Structure and evolution of the Australian continent : insights from seismic and mechanical heterogeneity and anisotropy

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2002.Includes bibliographical references (p. 235-261).In this thesis, I explore the geophysical structure and evolution of the Australian continental lithosphere. I combine insights from isotropic and anisotropic seismic surface-wave tomography with an analysis of the anisotropy in the mechanical properties of the lithosphere, inferred from the coherence between gravity anomalies and topography. With a new high-resolution waveform tomographic model of Australia, I demonstrate that the depth of continental high wave speed anomalies does not universally increase with age, but is dependent on the scale and the tectonic history of the region under consideration. I construct an azimuthally anisotropic three-dimensional model of the Australian upper mantle from Rayleigh-wave waveforms. I compare Bayesian inverse methods with discretely parameterized regularization methods, and explore the use of regular, tectonic and resolution-dependent tomographic grids. I advocate the use of multitaper spectral estimation techniques for coherence analysis of gravity and topography, applied to Australian isostasy. I investigate the importance of internal loading, the directional anisotropy of the gravitational response to loading, and the estimation bias affecting the long wavelengths of the coherence function. I develop a method for non-stationary coherence analysis which enables a complete characterization of continental strength by the dependency of gravity-topography coherence on wavelength, direction and geologic age. Combining high-resolution, depth-dependent anisotropy measurements from surface-wave tomography with the mechanical anisotropy from gravity/topography coherence, I assess the validity of two competing theories regarding the cause of continental anisotropy (vertically coherent deformation or simple asthenospheric flow) quantitatively for the very first time.by Frederik Jozef Maurits Simons.Ph.D

Statistical Characterization of Morphodynamic Signals Using Wavelet Analysis

Morphodynamic and hydrodynamic properties are concomitantly part of the entire dynamic of river systems and commonly present both temporal and spatial persistent variability. Therefore, the study of both river morphodynamic signals (e.g. bed forms and meandering and anabranching river morphometrics) and hydrodynamic signals (e.g. velocity fields, sediment concentrations) requires both temporal and spatial multi-scale signal representations. The present research is focused on the former type of signals and it is a first attempt to discriminate such signals and, subsequently, develop the theoretical background to link these processes at different spatial and temporal scales and determine the scales that have more influence on river evolution. The main contribution of this study are: [1] to design a methodology to discriminate bed form features (e.g. bars, dunes and ripples) via the combined application of robust spline filters and one-dimensional continuous wavelet transforms, allowing the quantitative recognition of bed form hierarchies. The methodology was tested by using synthetic bed form signals and subsequently applied to the analysis of bed form features from the Parana River, Argentina. [2] To develop a methodology for the statistical analysis of the spatial distribution of meandering rivers morphometrics by coupling the capabilities of one-dimensional wavelet transforms, principal component analysis and Frechet distance. A universal river classification method is also proposed. [3] To perform a novel study of the planimetric configuration of confluences in tropical free meandering rivers located in the upper Amazon catchment. River confluences in tropical environments represent areas where biota is concentrated; therefore, a better understanding and characterization of these features has a particular importance for the Amazonian ecosystem. [4] To evaluate the potential of two-dimensional wavelet transforms in the analysis of bed form features. The broader impact will be an improved understanding of river morphodynamics of the upper Amazon River for practical applications such as navigability. Furthermore, the project will provide an updated statistical analysis of the meandering rivers dynamics for practical applications, including erosion control, river ecology, and habitat restoration. The developed statistical tool will be included as an application of the RVR Meander platform (www.rvrmeander.org), which is a broadly used software for river restoration

Analysis of the structure of time-frequency information in electromagnetic brain signals

This thesis encompasses methodological developments and experimental work aimed at revealing information contained in time, frequency, and time–frequency representations of electromagnetic, specifically magnetoencephalographic, brain signals. The work can be divided into six endeavors. First, it was shown that sound slopes increasing in intensity from undetectable to audible elicit event-related responses (ERRs) that predict behavioral sound detection. This provides an opportunity to use non-invasive brain measures in hearing assessment. Second, the actively debated generation mechanism of ERRs was examined using novel analysis techniques, which showed that auditory stimulation did not result in phase reorganization of ongoing neural oscillations, and that processes additive to the oscillations accounted for the generation of ERRs. Third, the prerequisites for the use of continuous wavelet transform in the interrogation of event-related brain processes were established. Subsequently, it was found that auditory stimulation resulted in an intermittent dampening of ongoing oscillations. Fourth, information on the time–frequency structure of ERRs was used to reveal that, depending on measurement condition, amplitude differences in averaged ERRs were due to changes in temporal alignment or in amplitudes of the single-trial ERRs. Fifth, a method that exploits mutual information of spectral estimates obtained with several window lengths was introduced. It allows the removal of frequency-dependent noise slopes and the accentuation of spectral peaks. Finally, a two-dimensional statistical data representation was developed, wherein all frequency components of a signal are made directly comparable according to spectral distribution of their envelope modulations by using the fractal property of the wavelet transform. This representation reveals noise buried processes and describes their envelope behavior. These examinations provide for two general conjectures. The stability of structures, or the level of stationarity, in a signal determines the appropriate analysis method and can be used as a measure to reveal processes that may not be observable with other available analysis approaches. The results also indicate that transient neural activity, reflected in ERRs, is a viable means of representing information in the human brain.reviewe

Fast Fourier Transform at Nonequispaced Nodes and Applications

The direct computation of the discrete Fourier transform at arbitrary nodes requires O(NM) arithmetical operations, too much for practical purposes. For equally spaced nodes the computation can be done by the well known fast Fourier transform (FFT) in only O(N log N) arithmetical operations. Recently, the fast Fourier transform for nonequispaced nodes (NFFT) was developed for the fast approximative computation of the above sums in only O(N log N + M log 1/e), where e denotes the required accuracy. The principal topics of this thesis are generalizations and applications of the NFFT. This includes the following subjects: - Algorithms for the fast approximative computation of the discrete cosine and sine transform at nonequispaced nodes are developed by applying fast trigonometric transforms instead of FFTs. - An algorithm for the fast Fourier transform on hyperbolic cross points with nonequispaced spatial nodes in 2 and 3 dimensions based on the NFFT and an appropriate partitioning of the hyperbolic cross is proposed. - A unified linear algebraic approach to recent methods for the fast computation of matrix-vector-products with special dense matrices, namely the fast multipole method, fast mosaic-skeleton approximation and H-matrix arithmetic, is given. Moreover, the NFFT-based summation algorithm by Potts and Steidl is further developed and simplified by using algebraic polynomials instead of trigonometric polynomials and the error estimates are improved. - A new algorithm for the characterization of engineering surface topographies with line singularities is proposed. It is based on hard thresholding complex ridgelet coefficients combined with total variation minimization. The discrete ridgelet transform is designed by first using a discrete Radon transform based on the NFFT and then applying a dual-tree complex wavelet transform. - A new robust local scattered data approximation method is introduced. It is an advancement of the moving least squares approximation (MLS) and generalizes an approach of van den Boomgard and van de Weijer to scattered data. In particular, the new method is space and data adaptive

Applications of Ground Penetrating Radar to Structural Analysis of Carbonate Terraces on the Island of Bonaire, Caribbean Netherlands

This thesis utilized the method of ground penetrating radar to investigate the structural geology of carbonate units in relation to the evolution of the island of Bonaire, Caribbean Netherlands. Two surveys were completed on the island for this purpose: a long continuous cross-island transect, as well as a smaller set of lines that facilitated three-dimensional interpretation at an outcrop known as Seru Grandi. In the detailed processing workflow implemented for the collected datasets, steps were taken to remove unwanted signal noise, and advanced imaging techniques where then applied to generate interpretable subsurface cross-sections. A novel numerical interpretation tool was developed for use on the cross-island transect, which adapted a traditional k-means clustering algorithm for use with structure-parallel vectors derived from structure tensors. The results of this method were utilized in defining a set of radar facies for the cross-island transect. Mapping of these radar facies identified subsurface features related to subtidal-to-foreshore depositional sequences in the southern part of the transect, a potential lagoon system in the south-central portion, eolianites within the center of the transect, and clinoforms related to platform slope deposits in the northeast portions of the survey. Using the small-scale dataset at the Seru Grandi outcrop, subsurface geometries of a previously identified geologic unconformity were described. This unconformity was identified here to be the remnants of a wave cut-platform occurring at the site. The specific geometry of this feature was related to external controls on wave cut-platform development. In addition, the data collected at Seru Grandi identified a set of clinoform surfaces in the subsurface below the mapped unconformity. These observations were compared to previously identified clinoforms observed on the face of the outcrop. Observations and interpretations from both surveys in this study were used to provide additional information relating to the geologic evolution of Bonaire

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Magnetoencephalography

This is a practical book on MEG that covers a wide range of topics. The book begins with a series of reviews on the use of MEG for clinical applications, the study of cognitive functions in various diseases, and one chapter focusing specifically on studies of memory with MEG. There are sections with chapters that describe source localization issues, the use of beamformers and dipole source methods, as well as phase-based analyses, and a step-by-step guide to using dipoles for epilepsy spike analyses. The book ends with a section describing new innovations in MEG systems, namely an on-line real-time MEG data acquisition system, novel applications for MEG research, and a proposal for a helium re-circulation system. With such breadth of topics, there will be a chapter that is of interest to every MEG researcher or clinician

Book of Abstracts

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