Crenulation Cleavage Development and the Influence of Rock Microstructure on Crustal Seismic Anisotropy

This thesis investigates the cause of mass transfer during crenulation cleavage formation and the role that elastically anisotropic minerals and fabric development play in promoting seismic anisotropy in the crust. Crenulation cleavage is the most common fabric in multiplydeformed, phyllosilicate-rich metamorphic rocks. During its formation the originally planar fabric gets crenulated, eventually leading to the differentiation of quartz- and feldspar-rich regions (QFdomains) in the crenulation hinges, and phyllosilicate-rich regions (P-domains) in the crenulation limbs. This differentiation is driven by the dissolution of quartz and feldspar in the P-domains, and the precipitation of those minerals in the QF-domains. Finite element models are created to investigate how the elastic interactions of quartz and muscovite minerals affect the grain-scale stress and strain distributions at different stages of crenulation cleavage development. Gradients in mean stress and volumetric strain develop between the limbs and hinges of the microfolds during fabric formation and are sufficient to drive mass transfer between the two domains. v To study the influence of different microstructural variables on seismic wave speed anisotropy, simplified muscovite-quartz models are created with varying amounts of muscovite, varying quartz and muscovite orientations, and varying spatial distributions. The asymptotic expansion homogenization method coupled with finite element modeling (AEH-FE) is used to calculate bulk stiffness tensors and seismic wave speeds. Muscovite’s abundance and preferred orientation have significant influence of seismic wave speed anisotropy due to the extreme anisotropic elasticity of the mineral. The same method is employed to study the seismic behavior of rocks containing different stages of crenulation cleavage. Mineral orientation maps of rock samples were created, using electron backscatter diffraction, and used as input files for the AEH-FE program. Schists with a planar foliation are highly elastically anisotropic, but a rock with a well developed crenulation cleavage is much less anisotropic. These results imply that regions with larger scale crustal structures, such as folds and shear-zones, can be much more muted in their seismic signal than the schistose samples that make up those structures

Investigating carbon materials nanostructure using image orientation statistics

International audienceA new characterization method of the lattice fringe images of turbostratic carbons is proposed. This method is based on the computation of their orientation field without explicit detection of fringes. It allows meaningful insights into the material nanostructure and nanotexture at several scales, either qualitatively or quantitatively. The calculation of pairwise spatial statistics of the orientation field at short distance provides measurements of the coherence lengths along any direction, in particular along and orthogonally to the layers. These statistics also allow representing orientation coherence patterns typical of the observed nanostructure. At larger distances, the mean disorientation of the fringes is computed and information about the homogeneity of the sample is obtained. An experimental validation is carried out on various artificial images and an application to the characterization of four bulk turbostratic carbons is provided

Multiscale viscoplastic-viscodamage analysis of shape memory polymer fibers with application to self healing smart materials

Self-healing smart material systems have been introduced into the research arena and they have already been deployed into industrial applications. The Close-Then-Heal (CTH) healing mechanism for polymeric self-healing systems is addressed herein and then a new generation of Shape Memory Polymer (SMP) based self-healing system is proposed in this work. This system incorporates SMP fibers to close the cracks while the embedded Thermoplastic Particles (TPs) are diffused into the crack surfaces upon heating and provide a molecular level of healing. The SMP fiber manufacturing procedure is briefly addressed in this work in which the bobbin of SMP fibers are heat treated in a specific procedure and then they are wound to produce SMP fibers. The performance of the proposed healing system is highly dependent on mechanical responses of SMP fibers. The polyurethane SMP fibers are categorized as semicrystalline polymeric material systems. These semicrystalline SMP fibers are then constituted from two distinguishable phases, which are amorphous and crystalline polymers. Such a multiphase system can be evaluated through a multiscale analysis within the micromechanics framework in which the macroscopic mechanical responses are evolved through averaging the microscale mechanical fields. Then in this research the constitutive relation for each of the micro-constituents are utilized to compute the microscale mechanical fields and then these fields are correlated to the macroscopic field through the micromechanics framework. The cyclic viscoplastic and viscodamage of these fibers are of utmost importance for designing self-healing systems in which repeatability of the healing process and the healing efficiency for subsequent healing cycles are highly dependent on cyclic responses of these fibers. A new approach in measurement of cyclic damage of SMP fibers is proposed in this work in which the reduction in recoverable stress after each cyclic stress recovery is correlated to the damage. In this approach the damage is interpreted as failure of the polymeric bonds to recover their original shape (SM effect). In general the proposed self-healing scheme establishes a new generation of self-healing systems while the developed theoretical multiscale analysis provides a well-structured method to investigate the cyclic viscoplastic and viscodamage of the SMP fibers

Directional multiresolution image representations

Efficient representation of visual information lies at the foundation of many image processing tasks, including compression, filtering, and feature extraction. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. For practical applications, this representation has to be realized by structured transforms and fast algorithms. Recently, it has become evident that commonly used separable transforms (such as wavelets) are not necessarily best suited for images. Thus, there is a strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure of pictorial information. This thesis focuses on the development of new "true" two-dimensional representations for images. The emphasis is on the discrete framework that can lead to algorithmic implementations. The first method constructs multiresolution, local and directional image expansions by using non-separable filter banks. This discrete transform is developed in connection with the continuous-space curvelet construction in harmonic analysis. As a result, the proposed transform provides an efficient representation for two-dimensional piecewise smooth signals that resemble images. The link between the developed filter banks and the continuous-space constructions is set up in a newly defined directional multiresolution analysis. The second method constructs a new family of block directional and orthonormal transforms based on the ridgelet idea, and thus offers an efficient representation for images that are smooth away from straight edges. Finally, directional multiresolution image representations are employed together with statistical modeling, leading to powerful texture models and successful image retrieval systems

Subdivision Directional Fields

We present a novel linear subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the finite-element representation with discrete exterior calculus. By commuting with differential operators, our subdivision is structure-preserving: it reproduces curl-free fields precisely, and reproduces divergence-free fields in the weak sense. Moreover, our subdivision scheme directly extends to directional fields with several vectors per face by working on the branched covering space. Finally, we demonstrate how our scheme can be applied to directional-field design, advection, and robust earth mover's distance computation, for efficient and robust computation

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Fault-Adjacent Damage at the Base of the Seismogenic Zone and Seismic Anisotropy of Fold Structures

While earthquakes represent a major hazard to life and property, there are a number of open questions about how earthquake faults operate at depth, and how the energy released by earthquakes travels as elastic waves through Earth’s complexly deformed crustal rocks. The aims of my dissertation are to explore (a) the extent of co-seismic damage in an ancient earthquake fault exhumed from great depths, (b) the deformation processes and mechanics of the fault at depth during earthquake cycles, and (c) the role of different rock structures in determining the velocities of seismic waves. When tectonic plates collide, deformation tends to localize into narrow zones: frictional faults in the upper crust and high-temperature viscous shear zones in the lower crust. The transition in material behavior from the upper to lower crust is known as the frictional-to-viscous transition (FVT; ~10–20 km deep). During earthquake cycles, the FVT experiences transient brittle deformation followed by long-term viscous processes. Owing to this complex behavior over the earthquake cycle, the FVT is the most important horizon for understanding earthquake mechanics. Rareness of exposures of ancient earthquake faults at FVT depths has hindered studying of their brittle co-seismic damage structures and rheology of their deep portions during earthquake cycles. From the Sandhill Corner shear zone, a strand of the Norumbega fault system (an ancient seismogenic strike-slip fault at the FVT), I analyze fluid inclusion abundance in quartz as a proxy for transient co-seismic damage using secondary electron image and optical observation, and collect quantitative data of quartz across the shear zone such as grain-size, grain-shape, crystallographic orientation, misorientation, and fabric intensity through electron backscatter diffraction. The results indicate that brittle co-seismic damage occurs up to at least ~90 m in width at the FVT, and the inner shear zone (~40 m wide) experienced cycles of co-seismic microfracture-assisted grain-size reduction followed by post-seismic viscous deformation dominated by grain-size-sensitive processes, whereas the outer shear zone was deformed dominantly by grain-size-insensitive processes during earthquake cycles. My findings have important implications for the strength, or mechanics, of the fault/shear zone system, and may help determine 3-D volume of brittle damage zone. Measuring the extent of damage zone is critical for estimating the potential energy that an earthquake releases because the co-seismic damage zone acts as a dissipative energy sink by creating fracture surface areas. Earthquakes not only represent hazards but radiate energy as seismic waves. Since the direction-dependent nature of wave propagation velocities (called “seismic anisotropy”) changes in response to rock flow due to preferred orientation of elastically anisotropic minerals, the seismic anisotropy has been used to investigate Earth’s interior structure and deformation processes in tectonically active regions. However, this is a challenge for waves passing through the crust because their anisotropies are profoundly modified by macroscale folds, which are very common structures in ancient and current orogenic belts and shear zones. To evaluate the modification of seismic anisotropy by the deformation structures, I develop a new mathematical methodology for calculating bulk elastic tensors and seismic anisotropy of macroscale folds, assuming the seismic waves are much larger than the fold heterogeneity. The results show that the velocities of seismic waves propagating through macroscale folds in three dimensions are systematically related to fold shape and orientation. Because fold orientations are related to flow directions, it is now possible for real seismic observables to provide information on the directions of flow for actively deforming rocks at depth

Image coding using wavelets, interval wavelets and multi- layered wedgelets

Ph.DDOCTOR OF PHILOSOPH