Zugl.: Kassel, Univ., Diss., 2008

Universiẗat, Diss., 2003--Freiburg (Breisgau).

Würzburg, Univ., Diss., 2009. / Zsfassung in dt. Sprache.

This study is concerned with the computation of seismic first-arrival traveltimes in anisotropic media using finite difference eikonal methods. For this purpose, different numerical schemes that directly solve the eikonal equation are implemented and assessed numerically. Subsequently, they are used for pre-stack depth migration on synthetic and field data. The thesis starts with a detailed examination of different finite difference methods that have gained popularity in scientific literature for computing seismic traveltimes in isotropic media. The most appropriate for an extension towards anisotropic media are found to be the so-called Fast Marching/Sweeping methods. Both schemes rely on different iteration strategies, but incorporate the same upwind finite difference Godunov schemes that are implemented up to the second order. As a result, the derived methods exhibit high numerical accuracy and perform robustly even in highly contrasted velocity models. Subsequently, the methods are adapted for transversely isotropic media with vertical (VTI) and tilted (TTI) symmetry axes, respectively. Therefore, two different formulations for approximating the anisotropic phase velocities are tested, which are the weakly-anisotropic and the pseudo-acoustic approximation. As expected, the pseudo-acoustic formulation shows superior accuracy especially for strongly anisotropic media. Moreover, it turns out that the tested eikonal schemes are generally more accurate than anisotropic ray tracing approaches, since they do not require an approximation of the group velocity. Numerical experiments are carried out on homogeneous models with varying strengths of anisotropy and the industrial BP 2007 benchmark model. They show that the computed eikonal traveltimes are in good agreement with independent results from finite difference modelling of the isotropic and anisotropic elastic wave equations, and traveltimes estimated by ray-based wavefront construction, respectively. The computational performance of the TI eikonal schemes is largely increased compared to their original isotropic implementations, which is due to the algebraic complexity of the anisotropic phase velocity formulations. At this point, the Fast Marching Method is found to be more efficient on models containing up to 50 million grid points. For larger models, the anisotropic Fast Sweeping implementation gradually becomes advantageous. Here, both techniques perform independently well of the structural complexity of the underlying velocity model. The final step of this thesis is the application of the developed eikonal schemes in pre-stack depth migration. A synthetic experiment over a VTI/TTI layer-cake model demonstrates that the traveltime computation leads to accurate imaging results including a tilted, strongly anisotropic shale layer. The experiment shows further that the estimation of anisotropic velocity models solely from surface reflection data is highly ambiguous. In a second example, the eikonal solvers are applied for depth imaging of two-dimensional field data that were acquired for geothermal exploration in southern Tuscany, Italy. The developed methods also produce clear imaging results in this setting, which illustrates their general applicability for pre-stack depth imaging, particularly in challenging environments.

Perovskit-Oxide weisen eine große Bandbreite an physikalischen Eigenschaften bei gleichzeitig hoher struktureller Qualität in kleinsten Dimensionen auf. Die dramatischen Veränderungen ihrer Eigenschaften bei nur geringer Variation der stöchiometrischen Zusammensetzung sind sowohl für ein tieferes physikalisches Verständnis als auch für mögliche Anwendungsperspektiven interessant. In der vorliegenden Arbeit wurde der Einfluss von Ladungsübertragung an Grenz- flächen, Anisotropiemodifikation durch Verspannung und Oberflächeneffekte sowie magnetische und strukturelle Kopplung untersucht. Aufgrund ihrer kontrastierenden Eigenschaften im Hinblick auf Ferromagnetismus und Ladungstransport wurden dotiertes Lanthanmanganat und Strontiumruthenat (SRO) für die Untersuchungen ausgewählt. Durch ihre hervorragenden Wachstumseigenschaften mit fehlerlosen Grenzflächen auf atomarer Ebene erlauben sie als Modellsystem die Untersuchung elektronischer, magnetischer und struktureller Kopplung in Perovskit-Oxiden – mit folgenden Ergebnissen: Durch Ladungsübertragung an Grenzflächen wird Ferromagnetismus in Schichten von weniger als vier Einheitszellen in Manganaten stabilisiert. Die mikroskopische Struktur der Systeme kann aus der Analyse der durch die Anisotropie bedingten Symmetrie der winkelabhängigen Magnetotransport- messungen erschlossen werden. Bei abnehmender Schichtdicke verringert sich die intrinsische orthorhombische Symmetrie in SRO zugunsten einer tetragonalen aufgrund der Symmetriebrechung an der Grenzfläche. Die Untersuchungen des anormalen Hall Effekts unterstreichen seine Tensor-Natur und zeigen eine Abhängigkeit des Vorzeichens sowohl von der magnetischen Anisotropie als auch der mikroskopischen Schichtqualität. Die Beobachtung einer Anisotropie oberhalb der Übergangstemperatur von SRO in Manganatschichten einer Dicke von zwei bis sechs Einheitszellen weist auf eine strukturelle Kopplung über die Sauerstoffoktaederrotationen hin. Die komplexe Wechselwirkung zwischen antiferromagnetischer Kopplung und schichtdickenabhängiger Anisotropie und dem magnetischen Moment werden in einem 2-Schichten-Modell beschrieben. Übergitter mit Einzelschichten von weniger als drei Einheitszellen lassen sich nicht mehr mit individuellen Einzelschichten beschreiben sondern stellen einen künstlichen Ferrimagneten dar. / Perovskite oxides show a range of physical properties in combination with high structural quality in small dimensions. The dramatic change of their properties upon small variation in stoichiometry or external influences as pressure/strain are interesting for both a deeper understanding of fundamental condensed matter physics as well as electronic applications. In the present thesis the influence of charge transfer at interfaces, modification of the magnetic anisotropy by strain and surface effects, as well as magnetic and structural coupling was studied. In virtue of their contrasting ferromagnetic and transport properties, charge doped lanthanum manganite and strontium ruthenate (SRO) were chosen for this study. Their superior growth properties allowing atomically flat defect free interfaces make them a model system to study electronic magnetic and structural coupling phenomena in perovskite oxides − with the following findings: Charge transfer at interfaces stabilizes ferromagnetism in single layers of manganites down to one unit cell thickness similar to finite size scaling in ordinary transition metal ferromagnets. The microscopic structure of crystalline layers can be obtained from an analysis of the symmetries present in angle dependent magnetotransport measurements, which are determined by the anisotropy. Upon thickness reduction, the intrinsic orthorhombic symmetry in SRO is reduced in favour of a tetragonal one owing to the symmetry breaking at the interface. Studies on the anomalous Hall effect underline its tensorial nature and show a sign dependence on both magnetic anisotropy and microstructural quality. The observation of an in-plane anisotropy in manganite layers in the thickness range of two to six unit cells indicates a structural coupling via the oxygen octahedra. The complex interplay of antiferromagnetic coupling and layer thickness dependent anisotropy and magnetic moment are described in a bilayer model. Superlattices with individual layers of less than three unit cells cannot be described by the individual layer properties but represent an artificial ferrimagnet.

This study is concerned with the computation of seismic first-arrival traveltimes in anisotropic media using finite difference eikonal methods. For this purpose, different numerical schemes that directly solve the eikonal equation are implemented and assessed numerically. Subsequently, they are used for pre-stack depth migration on synthetic and field data. The thesis starts with a detailed examination of different finite difference methods that have gained popularity in scientific literature for computing seismic traveltimes in isotropic media. The most appropriate for an extension towards anisotropic media are found to be the so-called Fast Marching/Sweeping methods. Both schemes rely on different iteration strategies, but incorporate the same upwind finite difference Godunov schemes that are implemented up to the second order. As a result, the derived methods exhibit high numerical accuracy and perform robustly even in highly contrasted velocity models. Subsequently, the methods are adapted for transversely isotropic media with vertical (VTI) and tilted (TTI) symmetry axes, respectively. Therefore, two different formulations for approximating the anisotropic phase velocities are tested, which are the weakly-anisotropic and the pseudo-acoustic approximation. As expected, the pseudo-acoustic formulation shows superior accuracy especially for strongly anisotropic media. Moreover, it turns out that the tested eikonal schemes are generally more accurate than anisotropic ray tracing approaches, since they do not require an approximation of the group velocity. Numerical experiments are carried out on homogeneous models with varying strengths of anisotropy and the industrial BP 2007 benchmark model. They show that the computed eikonal traveltimes are in good agreement with independent results from finite difference modelling of the isotropic and anisotropic elastic wave equations, and traveltimes estimated by ray-based wavefront construction, respectively. The computational performance of the TI eikonal schemes is largely increased compared to their original isotropic implementations, which is due to the algebraic complexity of the anisotropic phase velocity formulations. At this point, the Fast Marching Method is found to be more efficient on models containing up to 50 million grid points. For larger models, the anisotropic Fast Sweeping implementation gradually becomes advantageous. Here, both techniques perform independently well of the structural complexity of the underlying velocity model. The final step of this thesis is the application of the developed eikonal schemes in pre-stack depth migration. A synthetic experiment over a VTI/TTI layer-cake model demonstrates that the traveltime computation leads to accurate imaging results including a tilted, strongly anisotropic shale layer. The experiment shows further that the estimation of anisotropic velocity models solely from surface reflection data is highly ambiguous. In a second example, the eikonal solvers are applied for depth imaging of two-dimensional field data that were acquired for geothermal exploration in southern Tuscany, Italy. The developed methods also produce clear imaging results in this setting, which illustrates their general applicability for pre-stack depth imaging, particularly in challenging environments.

The variation of rock strength and stiffness, known as mechanical anisotropy, is expected at different scales: large (rock mass) - or small (intact rock) - scales. It is always mandatory for engineering applications built either on or in anisotropic rock masses to investigate the strength and deformation behavior of those masses. To achieve this goal, continuum-based constitutive models are presented to analyze the mechanical anisotropy. One of both implemented models is named ‘Transubi model’ which considers the transverse isotropic elasticity into bi-linear Mohr-Coulomb strain hardening/softening plastic framework. Experimental investigations and numerical simulations focused mainly on the influence of the mechanical anisotropy on the plastic zoning around excavated openings in laminated rocks. Later, the Transubi model was applied to a tunnel excavated in a shaly facies formation of bedded argillaceous Opalinus clay in an URL (FE-tunnel) to obtain the short-term stability insights. Overall, the research outcomes may have a prospective impact regarding the understanding of anisotropy of laminated, bedded and foliated rocks which improves the deformation behaviour predictability using continuum-based numerical modeling tools.

In the early days of computer graphics, research was mainly driven by the goal to create realistic synthetic imagery. By contrast, non-photorealistic computer graphics, established as its own branch of computer graphics in the early 1990s, is mainly motivated by concepts and principles found in traditional art forms, such as painting, illustration, and graphic design, and it investigates concepts and techniques that abstract from reality using expressive, stylized, or illustrative rendering techniques. This thesis focuses on the artistic stylization of two-dimensional content and presents several novel automatic techniques for the creation of simplified stylistic illustrations from color images, video, and 3D renderings. Primary innovation of these novel techniques is that they utilize the smooth structure tensor as a simple and efficient way to obtain information about the local structure of an image. More specifically, this thesis contributes to knowledge in this field in the following ways. First, a comprehensive review of the structure tensor is provided. In particular, different methods for integrating the minor eigenvector field of the smoothed structure tensor are developed, and the superiority of the smoothed structure tensor over the popular edge tangent flow is demonstrated. Second, separable implementations of the popular bilateral and difference of Gaussians filters that adapt to the local structure are presented. These filters avoid artifacts while being computationally highly efficient. Taken together, both provide an effective way to create a cartoon-style effect. Third, a generalization of the Kuwahara filter is presented that avoids artifacts by adapting the shape, scale, and orientation of the filter to the local structure. This causes directional image features to be better preserved and emphasized, resulting in overall sharper edges and a more feature-abiding painterly effect. In addition to the single-scale variant, a multi-scale variant is presented, which is capable of performing a highly aggressive abstraction. Fourth, a technique that builds upon the idea of combining flow-guided smoothing with shock filtering is presented, allowing for an aggressive exaggeration and an emphasis of directional image features. All presented techniques are suitable for temporally coherent per-frame filtering of video or dynamic 3D renderings, without requiring expensive extra processing, such as optical flow. Moreover, they can be efficiently implemented to process content in real-time on a GPU. / In den Anfängen der Computergrafik war die Forschung hauptsächlich von dem Anspruch getragen, realistisch aussehende synthetische Bilder zu erstellen. Im Gegensatz dazu ist die nicht-photorealistische Computergraphik, ein Untergebiet der Computergrafik, welches in den frühen 1990er Jahren gegründet wurde, vor allem motiviert durch Konzepte und Prinzipien der traditionellen Kunst wie Malerei, Illustration und Grafikdesign. Diese Arbeit beschäftigt sich mit der künstlerischen Verarbeitung von zweidimensionalen Bildinhalten und präsentiert mehrere neue automatische Verfahren für die Erstellung von vereinfachten künstlerischen Darstellungen von Farbbildern, Videos und 3D- Renderings. Wichtigste Neuerung dieser Techniken ist die Verwendung des Strukturtensors als eine einfache und effiziente Möglichkeit, Informationen über die lokale Struktur eines Bildes zu erhalten. Konkret werden die folgenden Beiträge gemacht. Erstens wird eine umfassende übersicht über den Strukturtensor gegeben. Insbesondere werden verschiedene Methoden für die Integration des kleineren Eigenvektorfeldes des geglätteten Strukturtensors entwickelt, und die Überlegenheit des geglätteten Strukturtensors gegenüber dem populären Edge-Tangent-Flow demonstriert. Zweitens werden separable Implementierungen des bilateralen Filters und des Difference of Gaussians Filters vorgestellt. Durch die Anpassung der Filter an die lokale Struktur des Bildes werden Bildfehler vermieden, wobei der Vorgang rechnerisch effizient bleibt. Zusammengenommen bieten beide Techniken eine effektive Möglichkeit, um einen Cartoon-ähnlichen Effekt zu erzielen. Drittens wird eine Verallgemeinerung des Kuwahara-Filters vorgestellt. Durch die Anpassung von Form, Umfang und Orientierung der Filter an die lokale Struktur werden Bildfehler verhindert. Außerdem werden direktionale Bildmerkmale besser berücksichtigt und betont, was zu schärferen Kanten und einem malerischen Effekt führt. Neben der single-scale Variante wird auch eine multi-scale Variante vorgestellt, welche im Stande ist, eine höhere Abstraktion zu erzielen. Viertens wird eine Technik vorgestellt, die auf der Kombination von flussgesteuerter Glättung und Schock-Filterung beruht, was zu einer intensiven Verstärkung und Betonung der direktionalen Bildmerkmale führt. Alle vorgestellten Techniken erlauben die zeitlich kohärente Verarbeitung von Einzelbildern eines Videos oder einer dynamischen 3D-Szene, ohne dass andere aufwendige Verfahren wie zum Beispiel die Berechnung des optischen Flusses, benötigt werden. Darüberhinaus können die Techniken effizient implementiert werden und ermöglichen die Verarbeitung in Echtzeit auf einem Grafikprozessor (GPU).

Stoichiometric polyelectrolyte-surfactant complexes represent a type of comb-shaped polymers, in which every polymer chain unit has an electrostatically bound "side chain". These complexes are water-insoluble. In the solid state they assemble spontaneously into mesogenic structures. The [X,Y]-ionenes ([(CH2)XN+(CH3)2(CH2)YN+(CH3)2]nBr-2n) investigated formed stoichiometric complexes with alkyl sulfates. The ionene alkyl sulfate complexes display mesogenicity, i.e. optically isotropic dry complexes underwent lyotropic and thermotropic phase transitions to the optically anisotropic phase (and vice versa) under controlled relative humidity. The optically anisotropic phases exhibited hexagonal textures as revealed by polarizing microscopy. A new feature is the lyotropic transition brought about by the uptake of water through the gas phase. The complexes were all sensitive to both humidity and temperature. In principle, the effects can be applied to measure humidity.

The present work describes investigations on the anisotropic strength behavior of rocks in the splitting tensile test (Brazilian test). Three transversely isotropic rocks (gneiss, slate and sandstone) were studied in the Lab. A total of more than 550 indirect tensile strength tests were conducted, with emphasis was placed on the investigation of the influence of the spatial position of anisotropic weakness plane to the direction of the load on the fracture strength and fracture or fracture mode. In parallel, analytical solutions were evaluated for stress distribution and developed 3D numerical models to study the stress distribution and the fracture mode at the transversely isotropic disc. There were new findings on the fracture mode of crack propagation, the influence of the disc thickness, the influence of the applying loading angle and angle of the loading-foliation for transversely isotropic material. / Inhalt der Arbeit sind Untersuchungen zum anisotropen Festigkeitsverhalten von Gesteinen beim Spaltzugversuch (Brazilian Test). Laborativ wurden drei transversalisotrope Gesteine (Granit, Schiefer und Sandstein) untersucht. Insgesamt wurden mehr als 550 Spaltzugversuche durchgeführt, wobei der Schwerpunkt auf die Untersuchung des Einflusses der räumlichen Lage der Anisotropieebene zur Richtung des Lasteintrages auf die Bruchfestigkeit und das Bruchbild bzw. den Bruchmodus gelegt wurde. Parallel dazu wurden analytische Lösungen zur Spannungsverteilung ausgewertet sowie numerische 3D-Modelle entwickelt, um die Spannungsverteilung sowie den Bruchmodus bei einer transversalisotropen Scheibe zu untersuchen. Es wurden neue Erkenntnisse zum Bruchmodus, der Rissausbreitung, des Einflusses der Scheibendicke, dem Einfluss des Lasteinleitungswinkel sowie des Winkels Lasteintrag - Anisotropieebene für transversalisotropes Material gewonnen.