Fractured reservoirs, especially in low permeable carbonate rocks, are important target for hydrocarbon exploration and production because fractures can control fluid flow inside the reservoir. Hence, quantitative knowledge of fracture attributes is important for optimal hydrocarbon production. However, in some cases fractures can cause leakage of injected CO2 during enhanced oil recovery (EOR) or CO2 sequestration. Furthermore, CO2 can geochemically interact with reservoir fluids and host rock. Hence, time-lapse monitoring of the progress of CO2 in fractured reservoirs is also very important. In order to address these challenges, I have developed an integrated approach for studying fluid flow and seismic wave propagation in fractured media using Discrete Fracture Network (DFN) models. My seismic simulation study suggests that CO2 saturated reservoir shows approximately ten times more attenuation than brine saturated reservoir. Similarly, large P-wave velocity variation in CO2 saturated reservoir and amplitude variation with offset (AVO) results for our example model predicts that CO2 is easier to detect than brine in the fractured reservoirs. The effects of geochemical processes on seismics are simulated by time-lapse modeling for t = 1000 years. My modeling study suggests that intra-aqueous reactions are more significant during injection of CO2 for t = 6 years, while slower mineral reactions dominate after pressure equilibrium is achieved that is from t = 6 to 1000 years. Overall both types of geochemical reactions cause change in reflection coefficient of 2 to 5%, which may be difficult to detect in some cases. However, the significant change in the seismic properties at the boundary of the CO2 front can be used to detect the flow path of CO2 inside the reservoirs. Finally, a method for generating stochastic fracture models was extended and improved to more realistic field model for seismic and fluid modeling. My detail analysis suggests that fractures generated by isotropic stress field favor orthogonal sets of fractures in most subsurface rocks that can be converted to seismic model, similar to DFN study. The quality and validity of the models is assessed by comparisons to DFN models, including calculations of fractal dimension measures that can help to characterize fractured reservoirs.

Natural gas and oil from characteristically complex unconventional reservoirs, such as organic shale, tight gas and oil, coal-bed methane; are transforming the global energy market. These conventional reserves exist in complex geologic formations where conventional seismic techniques have been challenged to successfully image the subsurface. To acquire maximum benefits from these unconventional reserves, seismic anisotropy must be at the center of our modeling and inversion workflows. I present algorithms for fast traveltime computations in anisotropic media. Both ray-based and finite-difference solvers of the anisotropic eikonal equation are developed. The proposed algorithms present novel techniques to obtain accurate traveltime solutions for anisotropic media in a cost-efficient manner. The traveltime computation algorithms are then used to invert for anisotropy parameters. Specifically, I develop inversion techniques by using diffractions and diving waves in the seismic data. The diffraction-based inversion algorithm can be combined with an isotropic full-waveform inversion (FWI) method to obtain a high-resolution model for the anellipticity anisotropy parameter. The inversion algorithm based on diving waves is useful for building initial anisotropic models for depth-migration and FWI. I also develop the idea of 'effective elliptic models' for obtaining solutions of the anisotropic two-way wave equation. The proposed technique offers a viable alternative for wavefield computations in anisotropic media using a computationally cheaper wave propagation operator. The methods developed in the thesis lead to a direct cost savings for imaging and inversion projects, in addition to a reduction in turn-around time. With an eye on the next generation inversion methods, these techniques allow us to incorporate more accurate physics into our modeling and inversion framework.

[pt] O problema de Inversão Sísmica envolve a determinação das propriedades físicas da superfície a partir de dados amostrados na superfície. A construção de um modelo matemático da resposta da subsuperfície à excitação de uma fonte sísmica, tendo como parâmetros as propriedades físicas da subsuperfície, fornece um modelo sintético desta resposta para determinados valores dos parâmetros. Isto permite comparar dados amostrados e modelos sintético. A perturbação do modelo pela variação dos seus parâmetros pode aproximar dados amostrados e sintéticos e colocar o problema da Inversão como um problema de minimização de uma função de erro que os ajuste de forma adequada. Usualmente, os métodos que tentam minimizar a medida a medida de erro supõem um comportamento linear entre a perturbação do modelo e esta medida. Na maioria dos problemas geofísicos, esta medida apresenta um alto grau de não linearidade e uma grande quantidade de mínimos locais. Isto torna estes métodos baseados em aproximações lineares muito sensíveis à escolha de uma boa solução inicial, o que nem sempre está disponível. Como resolver este problema sem uma boa solução inicial? A teoria da Inferência Bayesiana oferece uma solução pelo uso de informação a priori sob o espaço dos parâmetros. O problema de Inversão volta então a ser um problema de otimização onde se precisa maximizar a probabilidade a posteriori dos parâmetros assumirem um certo valor dado que se obteve o resultado da amostragem dos dados. Este problema é resolvido pelo método do Simulated Annealing (SA), método de otimização global que faz uma busca aleatória direcionada no espaço de solução. Este método foi proposto por uma analogia entre o recozimento física de sólidos e problemas de otimização. O SA, na sua variante Very Fast Simulated Annealing (VFSA), é aplicado na solução de problemas de Inversão Sísmica 1 D para modelos acústico e elásticos gerados sinteticamente. A avaliação do desempenho do SA usando medidas de erro com diferentes normas é realizada para um modelo elástico adicionado de ruído aleatório. / [en] The seismic inverse problem involves determining the subsurface physical properties from data sampled at Earth`s surface. A mathematical model of the response of the subsurface excited by a seismic source, having physical properties as parameters, provides a synthetic model for this response. This makes possible to compare sampled and synthetic data. The perturbation in the model due to the variation of its parameters can approximate these data and states the inversion problem as the minimization of an error function that fits them adequately. Usually, the methods which attempt to minimize this error assume that a perturbation in the model is linearly relates with a perturbation in the measured response. Most geophysical inverse problems are highly nonlinear and are rife with local minima. Therefore these methods are very sensitive to the choice of the initial model and good starting solutions may not be available. What should be done, if there is no basis for an initial guess? The theory of Bayesian inference provides an answer to this question taking into account the prior information about the parameter space. The inverse problem can then be stated as an optimization problem whose goal is to maximize the posterior probability that the set of parameters has a certain value once given the result of the sample. This problem is solved by the Simulated Annealing method, a global optimization method that executes a oriented random search in the solution space. This method comes from an analogy between the physical annealing of solids and optimization problems. The Very Fast Simulated Annealing (VFSA), a variant of SA, is applied to the solution of 1 D seismic inverse problems generated synthetically by acoustic and alastic done by a elastic model with additive noise.

L’imagerie sismique du sous-sol à partir de données terrestres est très difficile à effectuer due à la complexité 3D de la proche surface. Dans cette zone, les ondes sismiques sous forme d’un paquet compact de phases souvent imbriquées sont dominées par des effets élastiques et viscoélastiques, couplés aux effets dus à la surface libre qui génèrent des ondes de surface de grande amplitude et dispersives.L’interaction des ondes sismiques avec une topographie plus ou moins complexe dans un contexte de fortes hétérogénéités de la proche surface induit d’importantes conversions des ondes avec de fortes dispersions d’énergie. Il est donc nécessaire de prendre en compte à la fois une représentation tridimensionnelle précise de la topographie et une physique correcte qui rend compte de la propagation du champ d’onde dans le sous-sol au niveau de précision réclamé par l’imagerie sismique. Dans ce manuscrit, nous présentons une stratégie d’inversion des formes d’onde complètes (FWI en anglais) efficace, autonome et donc flexible, pour la construction de modèles de vitesse à partir de données sismiques terrestres, plus particulièrement dans les environnements dits de chevauchements d’arrière pays(foothills en anglais) aux variations de vitesse importantes.Nous proposons une formulation efficace de cette problématique basée sur une méthode d’éléments spectraux en domaine temporel sur une grille cartésienne déformée, dans laquelle les variations de topographie sont représentées par une description détaillée de sa géométrie via une interpolation d’ordre élevé. La propagation du champ d’onde est caractérisée par une élasticité linéaire anisotrope et par une atténuation isotrope du milieu: cette deuxième approximation semble suffisante pour l’imagerie crustale considérée dans ce travail. L’implémentation numérique du problème direct inclut des produits matricevecteurefficaces pour résoudre des équations élastodynamiques composant un système différentielhyperbolique du second ordre, pour les géométries tridimensionnelles rencontrées dans l’exploration sismique. Les expressions explicites des gradients de la fonction écart entre les données et les prédictions sont fournies et inclut les contributions de la densité, des paramètres élastiques et des coefficients d’atténuation. Ces expressions réclament le champ incident venant de la source au même temps de propagation que le champ adjoint. Pour ce faire, lors du calcul du champ adjoint à partir de l’instant final, le champ incident est recalculé au vol à partir de son état final, de conditions aux bords préalablement sauvegardées et de certains états intermédiaires sans stockage sur disques durs. Le gradient est donc estimé à partir de quantités sauvegardées en mémoire vive. Deux niveaux de parallélisme sont implémentés, l’un sur les sources et l’autre sur la décomposition du domaine pour chaque source, cequi est nécessaire pour aborder des configurations tridimensionnelles réalistes. Le préconditionnement de ce gradient est réalisé par un filtre dit de Bessel, utilisant une implémentation différentielle efficace fondée sur la même discrétisation de l’espace du problème direct et formulée par une approche d’éléments spectraux composant un système linéaire symétrique résolu par une technique itérative de gradient conjugué. De plus, une contrainte non-linéaire sur le rapport des vitesses de compression et de cisaillement est introduite dans le processus d’optimisation sans coût supplémentaire: cette introductions’avére nécessaire pour traiter les données en présence de faibles valeurs de vitesse proche de la surface libre.L’inversion élastique multi-paramètres en contexte de chevauchement est illustrée à travers des exemples de données synthétiques dans un premier temps, ce qui met en évidence les difficultés d’une telle reconstruction…. / Seismic imaging of onshore targets is very challenging due to the 3D complex near-surface-related effects. In such areas, the seismic wavefield is dominated by elastic and visco-elastic effects such as highly energetic and dispersive surface waves. The interaction of elastic waves with the rough topography and shallow heterogeneities leads to significant converted and scattering energies, implying that both accurate 3D geometry representation and correct physics of the wave propagation are required for a reliable structured imaging. In this manuscript, we present an efficient and flexible full waveform inversion (FWI) strategy for velocity model building in land, specifically in foothill areas.Viscoelastic FWI is a challenging task for current acquisition deployment at the crustal scale. We propose an efficient formulation based on a time-domain spectral element method (SEM) on a flexible Cartesian-based mesh, in which the topography variation is represented by an accurate high-order geometry interpolation. The wave propagation is described by the anisotropic elasticity and isotropic attenuation physics. The numerical implementation of the forward problem includes efficient matrix-vector products for solving second-order elastodynamic equations, even for completely deformed 3D geometries. Complete misfit gradient expressions including attenuation contribution spread into density, elastic parameters and attenuation factors are given in a consistent way. Combined adjoint and forward fields recomputation from final state and previously saved boundary values allows the estimation of gradients with no I/O efforts. Two-levels parallelism is implemented over sources and domain decomposition, which is necessary for 3D realistic configuration. The gradient preconditioning is performed by a so-called Bessel filter using an efficient differential implementation based on the SEM discretization on the forward mesh instead of the costly convolution often-used approach. A non-linear model constraint on the ratio of compressional and shear velocities is introduced into the optimization process at no extra cost.The challenges of the elastic multi-parameter FWI in complex land areas are highlighted through synthetic and real data applications. A 3D synthetic inverse-crime illustration is considered on a subset of the SEAM phase II Foothills model with 4 lines of 20 sources, providing a complete 3D illumination. As the data is dominated by surface waves, it is mainly sensitive to the S-wave velocity. We propose a two-steps data-windowing strategy, focusing on early body waves before considering the entire wavefield, including surface waves. The use of this data hierarchy together with the structurally-based Bessel preconditioning make possible to reconstruct accurately both P- and S-wavespeeds. The designed inversion strategy is combined with a low-to-high frequency hierarchy, successfully applied to the pseudo-2D dip-line survey of the SEAM II Foothill dataset. Under the limited illumination of a 2D acquisition, the model constraint on the ratio of P- and S-wavespeeds plays an important role to mitigate the ill-posedness of the multi-parameter inversion process. By also considering surface waves, we manage to exploit the maximum amount of information in the observed data to get a reliable model parameters estimation, both in the near-surface and in deeper part.The developed FWI frame and workflow are finally applied on a real foothill dataset. The application is challenging due to sparse acquisition design, especially noisy recording and complex underneath structures. Additional prior information such as the logs data is considered to assist the FWI design. The preliminary results, only relying on body waves, are shown to improve the kinematic fit and follow the expected geological interpretation. Model quality control through data-fit analysis and uncertainty studies help to identify artifacts in the inverted models.

Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods o er a better control on the accuracy and more geometrical exibility than the Finite Di erence methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis are con rmed by numerical experiments performed using an implementation of these methods. The methods are tested using two benchmarks: Lamb's problems and the SEG/EAGE salt dome model. / text

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.

Understanding and modeling seismic wave propagation is important in regional and exploration seismology. Ray tracing is a powerful and popular method for this purpose. Wavefront construction (WFC) method handles wavefronts instead of individual rays, thereby controlling proper ray density on the wavefront. By adaptively controlling rays over a wavefront, it efficiently models wave propagation. Algorithms for a quasi-P wave wavefront construction method and a new coordinate system used to generate wavefront construction mesh are proposed and tested for numerical properties and modeling capabilities. Traveltimes, amplitudes, and other parameters, which can be used for seismic imaging such as migrations and synthetic seismograms, are computed from the wavefront construction method. Modeling with wavefront construction code is applied to anisotropic media as well as isotropic media. Synthetic seismograms are computed using the wavefront construction method as a new way of generating synthetics. To incorporate layered velocity models, the model based interpolation (MBI) ray tracing method, which is designed to take advantage of the wavefront construction method as well as conventional ray tracing methods, is proposed and experimental codes are developed for it. Many wavefront construction codes are limited to smoothed velocity models for handling complicated problems in layered velocity models and the conventional ray tracing methods suffer from the inability to control ray density during wave propagation. By interpolating the wavefront near model boundaries, it is possible to handle the layered velocity model as well as overcome ray density control problems in conventional methods. The test results revealed this new method can be an effective modeling tool for accurate and effective computing.

The Woodford Shale is an important unconventional oil and gas resource. It can act as a source rock, seal and reservoir, and may have significant elastic anisotropy, which would greatly affect seismic response. Understanding how anisotropy may affect the seismic response of the Woodford Shale is important in processing and interpreting surface reflection seismic data. The objective of this study is to identify the differences between isotropic and anisotropic seismic responses in the Woodford Shale, and to understand how these anisotropy parameters and physical properties influence the resultant synthetic seismograms. I divide the Woodford Shale into three different units based on the data from the Pioneer Reliance Triple Crown #1 (RTC #1) borehole, which includes density, gamma ray, resistivity, sonic, dipole sonic logs, part of imaging (FMI) logs, elemental capture spectroscopy (ECS) and X-ray diffraction (XRD) data from core samples. Different elastic parameters based on the well log data are used as input models to generate synthetic seismograms. I use a vertical impulsive source, which generates P-P, P-SV and SV-SV waves, and three component receivers for synthetic modeling. Sensitivity study is performed by assuming different anisotropic scenarios in the Woodford Shale, including vertical transverse isotropy (VTI), horizontal transverse isotropy (HTI) and orthorhombic anisotropy. Through the simulation, I demonstrate that there are notable differences in the seismic response between isotropic and anisotropic models. Three different types of elastic waves, i.e., P-P, P-SV and SV-SV waves respond differently to anisotropy parameter changes. Results suggest that multicomponent data might be useful in analyzing the anisotropy for the surface seismic data. Results also indicate the sensitivity offset range might be helpful in determining the location for prestack seismic amplitude analysis. All these findings demonstrate the potentially useful sensitivity parameters to the seismic data. The paucity of data resources limits the evaluation of the anisotropy in the Woodford. However, the seismic modeling with different type of anisotropy assumptions leads to understand what type of anisotropy and how this anisotropy affects the change of seismic data. / text

Monitoring of the seafloor for gas hydrate dissociation around boreholes during hydrocarbon production is likely to involve seismic methods because of the strong sensitivity of P-wave velocity to gas in sediment pores. Here, based on geomechanical models, we apply commonly used rock physics modeling to predict the seismic response to gas hydrate dissociation with a focus on P-impedance and performed sensitivity tests. For a given initial gas hydrate saturation, the mode of gas hydrate distribution (cementation, frame-bearing, or pore-filling) has the strongest effect on P-impedance, followed by the mesoscopic distribution of gas bubbles (evenly distributed in pores or “patchy”), gas saturation, and pore pressure. Of these, the distribution of gas is likely to be most challenging to predict. Conceptual 2-D FD wave-propagation modeling shows that it could be possible to detect gas hydrate dissociation after a few days.

Our knowledge of elastic wave propagation in general heterogeneous media with complex geological structures comes principally from numerical simulations. In this dissertation, I demonstrate through rigorous theoretical analyses and comprehensive numerical experiments that the Fourier method is a suitable method of choice for large scale 3D seismic modeling and imaging problems, due to its high accuracy and computational efficiency. The most attractive feature of the Fourier method is its ability to produce highly accurate solutions on relatively coarser grids, compared with other numerical methods for solving wave equations. To further advance the Fourier method, I identify two aspects of the method to focus on in this work, i.e., its implementation on modern clusters of computers and efficient high-order time stepping schemes. I propose two new parallel algorithms to improve the efficiency of the Fourier method on distributed memory systems using MPI. The first algorithm employs non-blocking all-to-all communications to optimize the conventional parallel Fourier modeling workflows by overlapping communication with computation. With a carefully designed communication-computation overlapping mechanism, a large amount of communication overhead can be concealed when implementing different kinds of wave equations. The second algorithm combines the advantages of both the Fourier method and the finite difference method by using convolutional high-order finite difference operators to evaluate the spatial derivatives in the decomposed direction. The high-order convolutional finite difference method guarantees a satisfactory accuracy and provides the flexibility of using non-blocking point-to-point communications for efficient interprocessor data exchange and the possibility of overlapping communication and computation. As a result, this hybrid method achieves an optimized balance between numerical accuracy and computational efficiency. To improve the overall accuracy of time domain Fourier simulations, I propose a family of new high-order time stepping schemes, based on a novel algorithm for designing time integration operators, to reduce temporal derivative discretization errors in a cost-effective fashion. I explore the pseudo-analytical method and propose high-order formulations to further improve its accuracy and ability to deal with spatial heterogeneities. I also extend the pseudo-analytical method to solve the variable-density acoustic and elastic wave equations. I thoroughly examine the finite difference method by conducting complete numerical dispersion and stability analyses. I comprehensively compare the finite difference method with the Fourier method and provide a series of detailed benchmarking tests of these two methods under a number of different simulation configurations. The Fourier method outperforms the finite difference method, in terms of both accuracy and efficiency, for both the theoretical studies and the numerical experiments, which provides solid evidence that the Fourier method is a superior scheme for large scale seismic modeling and imaging problems. / text