de Corinthe, en Grèce, s'ouvre à une vitesse d'environ 15 mm par an générant un taux de déformation parmi les plus élevés au monde, quelques séismes destructeurs de magnitude M>6 par décennie, et une forte activité microsismique irrégulière spatialement et temporellement. Afin de mieux comprendre les mécanismes liés à cette déformation crustale et de préciser les structures majeures actives, ce travail de recherche exploite la base de données sismologiques du Corinth Rift Laboratory de 2000 à 2015 en analysant finement les microséismes et leur évolution spatio-temporelle. La relocalisation globale des sources sismiques ainsi que leur classification en multiplets ont permis de préciser la géométrie des failles et d'identifier des comportements mécaniques différents. La zone ouest, au milieu du golfe, est affectée par des variations de pressions de fluides dans une couche géologique, entraînant des migrations des essaims de microséismes à des vitesses d'environ 50 m par jour. Les multiplets profonds de la partie centrale, près de la côte nord, sont persistants et semblent déclenchés par des épisodes de glissements lents asismiques sur un détachement immature pouvant atteindre la croûte ductile. Le faible pourcentage de déclenchement dynamique par les ondes sismiques suggère que l'état global du système de failles n'est pas au seuil critique de rupture. La magnitude des séismes est corrélée à l'impulsivité initiale de la rupture. Ces résultats précisent la dynamique de déformation du rift, les interactions sismique-asismiques, et permettront d'améliorer les modèles d'aléas sismiques de la région / The western part of the Corinth Rift in Greece is opening at about 15 mm per year, generating one of the highest deformation rates in the world, some destructive earthquakes of magnitude M>6 per decade, and high microseismic activity irregular in space and time. In order to better understand the mechanisms related to this crustal deformation and to specify the major active structures, this research work makes use of the seismological database of the Corinth Rift Laboratory from 2000 to 2015 by finely analyzing microearthquakes and their spatio-temporal evolution. The global relocation of the seismic sources and their classification into multiplets enable to refine the geometry of the faults and to identify different mechanical behaviors. The western zone, in the middle of the gulf, is affected by fluctuations of fluid pore pressures in a geological layer, resulting in microseismic swarm migrations at a velocity of about 50 m per day. The deep multiplets of the central part, near the northern coast, are persistent and appear to be triggered by episodes of slow aseismic slip along an immature detachment, which can reach the ductile crust. The low percentage of dynamic triggering by passing seismic waves suggests that the overall state of the fault system is not at the critical breaking point. The magnitude of earthquakes is correlated with the initial impulsiveness of the rupture. These results specify the dynamics of the rift deformation, the seismic-aseismic interactions, and will make possible the improvement of the seismic hazard models of the region