ABSTRACT The semi-finite cone model is adopted and modified to discuss the dynamic responses of the foundations, when the problem of liquefaction under the effect of cyclic loading is considered. The dynamic responses of the foundations caused by variation of the soil properties are also included. To achieve a better simulative of the physical phenomenon, this research employs the concept of wave reflections between soil layers. The responses observed for the foundation are vertical displacements, horizontal displacements, rotational angles, and twist angles in different seismic waves. Time-domain analysis is applied, so the research is constructed in time-domain completely. The soil conditions in this research are simulated as a single layer and layered system. Two types of the force simulation are employed; one is regular cycle force, and the other is irregular. To better understand the liquefaction, behavior of the variation of pore water pressure has been taken into accounts and analyzed focusly.

In Chapter 2, we consider the hydrostatic equilibrium figure of a rotating earth model with arbitrary radial density profile. We derive an exact non-linear partial differential equation describing the equilibrium figure. Perturbation theory is used to obtain approximate forms of this equation, and we show that the first-order theory is equivalent to Clairaut's equation. In Chapter 3, a method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. All other solutions can be written as the sum of this equilibrium stress field and a divergence-free stress tensor field whose boundary tractions vanish. In Chapter 4, we consider the minor vector method for the stable numerical solution of systems of linear ordinary differential equations. Results are presented for the application of the method to the calculation of seismic displacement fields in spherically symmetric, self-gravitating earth models. In Chapter 5, we present a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. Numerical tests are presented to demonstrate the validity and effectiveness of this method for performing large mode coupling calculations. In Chapter 6, we consider the theoretical basis for the viscoelastic normal mode method which is used in studies of seismic wave propagation, post-glacial rebound, and post-seismic deformation. We show how the time-domain solution to the viscoelastodynamic equation can be written as a normal mode sum in a rigorous manner.

My dissertation focuses primarily on the following three aspects associated with passing seismic waves in the field of earthquake seismology: temporal changes of fault zone properties, nonlinear site response, and dynamic triggering. Quantifying the temporal changes of material properties within and around active fault zones (FZ) is important for better understanding of rock rheology and estimating the strong ground motion that can be generated by large earthquakes. As high-amplitude seismic waves propagate through damaged FZ rocks and/or shallow surface layers, they may produce additional damage leading to nonlinear wave propagation effects and temporal changes of material properties (e.g., seismic velocity, attenuation). Previous studies have found several types of temporal changes in material properties with time scales of tens of seconds to several years. Here I systematically analyze temporal changes of fault zone (FZ) site response along the Karadere-Düzce branch of the North Anatolian fault that ruptured during the 1999 İzmit and Düzce earthquake sequences. The coseismic changes are on the order of 20-40%, and are followed by a logarithmic recovery over an apparent time scale of ~1 day. These results provide a bridge between the large-amplitude near-instantaneous changes and the lower-amplitude longer-duration variations observed in previous studies. The temporal changes measured from this high-resolution spectral ratio analysis also provide a refinement for the beginning of the longer more gradual process typically observed by analyzing repeating earthquakes. An improved knowledge on nonlinear site response is critical for better understanding strong ground motions and predicting shaking induced damages. I use the same sliding-window spectral ratio technique to analyze temporal changes in site response associated with the strong ground motion of the Mw6.6 2004 Mid-Niigata earthquake sequence recorded by the borehole stations in Japanese Digital Strong-Motion Seismograph Network (KiK-Net). The coseismic peak frequency drop, peak spectral ratio drop, and the postseismic recovery time roughly scale with the input ground motions when the peak ground velocity (PGV) is larger than ~5 cm/s, or the peak ground acceleration (PGA) is larger than ~100 Gal. The results suggest that at a given site the input ground motion plays an important role in controlling both the coseismic change and postseismic recovery in site response. In a follow-up study, I apply the same sliding-window spectral ratio technique to surface and borehole strong motion records at 6 KiK-Net sites, and stack results associated with different earthquakes that produce similar PGAs. In some cases I observe a weak coseismic drop in the peak frequency when the PGA is as small as ~20-30 Gal, and near instantaneous recovery after the passage of the direct S waves. The percentage of drop in the peak frequency starts to increase with increasing PGA values. A coseismic drop in the peak spectral ratio is also observed at 2 sites. When the PGA is larger than ~60 Gal to more than 100 Gal, considerably stronger coseismic drops of the peak frequencies are observed, followed by a logarithmic recovery with time. The observed weak reductions of peak frequencies with near instantaneous recovery likely reflect nonlinear response with essentially fixed level of damage, while the larger drops followed by logarithmic recovery reflect the generation (and then recovery) of additional rock damage. The results indicate clearly that nonlinear site response may occur during medium-size earthquakes, and that the PGA threshold for in situ nonlinear site response is lower than the previously thought value of ~100-200 Gal. The recent Mw9.0 off the Pacific coast of Tohoku earthquake and its aftershocks generated widespread strong shakings as large as ~3000 Gal along the east coast of Japan. I systematically analyze temporal changes of material properties and nonlinear site response in the shallow crust associated with the Tohoku main shock, using seismic data recorded by the Japanese Strong Motion Network KIK-Net. I compute the spectral ratios of windowed records from a pair of surface and borehole stations, and then use the sliding-window spectral ratios to track the temporal changes in the site response of various sites at different levels of PGA The preliminary results show clear drop of resonant frequency of up to 70% during the Tohoku main shock at 6 sites with PGA from 600 to 1300 Gal. In the site MYGH04 where two distinct groups of strong ground motions were recorded, the resonant frequency briefly recovers in between, and then followed by an apparent logarithmic recovery. I investigate the percentage drop of peak frequency and peak spectral ratio during the Tohoku main shock at different PGA levels, and find that at most sites they are correlated. The third part of my thesis mostly focuses on how seismic waves trigger additional earthquakes at long-range distance, also known as dynamic triggering. Previous studies have shown that dynamic triggering in intraplate regions is typically not as common as at plate-boundary regions. Here I perform a comprehensive analysis of dynamic triggering around the Babaoshan and Huangzhuang-Gaoliying faults southwest of Beijing, China. The triggered earthquakes are identified as impulsive seismic arrivals with clear P- and S-waves in 5 Hz high-pass-filtered three-component velocity seismograms during the passage of large amplitude body and surface waves of large teleseismic earthquakes. I find that this region was repeatedly triggered by at least four earthquakes in East Asia, including the 2001 Mw7.8 Kunlun, 2003 Mw8.3 Tokachi-oki, 2004 Mw9.2 Sumatra, and 2008 Mw7.9 Wenchuan earthquakes. In most instances, the microearthquakes coincide with the first few cycles of the Love waves, and more are triggered during the large-amplitude Rayleigh waves. Such an instantaneous triggering by both the Love and Rayleigh waves is similar to recent observations of remotely triggered 'non-volcanic' tremor along major plate-boundary faults, and can be explained by a simple Coulomb failure criterion. Five earthquakes triggered by the Kunlun and Tokachi-oki earthquakes were recorded by multiple stations and could be located. These events occurred at shallow depth (< 5 km) above the background seismicity near the boundary between NW-striking Babaoshan and Huangzhuang-Gaoliying faults and the Fangshan Pluton. These results suggest that triggered earthquakes in this region likely occur near the transition between the velocity strengthening and weakening zones in the top few kms of the crust, and are likely driven by relatively large dynamic stresses on the order of few tens of KPa.

Orientador: Joerg Schleicher / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T08:06:07Z (GMT). No. of bitstreams: 1 Carvalho_RafaelAleixode_M.pdf: 679174 bytes, checksum: 087a9c376b3ab246bf6fe8cd05ae5d41 (MD5) Previous issue date: 2007 / Resumo: As equações da onda imagem para os problemas de remigração na profundidade eno tempo em meios elipticamente anisotrópicos são equações diferenciais parciais de segunda ordem similares a equação da onda acústica. A variável de propagação é a velocidade vertical ou a elipticidade do meio. Essas equações são deduzidas a partir das propriedades cinemáticas da remigração em meios anisotrópicos. O objetivo é propiciar a construção de imagens do subsolo que correspondam a diferentes velocidades verticais e/ou diferentes graus de anisotropia do meio diretamente de uma imagem migrada. ?Painéis de anisotropia? podem ser obtidos de maneira completamente análoga aos painéis de velocidade para a análise de velocidade de migração. Um exemplo numérico mostra a validade desta teoria / Abstract: The image-wave equations for the problems of depth and time remigration in elliptically anisotropic media are second-order partial differential equations similar to the acoustic wave equation. The propagation variable is the vertical velocity or the medium ellipticity. These differential equations are derived from the kinematic properties of anisotropic remigration. The objective is to enable the construction of subsurface images that correspond to different vertical velocity and/or different degrees of medium anisotropy directly from a single migrated image. In this way, ?anisotropy panels? can be obtained in a completely analogous way to velocity panels for a migration velocity analysis. A simple numerical example demonstrates the validity of the theory / Mestrado / Mestre em Matemática Aplicada

Dans cette thèse, on s'intéresse à la propagation d'ondes en milieu fortement hétérogène modélisée par l'équation d'Helmholtz. Les méthodes numériques permettant de résoudre ce problème souffrent de dispersion numérique, en particulier à haute fréquence. Ce phénomène, appelé "effet de pollution", est largement analysé dans la littérature quand le milieu de propagation est homogène et l'utilisation de "méthodes d'ordre élevé" est souvent proposée pour minimiser ce problème. Dans ce travail, on s'intéresse à un milieu de propagation hétérogène, cas pour lequel on dispose de moins de connaissances. On propose d'adapter des méthodes éléments finis d'ordre élevé pour résoudre l'équation d'Helmholtz en milieu hétérogène, afin de réduire l'effet de pollution. Les méthodes d'ordre élevé étant généralement basées sur des maillages "larges", une stratégie multi-échelle originale est développée afin de prendre en compte des hétérogénéités de petite échelle. La convergence de la méthode est démontrée. En particulier, on montre que la méthode est robuste vis-a-vis de l'effet de pollution. D'autre part, on applique la méthode a plusieurs cas-tests numériques. On s'intéresse d'abord à des problèmes académiques, qui permettent de valider la théorie de convergence développée. On considère ensuite des cas-tests "industriels" appliqués à la Géophysique. Ces derniers nous permettent de conclure que la méthode multi-échelle proposée est plus performante que les éléments finis "classiques" et que des problèmes 3D réalistes peuvent être considérés. / The main objective of this work is the design of an efficient numerical strategy to solve the Helmholtz equation in highly heterogeneous media. We propose a methodology based on coarse meshes and high order polynomials together with a special quadrature scheme to take into account fine scale heterogeneities. The idea behind this choice is that high order polynomials are known to be robust with respect to the pollution effect and therefore, efficient to solve wave problems in homogeneous media. In this work, we are able to extend so-called "asymptotic error-estimate" derived for problems homogeneous media to the case of heterogeneous media. These results are of particular interest because they show that high order polynomials bring more robustness with respect to the pollution effect even if the solution is not regular, because of the fine scale heterogeneities. We propose special quadrature schemes to take int account fine scale heterogeneities. These schemes can also be seen as an approximation of the medium parameters. If we denote by h the finite-element mesh step and by e the approximation level of the medium parameters, we are able to show a convergence theorem which is explicit in terms of h, e and f, where f is the frequency. The main theoretical results are further validated through numerical experiments. 2D and 3D geophysica benchmarks have been considered. First, these experiments confirm that high-order finite-elements are more efficient to approximate the solution if they are coupled with our multiscale strategy. This is in agreement with our results about the pollution effect. Furthermore, we have carried out benchmarks in terms of computational time and memory requirements for 3D problems. We conclude that our multiscale methodology is able to greatly reduce the computational burden compared to the standard finite-element method

Ground vibrations from blasting are acoustic waves that propagate through the earth. They are also termed seismic waves because their propagation characteristics are similar to the ground motions produced by earthquakes. Amplitude of ground vibration induced by blasting may vary significantly at or around an open pit mine depending on parameters such as the maximum amount of explosive detonating at a time interval and the physical distance between the shot and the location of concern, whereas the frequency of vibration mainly vary depending on the geology and blast delay intervals. Therefore evaluation and assessment of ground vibration condition at or around an open pit mine is necessary. The objective of the proposed research study is to monitor and record the ground vibration and to investigate and assess the vibration conditions at neighbouring districts that are induced by production blasting operations at Usak KiSladag Gold Mine. In this research study, several parameters such as the ground vibration velocity, the amount of charge per delay, the physical distance to the location of monitoring device or residential structures are recorded, analyzed and evaluated together with the frequencies of the seismic waves. The determined ground vibration velocities are compared with the allowable limits given in Turkish Regulation and US Federal Regulation. Thus, the compliance of the ground vibrations with the above mentioned regulations are discussed and assessed. Furthermore, the parameters which affect the ground vibration are discussed and determined. In this study, the monitored and the recorded ground vibrations are evaluated from structural damage potential and human disturbance points of views. It is determined that the ground vibration levels recorded during this study and analyzed from the past records comply with Turkish and US Federal regulations. It is concluded that no damage has been occurred in structures at surrounding settlements and the occupants were not disturbed by the direct effect of vibrations in the past and at present. The analysis proved that the blasting operations to be conducted in the future will not create any damage and disturbance provided that the charge detonated per delay is kept less than 155 kg&amp / #8217 / s.

Y&ouml / rg&uuml / &ccedil / village is within the close neighbourhood of the Western Lignite Corporation Y-3 panel. Although the nearest part of the mine is 1100 m and the farthest part is 2500 m from the village at present, some of the villagers complained about the ground vibration at the past. Therefore the assessment of damage risk and, if any, control and minimization of vibrations constitutes the aim and the scope of this research work. The researh work consists of monitoring of vibration, characterising of the seismic waves by full wave form analysis, and determination of magnitude and frequency of the waves from round blasting practice. Also dominant frequencies are determined, using single-hole blasting records by special software. The analyses are continued by a critical discussion and evaluation, and, proposals for new firing methods are made. The proposed firing methods are validated by further monitoring. As a result the best blasting practice was selected and offered to control and minimize the ground vibration.

Orientadores: Joerg Schleicher, Amelia Novais / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T03:30:50Z (GMT). No. of bitstreams: 1 Munerato_FernandoPerin_M.pdf: 1553622 bytes, checksum: 5cb80dbf31a93da9d201b78855292dfc (MD5) Previous issue date: 2006 / Resumo: Este trabalho aborda a questão de como resolver a equação da onda imagem para o problema de remigração na profundidade através de métodos numéricos. O objetivo deste problema é a reconstrução de uma imagem das camadas geológicas do subsolo a partir de uma imagem previamente migrada com um modelo de velocidade, geralmente, incorreto. Nosso principal objetivo neste trabalho é a investigação de possíveis métodos que possam resolver os problemas que surgiram ao usarmos esquemas explícitos do método de diferenças _nitas na solução da equação da onda imagem em trabalhos anteriores, como, por exemplo, a dispersão numérica. Para isso, estudamos aqui o método de volumes _nitos, assim como esquemas implícitos do método de diferenças _nitas. O método de volumes _nitos possui como característica principal propagar as médias das células da malha ao invés de simplesmente os dados pontuais como é feito no método de diferenças _nitas. As outras tentativas para solucionar o problema da dispersão foram dois tipos de implementação de esquemas implícitos do método de diferenças _nitas, isto é, implementações implícitas de esquemas convencionais avaliados em pontos da malha e um esquema avaliado nos centros das células. A qualidade dos algoritmos estudados foi testada numericamente. Estes testes numéricos mostram que o método de volumes _nitos não é adequado para resolver o problema da dispersão, uma vez que a média calculada a cada passo aumenta o estiramento do pulso. Além disso, as implementações implícitas dos esquemas convencionais mostram o mesmo comportamento de dispersão que as implementações explícitas. Unicamente o esquema centrado foi capaz de melhorar a dispersão numérica em comparação com as implementações anteriores,porém somente para dados contendo exclusivamente baixas freqüências / Abstract: This work approaches the question of how to solve the image-wave equation for depth remigration by numerical methods. The objective is the reconstruction of an image of the geologic layers of the subsoil from a previously migrated image with a different velocity model. Our main objective in this work is the investigation of possible methods that can solve the problems that appeared when using explicit _nite-difference schemes for the solution of the image-wave equation in previous works, particularly numerical dispersion. For this purpose, we study the method of _nite volumes, as well as implicit _nite-difference schemes. The main characteristic of the _nite-volume method is to simply propagate the averages in the cells of the mesh instead of the discretized data themselves as it is done in the _nitedifference method. As another attempt to solve the problem of the dispersion, we study two types of implementation of implicit _nite-difference schemes, that is, implicit implementations of conventional schemes evaluated out the edge of the cell and a scheme evaluated in the center of the cell. The quality of the studied algoritms has been tested numerically. These numerical tests show that the method of _nite volumes is not adequate to solve the problem of dispersion, for the average calculated in each step additionally increases the pulse stretch. Moreover, the implicit implementations of the conventional schemes show the same dispersion behavior as the explicit implementations. Solely the centered scheme was capable to improve the numerical dispersion in comparison with the previous implementations, however only for data containing / Mestrado / Geofisica Computacional / Mestre em Matemática Aplicada

Les modèles géologiques numériques 2D et 3D permettent de comprendre l'organisation spatiale des roches du sous-sol. Ils sont également conçus pour réaliser des simulations numériques afin d’étudier ou de prédire le comportement physique du sous-sol. Pour résoudre les équations qui gouvernent les phénomènes physiques, les structures internes des modèles géologiques peuvent être discrétisées spatialement à l’aide de maillages. Cependant, la qualité des maillages peut être considérablement altérée à cause de l’inadéquation entre, d’une part, la géométrie et la connectivité des objets géologiques à représenter et, d’autre part, les contraintes requises sur le nombre, la forme et la taille des éléments des maillages. Dans ce cas, il est souhaitable de modifier un modèle géologique afin de pouvoir générer des maillages de bonne qualité permettant la réalisation de simulations physiques fidèles en un temps raisonnable. Dans cette thèse, j’ai développé des stratégies de réparation et de simplification de modèles géologiques 2D dans le but de faciliter la génération de maillages et la simulation de processus physiques sur ces modèles. Je propose des outils permettant de détecter les éléments des modèles qui ne respectent pas le niveau de détail et les prérequis de validité spécifiés. Je présente une méthode pour réparer et simplifier des coupes géologiques de manière locale, limitant ainsi l’extension des modifications. Cette méthode fait appel à des opérations d’édition de la géométrie et de la connectivité des entités constitutives des modèles géologiques. Deux stratégies sont ainsi explorées : modifications géométriques (élargissements locaux de l'épaisseur des couches) et modifications topologiques (suppressions de petites composantes et fusions locales de couches fines). Ces opérations d’édition produisent un modèle sur lequel il est possible de générer un maillage et de réaliser des simulations numériques plus rapidement. Cependant, la simplification des modèles géologiques conduit inévitablement à la modification des résultats des simulations numériques. Afin de comparer les avantages et les inconvénients des simplifications de modèles sur la réalisation de simulations physiques, je présente trois exemples d'application de cette méthode : (1) la simulation de la propagation d'ondes sismiques sur une coupe au sein du bassin houiller lorrain, (2) l’évaluation des effets de site liés à l'amplification des ondes sismiques dans le bassin de la basse vallée du Var, et (3) la simulation d'écoulements fluides dans un milieu poreux fracturé. Je montre ainsi (1) qu'il est possible d’utiliser les paramètres physiques des simulations, la résolution sismique par exemple, pour contraindre la magnitude des simplifications et limiter leur impact sur les simulations numériques, (2) que ma méthode de simplification de modèles permet de réduire drastiquement le temps de calcul de simulations numériques (jusqu’à un facteur 55 sur une coupe 2D dans le cas de l’étude des effets de site) tout en conservant des réponses physiques équivalentes, et (3) que les résultats de simulations numériques peuvent être modifiés en fonction de la stratégie de simplification employée (en particulier, la modification de la connectivité d’un réseau de fractures peut modifier les écoulements fluides et ainsi surestimer ou sous-estimer la quantité des ressources produites). / Numerical geological models help to understand the spatial organization of the subsurface. They are also designed to perform numerical simulations to study or predict the rocks physical behavior. The internal structures of geological models are commonly discretized using meshes to solve the physical governing equations. The quality of the meshes can be, however, considerably degraded due to the mismatch between, on the one hand, the geometry and the connectivity of the geological objects to be discretized and, on the other hand, the constraints imposed on number, shape and size of the mesh elements. As a consequence, it may be desirable to modify a geological model in order to generate good quality meshes that allow realization of reliable physical simulations in a reasonable amount of time. In this thesis, I developed strategies for repairing and simplifying 2D geological models, with the goal of easing mesh generation and simulation of physical processes on these models. I propose tools to detect model elements that do not meet the specified validity and level of detail requirements. I present a method to repair and simplify geological cross-sections locally, thus limiting the extension of modifications. This method uses operations to edit both the geometry and the connectivity of the geological model features. Two strategies are thus explored: geometric modifications (local enlargements of the layer thickness) and topological modifications (deletions of small components and local fusions of thin layers). These editing operations produce a model on which it is possible to generate a mesh and to realize numerical simulations more efficiently. But the simplifications of geological models inevitably lead to the modification of the numerical simulation results. To compare the advantages and disadvantages of model simplifications on the physical simulations, I present three applications of the method: (1) the simulation of seismic wave propagation on a cross-section within the Lorraine coal basin, (2) the site effects evaluation related to the seismic wave amplifications in the basin of the lower Var river valley, and (3) the simulation of fluid flows in a fractured porous medium. I show that (1) it is possible to use the physical simulation parameters, like the seismic resolution, to constrain the magnitude of the simplifications and to limit their impact on the numerical simulations, (2) my method of model simplification is able to drastically reduce the computation time of numerical simulations (up to a factor of 55 in the site effects case study) while preserving an equivalent physical response, and (3) the results of numerical simulations can be changed depending on the simplification strategy employed (in particular, changing the connectivity of a fracture network can lead to a modification of fluid flow paths and overestimation or underestimation of the quantity of produced resources).

Quantifying uncertainties in large-scale forward and inverse PDE simulations has emerged as a central challenge facing the field of computational science and engineering. The promise of modeling and simulation for prediction, design, and control cannot be fully realized unless uncertainties in models are rigorously quantified, since this uncertainty can potentially overwhelm the computed result. While statistical inverse problems can be solved today for smaller models with a handful of uncertain parameters, this task is computationally intractable using contemporary algorithms for complex systems characterized by large-scale simulations and high-dimensional parameter spaces. In this dissertation, I address issues regarding the theoretical formulation, numerical approximation, and algorithms for solution of infinite-dimensional Bayesian statistical inverse problems, and apply the entire framework to a problem in global seismic wave propagation. Classical (deterministic) approaches to solving inverse problems attempt to recover the “best-fit” parameters that match given observation data, as measured in a particular metric. In the statistical inverse problem, we go one step further to return not only a point estimate of the best medium properties, but also a complete statistical description of the uncertain parameters. The result is a posterior probability distribution that describes our state of knowledge after learning from the available data, and provides a complete description of parameter uncertainty. In this dissertation, a computational framework for such problems is described that wraps around the existing forward solvers, as long as they are appropriately equipped, for a given physical problem. Then a collection of tools, insights and numerical methods may be applied to solve the problem, and interrogate the resulting posterior distribution, which describes our final state of knowledge. We demonstrate the framework with numerical examples, including inference of a heterogeneous compressional wavespeed field for a problem in global seismic wave propagation with 10⁶ parameters.