Ground-based weather radars provide information on the temporal evolution and the spatial distribution of precipitation on a macroscopic scale over a large area. However, the echoes measured by weather radars are always a superposition of forward and backward scattering effects which complicates their interpretation. The use of polarisation diversity enhances the number of independent observables measured simultaneously. This allows an effective separation of forward and backward scattering effects. Furthermore, it extends the capability of weather radars to retrieve also microphysical information about the precipitation. The dissertation at hand introduces new aspects in the field of polarimetric, ground-based, monostatic weather radars at S-, C-, and X-band. Relations are provided to change the polarisation basis of reflectivities. A fully polarimetric weather radar measurement at circular polarisation basis is analysed. Methods to check operationally the polarimetric calibration of weather radars operating at circular polarisation basis are introduced. Moreover, attenuation correction methods for weather radar measurements at linear horizontal / vertical polarisation basis are compared to each other, and the robustly working methods are identified. / Bodengebundene Wetterradare bieten Informationen über die zeitliche Entwicklung und die räumliche Verteilung von Niederschlag in einer makroskopischen Skala über eine große Fläche. Die Interpretation der Wetterradarechos wird erschwert, da sie sich aus einer Überlagerung von Vorwärts- und Rückwärtsstreueffekten ergeben. Die Anzahl der unabhängigen Wetterradarmessgrößen kann durch den Einsatz von Polarisationsdiversität erhöht werden. Dies ermöglicht eine effektive Trennung von Vorwärts- und Rückwärtsstreueffekten. Desweiteren erlaubt es die Bestimmung von mikrophysikalischen Niederschlagsparametern. Die vorliegende Dissertation betrachtet neue Aspekte für polarimetrische, bodengebundene, monostatische Wetterradare im S-, C- und X-Band. Gleichungen zur Polarisationsbasistransformation von Reflektivitätsmessungen werden eingeführt. Eine vollpolarimetrische Wetterradarmessung in zirkularer Polarisationsbasis wird analysiert. Neue Methoden, die eine Überprüfung der polarimetrischen Kalibrierung von Wetterradarmessungen in zirkularer Polarisationsbasis erlauben, werden betrachtet. Weiterhin werden Methoden zur Dämpfungskorrektur von Wetterradarmessungen in linearer horizontaler / vertikaler Polarisationsbasis miteinander verglichen und Empfehlungen von zuverlässigen Methoden gegeben.

Temporal changes of seismic velocity and anisotropy in the shallow crust are quantified using local earthquakes recorded at a 200-m-deep borehole station CHY in Taiwan. This station is located directly above the hypocenter of the 10/22/1999, M6.4 Chia-Yi earthquake. Three-component seismograms recorded at this station show clear direct (up-going) and surface-reflected (down-going) P- and S-waves, and S-wave splitting signals. The two-way travel times in the top 200 m is obtained by measuring the time delays between the up-going and down-going waves in the auto-correlation function. The S-wave travel times measured in two horizontal components increase by ~1-2% at the time of Chia-Yi main shock, and followed by a logarithmic recovery, while the temporal changes of S-wave splitting and P-wave are less than 1% and are not statistically significant. We obtain similar results by grouping earthquakes into clusters according to their locations and waveform similarities. This suggests that the observed temporal changes are not very sensitive to the seismic ray path below CHY, but are mostly controlled by the variation of material property in the top 200 m of the crust. We propose that strong ground motions of the Chia-Yi main shock cause transient openings of fluid-filled microcracks and increases the porosity in the near-surface layers, followed by a relatively long healing process. Because we observe no clear changes in the shear wave anisotropy, we infer that the co-seismic damages do not have a preferred orientation. Our results also show a gradual increase of time delays for both the fast and slow S-waves in the previous 7 years before the Chia-Yi main shock. Such changes might be caused by variations of water table, sediment packing or other surficial processes.

Gravity waves have a significant dynamic effect in the mesosphere. In particular, they drive the mesospheric circulation and are the reason that the summer polar mesosphere is cooler than the winter polar mesosphere. This thesis examines whether the effects of gravity waves are largely determined by filtering effects which allow only gravity waves with certain properties to propagate into the atmosphere. The filtering of gravity waves above Scott Base, Antarctica is examined using a radiosonde derived gravity wave source function, an MF-radar derived mesospheric gravity wave climatology, and a model derived filtering function. Least squares fitting of the source function and filtering function to the observed mesospheric gravity wave climatology allows us to determine which gravity wave phase velocities and propagation direction are likely to be present in the mesosphere and the relative importance of filtering and sources in this region. It is concluded the blocking of eastward gravity waves is important in winter and westward waves in summer.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, December 2004. / Thesis advisor(s): David C. Jenn. Includes bibliographical references (p. 93-94). Also available online.

Leakage and blockage of oil and gas pipeline systems, water pipelines, pipe-work of process plants and other pipe networks can cause serious environmental, health and economic problems. There are a number of non-destructive testing (NDT) methods for detecting these defects in pipeline systems such as radiographic, ultrasonic, magnetic particle inspection, pressure transient and acoustic wave methods. In this study, the acoustic wave method and a modal frequency technique, which based on a roving mass method, are used. The aim of the thesis is to employ acoustic wave propagation based methods in conjunction with stationary wavelet transform (SWT) to identify leakage and blockage in pipe systems. Moreover, the research is also aimed at using the difference of modal frequencies of fluid-filled pipes with and without defects and a roving mass, and consequently, to develop a roving mass-based defect detection method for pipelines. In the study, the acoustic finite-element analysis (AFEA) method is employed to simulate acoustic wave propagation in small and large air-filled water-filled straight pipe and pipe networks with leakage and blockage but without flow. Computational fluid dynamics (CFD) analysis was also employed to simulate acoustic wave propagation in air-and water-filled pipes with flow, leakage and blockage. In addition, AFEA was used to predict the modal frequencies of air- and water-filled pipes with leakage and blockage in the presence of a roving mass that was traversed along the axis of the pipes. Experimental testing was conducted to validate some of the numerical results. Two major experiments were performed. The first set of experiments consisted of the measurement of acoustic wave propagation in a straight air-filled pipe with leakage and blockage. The second set of experiments concerned the measurement of acoustic wave propagation in an air-filled pipe network comprising straight pipe, elbows and T-piece and flange. The AFEA and CFD analysis of fluid-filled pipe can be used to simulate the acoustic wave propagation and acoustic wave reflectometry of a fluid-filled pipe with leakage and blockage of different sizes down to a small leakage size of 1mm diameter and a blockage depth of 1.2mm in a pipe. Similarly, the AFEA method of a static fluid-filled pipe can be used to simulate acoustic wave modal frequency analysis of a fluid-filled pipe with leakage and blockage of different sizes down to a leakage of 1mm diameter and a blockage depth of 1.2mm. Moreover, the measured signal of acoustic wave propagation in an air-filled can be successfully decomposed and de-noised using the SWT method to identify and locate leakages of different sizes down to 5mm diameter, and small blockage depth of 1.2mm. Also, the SWT approximation coefficient, detail and de-noised detail coefficient curves of an air-filled pipe with leakage and blockage and a roving mass give leakage and blockage indications that can be used to identify, locate and estimate the size of leakage and blockage in a pipe.

La résolution de l'équation des ondes acoustiques et élastiques en 3D dans le domaine fréquentiel représente un enjeu majeur dans le cadre de l'inversion des formes d'ondes pour l'imagerie haute résolution de cibles crustales (Virieux, 2009). Après discrétisation, ce problème revient à résoudre un système linéaire à valeurs complexes, creux, de grande taille non défini et mal conditionné. Les méthodes d'inversion sismique requièrent la solution de ce problème pour l'évaluation du problème direct pour un grand nombre de sources (plusieurs milliers voir dizaines de milliers). Dans l'approximation acoustique, les méthodes directes sont privilégiées. Cependant, le coût mémoire de ces méthodes les rendent aujourd'hui inutilisables pour résoudre les problèmes élastiques 3D. En raison de leur plus faible coût mémoire, les méthodes itératives pour les équations en fréquence peuvent être considérées pour l'élastodynamique. Cependant, une convergence rapide passe par des préconditionneurs adaptés pour les solveurs itératifs. Par ailleurs, les stratégies pour résoudre des systèmes linéaires avec des seconds membres multiples ne sont pas aussi efficaces que pour les méthodes directes. La modélisation dans le domaine temporelle quant à elle présente une importante complexité en coût de calcul et cette complexité croît linéairement avec le nombre de sources.Dans cette thèse, l'approche utilisant un solveur itératif est considérée. Le solveur itératif CARP-CG introduit par Gordon (2010) est considéré. Cette méthode est basée sur la méthode de Kaczmarz qui transforme un système linéaire mal conditionné en un système hermitien, positif et qui peut être résolu en utilisant les méthodes du type gradient conjugué (CG). Dans des configurations de forts contrastes et hétérogénéités, ce solveur s'est révélé être extrêmement robuste alors que les méthodes itératives standards basées sur les sous-espaces de Krylov telles que GMRES et BiCGSTAB nécessitent l'utilisation d'un préconditionneur pour converger (Li, 2015). Malgré les bonnes propriétés de la méthode CARP-CG, le nombre d'itérations nécessaires pour atteindre une précision suffisante reste néanmoins élevé. Je présente alors une stratégie de préconditionnement adaptée au problème de propagation des ondes et à la méthode CARP-CG. Ce préconditionneur est un inverse creux et approché d'un opérateur de propagation des ondes fortement amorti. Le calcul du préconditionneur est réalisé grâce un algorithme massivement parallèle pour les architectures à mémoire distribuée.La méthode développée est appliquée à des cas d'étude réalistes. Les applications sont faites sur des modèles synthétiques 2D dans l'approximation visco-acoustique pour des fréquences allant jusqu'à 40 Hz puis dans l'approximation élastique pour des fréquences allant jusqu'à 20 Hz. Ces études montrent l'efficacité de la méthode CARP-CG munie de la stratégie de préconditionnement. Le nombre d'itérations est fortement réduit (jusqu'à un facteur 9) permettant d'améliorer considérablement la complexité de la méthode CARP-CG. Des gains en temps de calcul allant jusqu'à un facteur 3.5 sont ainsi obtenus. La méthode est ensuite appliquée à un cas 3D synthétique et réaliste dans l'approximation visco-élastique pour des fréquences allant de 1.25 Hz à 7.5 Hz. Des résultats encourageants sont obtenus. Munie du préconditioneur, la méthode CARP-CG permet de résoudre ces systèmes linéaires deux fois plus rapidement.La stratégie de préconditionnement implique la nécessité de plus grandes ressources en mémoire pour le solveur itératif; cependant, elles ne constituent pas une limitation pour la méthode et restent très négligeables devant celles requises par les solveurs directs. La principale limitation réside dans le temps de calcul qui demeure assez significatif. Cependant, cette méthode constitue un solveur compétitif comparé aux autres solveurs en temps et direct utilisés aujourd'hui dans le cadre de l'inversion des formes d'ondes. / A robust and efficient wave modeling method is the cornerstone of high resolution seismic inversion methods such as the frequency-domain Full Waveform Inversion (Virieux, 2009). After discretization, frequency-domain wave modeling amounts to the solution of large (up to several billion of unknowns for realistic case studies), sparse, indefinite and ill-conditioned linear systems. Furthermore, seismic inversion methods require the solution of this problem for numerous sources (from several thousands up to tens of thousands). In the acoustic approximation, 3D real case studies can be handled efficiently using direct solvers. However because of their tremendous intrinsic memory requirements, they are not yet adapted to the solution of the 3D elastodynamics equations. Iterative solvers provide an alternative to direct solvers. However, they require a preconditioning strategy to ensure convergence for the frequency-domain wave equation. Besides, multiple right-hand sides linear systems are not treated as efficiently as direct solvers do.In this thesis, we are interested in the use of a robust iterative solver adapted to the solution of these systems called CARP-CG (Gordon, 2010). The CARP-CG method has shown robust convergence properties for 2D and 3D elastic problems in highly heterogeneous media compared to standard Krylov methods such as GMRES or Bi-CGSTAB which require the use of a preconditioner to ensure convergence (Li, 2015). Despite the good convergence properties of CARP-CG, the latter still requires a large number of iterations to reach sufficient accuracy. I introduce an efficient preconditioning strategy adapted to the CARP-CG method and the frequency-domain wave problem. This preconditioner is computed as a sparse approximate inverse of a strongly damped wave propagation operator. The computation of the preconditioner is performed in a massively parallel algorithm for distributed memory architectures.The efficiency of the preconditioner is evaluated on several case studies. First, applications are performed on realistic synthetic models in the 2D visco-acoustic approximation (up to $40$ Hz) and the 2D visco-elastic approximation (up to $20$ Hz). These studies show that the CARP-CG method together with the preconditioning strategy is robust and efficient. The number of iterations is significantly reduced (up to a factor $9$) enabling a speedup in the computation time by a factor up to $3.5$. Second, this method is investigated in the 3D elastic approximation on a realistic synthetic case study on the range of frequencies 1.25 to 7.5 Hz. Very encouraging results are obtained with a significant reduction in the number of iterations. A slow increase of the number of iterations with respect to the frequency is noted.This preconditioning strategy adapted to the CARP-CG method implies larger memory requirements. However, this extra memory cost remains one order lower compared to direct solver memory requirement, and should be affordable on standard HPC facilities. The main bottleneck preventing from the possible use of this iterative solver for 3D elastic FWI remains the computation time for the wave equation solves.

Este trabalho trata da simulação da propagação de ondas eletromagnéticas (1-D) em meios geológicos de propriedades físicas conhecidas (espessura, condutividade e permissividade elétrica), do registro das ondas EM refletidas (dados sintéticos) para uma antena receptora, e do uso desse registro em algoritmos de inversão e otimização que procuram estimar as propriedades físicas dos meios geológicos. Adotou-se modelos geológicos estratificados de pequena espessura (< 1,2 m) e altas frequências para a onda eletromagnética (800, 1000 e 1200 MHz). A propagação da onda eletromagnética é modelada por meio da resolução das equações de Maxwell no método FDTD. Os métodos de inversão Quasi-Newton e Otimização Ant Colony modificado são aplicados sobre os dados sintéticos para estimar os parâmetros elétricos para cada camada geológica. Ambos os métodos foram aplicados alternadamente para aumentar a precisão e a convergência ao longo da profundidade. Os métodos de inversão foram capazes de estimar simultaneamente duas propriedades eletromagnéticas do modelo geológico: a permissividade elétrica e a condutividade elétrica. Os métodos de inversão alcançaram bons resultados quando executados simultaneamente sobre os dados sintéticos em 3 diferentes frequências. Exemplos de estimativas dos perfis de condutividade e permissividade elétricas unidimensionais são apresentados, com e sem inserção de ruídos nos dados. Os resultados indicam que a combinação dos métodos de inversão (ACO modificado e Quasi-Newton) pode fornecer bons resultados para as estimativas dos parâmetros físicos de meios geológicos e geotécnicos em meios rasos. Além disso, essa combinação de métodos de inversão abre novas perspectivas para o processamento de dados georradar multi-canais. As investigações também mostram que a simulação dos perfis sintéticos por meio do método FDTD pode propagar erros em espessuras maiores de subsolo, devido ao fato de ser um método explícito. / This work deals with simulation of a 1-D electromagnetic wave propagating into a geological structure of known physical properties (thickness, electric conductivity and permittivity), the record of the reflected EM wave (synthetic data), and the use of these records in inversion and optimization algorithms to estimate back the physical properties of the geological structure. A stratified and thin (< 1.2 m) geological structure was initially constructed in order to be scanned by high frequency EM waves (800, 1000, and 1200 MHz). The EM wave propagation is simulated by Maxwell equations through FDTD method. The Quasi-Newton inversion and Ant Colony Optimization methods were applied into synthetic data to estimate original physical parameters of each geological layer. Both methods were applied in order to increase precision and convergence along depth. These methods were able to simultaneously estimate two physical properties of the geological structure: electrical permittivity and conductivity. The methods showed good results when applied simultaneously upon synthetic data of all three frequencies. Electric permittivity and conductivity profiles are shown with and without noise in the data. The results indicate that combined inversion methods can show good results to estimate physical properties of thin geological and geothecnical structures. The combined inversion methods open new perspectives to multichannel GPR data processing. The investigations also show that simulation of synthetic data through FDTD can propagate errors when dealing with thick geological structures, due to the fact that FDTD is an explicit method.

Este trabalho trata da simulação da propagação de ondas eletromagnéticas (1-D) em meios geológicos de propriedades físicas conhecidas (espessura, condutividade e permissividade elétrica), do registro das ondas EM refletidas (dados sintéticos) para uma antena receptora, e do uso desse registro em algoritmos de inversão e otimização que procuram estimar as propriedades físicas dos meios geológicos. Adotou-se modelos geológicos estratificados de pequena espessura (< 1,2 m) e altas frequências para a onda eletromagnética (800, 1000 e 1200 MHz). A propagação da onda eletromagnética é modelada por meio da resolução das equações de Maxwell no método FDTD. Os métodos de inversão Quasi-Newton e Otimização Ant Colony modificado são aplicados sobre os dados sintéticos para estimar os parâmetros elétricos para cada camada geológica. Ambos os métodos foram aplicados alternadamente para aumentar a precisão e a convergência ao longo da profundidade. Os métodos de inversão foram capazes de estimar simultaneamente duas propriedades eletromagnéticas do modelo geológico: a permissividade elétrica e a condutividade elétrica. Os métodos de inversão alcançaram bons resultados quando executados simultaneamente sobre os dados sintéticos em 3 diferentes frequências. Exemplos de estimativas dos perfis de condutividade e permissividade elétricas unidimensionais são apresentados, com e sem inserção de ruídos nos dados. Os resultados indicam que a combinação dos métodos de inversão (ACO modificado e Quasi-Newton) pode fornecer bons resultados para as estimativas dos parâmetros físicos de meios geológicos e geotécnicos em meios rasos. Além disso, essa combinação de métodos de inversão abre novas perspectivas para o processamento de dados georradar multi-canais. As investigações também mostram que a simulação dos perfis sintéticos por meio do método FDTD pode propagar erros em espessuras maiores de subsolo, devido ao fato de ser um método explícito. / This work deals with simulation of a 1-D electromagnetic wave propagating into a geological structure of known physical properties (thickness, electric conductivity and permittivity), the record of the reflected EM wave (synthetic data), and the use of these records in inversion and optimization algorithms to estimate back the physical properties of the geological structure. A stratified and thin (< 1.2 m) geological structure was initially constructed in order to be scanned by high frequency EM waves (800, 1000, and 1200 MHz). The EM wave propagation is simulated by Maxwell equations through FDTD method. The Quasi-Newton inversion and Ant Colony Optimization methods were applied into synthetic data to estimate original physical parameters of each geological layer. Both methods were applied in order to increase precision and convergence along depth. These methods were able to simultaneously estimate two physical properties of the geological structure: electrical permittivity and conductivity. The methods showed good results when applied simultaneously upon synthetic data of all three frequencies. Electric permittivity and conductivity profiles are shown with and without noise in the data. The results indicate that combined inversion methods can show good results to estimate physical properties of thin geological and geothecnical structures. The combined inversion methods open new perspectives to multichannel GPR data processing. The investigations also show that simulation of synthetic data through FDTD can propagate errors when dealing with thick geological structures, due to the fact that FDTD is an explicit method.

abstract: In order to verify the dispersive nature of transverse displacement in a beam, a deep understanding of the governing partial differential equation is developed. Using the finite element method and Newmark’s method, along with Fourier transforms and other methods, the aim is to obtain consistent results across each numerical technique. An analytical solution is also analyzed for the Euler-Bernoulli beam in order to gain confidence in the numerical techniques when used for more advance beam theories that do not have a known analytical solution. Three different beam theories are analyzed in this report: The Euler-Bernoulli beam theory, Rayleigh beam theory and Timoshenko beam theory. A comparison of the results show the difference between each theory and the advantages of using a more advanced beam theory for higher frequency vibrations. / Dissertation/Thesis / Masters Thesis Civil Engineering 2016

Des panneaux sandwichs en nid d'abeilles sont largement utilisés, notamment dans l’industrie aérospatiale et aéronautique, à cause du très bon rapport entre rigidité en flexion et poids. Concernant leur modélisation, ils sont considérés classiquement comme de milieux homogénéisés équivalents afin d'éviter des modèles numériques prohibitifs en coûts de calculs. Cependant, des travaux précédents ont montré que, si le comportement dynamique en membrane des sandwichs peut être correctement représenté par des modèles homogénéisés classiques dans une large gamme de fréquences, ces mêmes modèles ne permettent malheureusement pas de bien décrire le comportement en flexion dans le domaine de hautes fréquences (HF). En effet, la couche centrale en nid d'abeilles joue un rôle important dans le comportement en flexion du sandwich, il est donc indispensable de la modéliser de manière appropriée. Or, lorsque les longueurs d’onde impliquées deviennent aussi petites que les longueurs caractéristiques des cellules du nid d’abeilles, cette microstructure cellulaire interagit fortement avec les ondes et génère des effets d’interaction non négligeables, qui ne sont malheureusement pas pris en compte par des modèles homogénéisés classiques. Dans le cadre de cette thèse, on s’intéresse donc à l'amélioration de l’analyse théorique et numérique de la propagation d’ondes élastiques HF dans ces panneaux composites. On exploite les caractéristiques périodiques du nid d'abeilles en utilisant sur une approche numérique basée sur la théorie des ondes de Bloch. En effet, en décomposant des solutions non périodiques sur une base composée de modes périodiques de Bloch, il est possible de développer des modèles numériques, qui considèrent des phénomènes de propagation des ondes à l’intérieur d’une seule cellule de base et captent toutes les interactions. Ces modèles numériques sont donc de taille raisonnable, par rapport aux dimensions souvent très importantes des structures industrielles. Des analyses théoriques et des outils de modélisation ont été développés pour des milieux périodiques composés de structures minces : poutres ou plaques. Notre approche a été développée et validée pour des structures périodiques uni- puis bi-dimensionnelles composées de poutres. Pour les cas 2D, la forme de la cellule est hexagonale ou rectangulaire. Nous avons aussi considéré des plaques sandwichs en nid d’abeilles. Pour toutes ces structures, en identifiant les valeurs propres et les modes propres de Bloch sur une cellule primitive pour tous les vecteurs d’onde de Bloch situés dans la première zone de Brillouin dans l’espace de phase, la relation de dispersion entre le vecteur d'onde de Bloch et la valeur propre est calculée. En analysant cette relation de dispersion, les résultats importants sont obtenus, tels que les bandes de fréquences passantes et bloquantes et les caractéristiques d'anisotropie et dispersives des structures périodiques, la comparaison quantitative entre les premiers modes de Bloch et ceux des modèles homogénéisés classiques en vue d’une définition précise du domaine validation en fréquence de ceux-derniers et la mise en évidence des modes de Bloch « rétro-propagatifs » munis d’une vitesse de groupe négative. / Honeycomb core sandwich panels are widely used in the aeronautic industry due to their excellent flexural stiffness to weight ratio. Generally, classical homogenized model is used to model honeycomb core sandwiches in order to have an efficient but not expensive numerical modeling. However, previous works have shown that, while the homogenized models could correctly represent the membrane waves’ behavior of sandwiches in a large frequency range, they could not give satisfying simulation results for the flexural waves’ behavior in the high frequency range (HF). In fact, the honeycomb core layer plays an important role in the propagation of the flexural waves, so that when the involved wavelengths become close to the characteristic lengths of honeycomb cells, the cellular microstructure starts interacting strongly with the waves and its effect should no longer be neglected, which is unfortunately not the case of the homogenized models. In the present work, we are interested in improving the theoretical and numerical analysis of HF elastic waves’ propagation in honeycomb core sandwich panels by a numerical approach based on the Bloch wave theorem, which allows taking into account the periodic characteristics of the honeycomb core. In fact, by decomposing non-periodic wave solutions into their periodic Bloch wave basis modes, numerical models are defined on a basic cell and solved in a efficient way, and provide a better description and so a better understanding of the interaction between HF wave propagation phenomena and the periodic structures. Our numerical approach is developed and validated in the cases of one-dimensional periodic beam structures, of two-dimensional periodic hexagonal and rectangular beam structures and of honeycomb core sandwich plates. By solving the eigenvalue problem of the Bloch wave modes in one primitive cell of the periodic structure for all the wave vectors located in the corresponding first Brillouin zone in the phase space, the dispersion relation between the wave vector and the eigenvalue is calculated. The analysis of the dispersion relation provides important results such as: the frequency bandgaps and the anisotropic and dispersive characteristics of periodic structures, the comparison between the first Bloch wave modes to those of the classical equivalent homogenized models and the existence of the retro-propagating Bloch wave modes with a negative group velocity.