An Adaptive Frequency Sweeping Algorithm of MoM Impedance Matrices in Full-Wave Analysis of Microstrip Patch Antennas

Abstract-In this paper, a study on frequency interpolation algorithms of method of moments (MoM) impedance matrices is discussed in detail, which is successfully applied into the full-wave analysis of a microstrip patch antenna in a relatively wide band. By using Lagrange interpolation scheme in an adaptive system, two interpolating rules are realized and their accuracies are defined by Frobenius norms of the impedance matrices in entire frequency band. A microstrip fed patch antenna is considered to verify the algorithm from 1 to 5 GHz. The numerical results have shown that by selecting the Chebyshev zeros in the frequency band for polynomial interpolation is of high accuracy and the simulation efficiency can be highly elevated simultaneously. Besides, a statistical conclusion on the tradeoff between accuracy and efficiency issue has also been made quantitatively

Finite difference solutions to the equations of elastic wave-propagation, with application to Love waves over dipping interfaces.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Sciences, 1970.Vita.Bibliography: leaves 234-249.Ph.D

Earth's structure from a bayesian analysis of seismic signals and noise

The prevailing drive of modern seismology is to improve our knowledge of the Earth's structure, composition, and dynamics through an analysis of seismic waveforms. With increasing computing power, number and quality of seismic stations, and length of data records, the resolution and spatial coverage of current Earth models has improved substantially over the past few decades. Yet many limitations remain. The advent of ambient noise seismology has provided the solution to many issues, such as the irregular distribution of earthquakes, biases from structures outside the model region, earthquake location errors, and lack of near-surface resolution. Despite improvements to data quality and quantity and the introduction of unconventional datasets such as ambient seismic noise, a persisting shortcoming of many tomographic inversions is ad-hoc error estimation, parameterization, and regularization, which prevent a meaningful portrayal of model complexity and uncertainty. With the rapid increase in computing power, non-linear techniques based on densely sampling favorable regions of model space are now becoming tractable for real-world tomographic problems and directly address these shortcomings. One such recently introduced and promising method is transdimensional and hierarchical Bayesian inference. This alternate approach allows model parameterization and resolution to be driven by the data. This thesis presents a collection of seismic inverse problems using real world datasets, some of which are tackled using fully non-linear Bayesian statistics. The benefits of a probabilistic approach are demonstrated for datasets targeting the uppermost crust down to the core through the development of novel methods of inversion and uncertainty quantification. To begin, an unconventional methodology for studying earthquake focal mechanisms in intraplate settings is presented through the inversion of ambient noise, receiver functions, and dispersion curves. The ambient seismic noise imaging approach of this study is subsequently applied to Tasmania - to which it is highly suited - and the resulting group and phase velocity maps help decipher Tasmania's enigmatic tectonic history. The same ambient noise dataset is further manipulated to yield a 3D shear velocity model of the region using a two-step transdimensional, hierarchical ensemble inference approach. Two prominent low-velocity anomalies offer insight into the Paleozoic evolution of the east Gondwana margin and support a connection between Tasmania and mainland Australia since the Cambrian. This approach is also applied to a larger dataset encompassing much of mainland southeast Australia. The Bayesian approach is also applied to a global dataset of differential body wave travel times in an effort to reveal P-wave velocity heterogeneity in the lowermost mantle. Another deep Earth application is demonstrated through an inversion for the time-dependent differential rotation of the inner core with respect to the rest of the mantle using careful measurements of earthquake doublets. The transdimensional nature of the inversion problem means that the data drive the number of free parameters constraining the differential rotation pattern, which exhibits much more complexity than the simple linear trend long-promoted by previous studies. The contents of this thesis help augment the diverse and wide-reaching applications for Bayesian statistics, which will continue to improve with future increases in computational power

Electromagnetic Scattering from Semi-Infinite Planar Arrays

A hybrid method of moments (MM) based numerical model for the electromagnetic scattering from large finite by infinite planar slot arrays is developed. The method incorporates the novel concept of a physical basis function (PBF) to dramatically reduce the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance, allowing one to tailor the edge currents to provide a desired echo width pattern. The surface equivalence theorem is used to convert the original slotted ground plane geometry to an equivalent unbroken ground plane with magnetic surface currents. An integral equation based on these magnetic scattering currents is solved via the MM. The magnetic currents are approximated by a set of basis functions composed of periodic basis functions representing the edge slot columns and a single PBF representing the interior slot columns. In particular, the PBF captures the behavior of the central portion of the array where the perturbations from the edges have become negligible. Based on Floquet\u27s theorem, the PBF is able to represent an arbitrarily large number of slot columns with just one unknown. The array scanning method (ASM) provides the contributions from the individual edge columns. Finally, a newly developed one sided Poisson sum formulation provides an efficient means to account for the stratified dielectric media via a spectral domain conversion. The hybrid method is validated using both MM reference codes and measured data. The results clearly demonstrate the method\u27s accuracy as well as its ability to handle array problems too large for traditional MM solutions

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Surface and shear-wave velocity modelling of the Tongariro Volcanic Centre, New Zealand, using ambient noise cross-correlation

We use continuous seismic data from permanent and temporary, broadband and short-period stations that were operating during 2001 and 2008 to investigate the subsurface velocity structure of the Tongariro Volcanic Centre (TgVC) of New Zealand, particularly the highly active but poorly understood Ruapehu and Tongariro Volcanoes. Stacks of cross-correlation of two concurrent ambient noise seismograms can be used to estimate the interstation Green's Function, i.e., the impulse response of the earth between the two receivers. The Green's Functions are used to retrieve the dispersion relation (frequency-dependent velocity) of surface waves at different periods, which reflects the shear-wave velocity structure in the Fresnel volume of the propagating surface waves. Several studies have used dispersion measurements from ambient noise cross-correlations to investigate the shallow subsurface shear-wave velocity structure of active volcanoes around the world. Most use vertical components to retrieve the Rayleigh waves, but it is becoming increasingly common to use the horizontal seismogram components in addition to the vertical, giving further constraints to Rayleigh-wave measurements and introducing data relating to Love waves. We compute 1,048,968 daily cross-correlations for 955 viable station pairs across the two periods, including all nine-components of the cross-correlation tensor where possible. These daily functions are then stacked into 7458 full-stacks, of which we make group velocity dispersion measurements for 2641 RR-, RZ-, TT-, ZR- and ZZ-component stacks. Cross-correlation quality varies across the networks, with some station pairs possibly contaminated with timing errors. We observe both the fundamental and rst higher-order modes within our database of dispersion measurements. However, correctly identifying the mode of some measurements is challenging as the range of group velocities measured reflects both presence of multiple modes and heterogeneity of the local velocity structure. We assign modes to over 1900 measurements, of which we consider 1373 to be high quality. We invert fundamental mode Rayleigh- and Love-wave dispersion curves independently and jointly for one dimensional shear-wave velocity profiles at Ruapehu and Tongariro Volcanoes, using dispersion measurements from two individual station pairs and average dispersion curves from measurements within specifi c areas on/around the volcanoes. Our Ruapehu profiles show little velocity variation with depth, suggesting that volcanic edifice is made of material that is compacting and being hydrothermally altered with depth. At Tongariro, we observe larger increases in velocity with depth, which we interpret as different layers within Tongariro's volcanic system. Slow shear-wave velocities, on the order of 1-2 km/s, are consistent with both P-wave velocities from existing velocity pro files of areas within the TgVC, and the observations of worldwide studies of shallow volcanic systems that used ambient noise cross-correlation. A persistent observation across the majority of our dispersion measurements is that group velocities of the fundamental mode Love-wave group velocity measurements are slower than those of fundamental mode Rayleigh-waves, particularly in the frequency range of 0.25-1 Hz. Similarly, first higher-order mode Love-wave group velocities are slower than first higher-mode Rayleigh-wave velocities. This is inconsistent with the differences between synthetic dispersion curves that were calculated using isotropic, layered velocity models appropriate for Ruapehu and Tongariro. We think the Love-Rayleigh discrepancy is due to structures such as dykes or cracks in the vertical plane having greater influence than horizontal layering on surface-wave propagation. However, several measurements where Love-wave group velocities are faster than Rayleigh-wave group velocities suggests that in some places horizontal layering is the stronger influence. We also observe that the differences between the Love- and Rayleigh-wave dispersion curves vary with the azimuth of the interstation path across Ruapehu and Tongariro Volcanoes. Some significant differences between Rayleigh-wave velocities of measurements with different interstation orientations are also observed, as are differences between Love-wave velocities. This suggests a component of azimuthal anisotropy within the volcanic structures, which coupled with the radial anistropy makes the shear-wave velocity structures of Ruapehu and Tongariro Volcanoes anisotropic with orthorhombic symmetry. We suggest that further work to determine three-dimensional structure should include provisions for anisotropy with orthorhombic or lower symmetry

Performance bounds on matched-field methods for source localization and estimation of ocean environmental parameters

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2001Matched-field methods concern estimation of source location and/or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation. Typical estimation performance demonstrates two fundamental limitations. First, sidelobe ambiguities dominate the estimation at low signal-to-noise ratio (SNR), leading to a threshold performance behavior. Second, most matched-field algorithms show a strong sensitivity to environmental/system mismatch, introducing some biased estimates at high SNR. In this thesis, a quantitative approach for ambiguity analysis is developed so that different mainlobe and sidelobe error contributions can be compared at different SNR levels. Two large-error performance bounds, the Weiss-Weinstein bound (WWB) and Ziv-Zakai bound (ZZB), are derived for the attainable accuracy of matched-field methods. To include mismatch effects, a modified version of the ZZB is proposed. Performance analyses are implemented for source localization under a typical shallow water environment chosen from the Shallow Water Evaluation Cell Experiments (SWellEX). The performance predictions describe the simulations of the maximum likelihood estimator (MLE) well, including the mean square error in all SNR regions as well as the bias at high SNR. The threshold SNR and bias predictions are also verified by the SWellEX experimental data processing. These developments provide tools to better understand some fundamental behaviors in matched-field performance and provide benchmarks to which various ad hoc algorithms can be compared.Financial support for my research was provided by the Office of Naval Research and the WHOI Education Office

Multistation Methods for Geotechnical Characterization using Surface Waves

This dissertation deals with soil characterization methods based on surface wave propagation applied to geotechnical engineering purposes. This topic has gained much interest in the last decade because of the appealing possibilities given by non-invasive methods, which are at once very flexible and cost effective. An overview of the properties of Rayleigh waves in layered linear elastic and linear viscoelastic media is presented, together with their applications for site characterization, of whose the SASW (Spectral Analysis of Surface Waves) method is by far the most well-known in geotechnical engineering. The research has been mainly focused on the application of multistation methods, compared with the classical two-station approach typical of the SASW method. Results from both numerical simulations and experimental testing are reported to compare two-station and multistation methods and to clarify the advantages that can be obtained using the latter ones. In particular the research has been developed following two different directions: on the one hand the application of classical geophysical analysis tools (such as domain analysis and slant stack transform) to tests performed with impulsive sources. On the other one the possibility of obtaining from surface wave testing not only a stiffness profile, but also a damping ratio profile for the site. In this respect a new method for simultaneous measurements of Rayleigh dispersion and attenuation curves is proposed. Regarding the first topic, the necessity of a multistation approach to determine the experimental dispersion test is essentially related to the spatial variation of phase velocity. Analyses in the frequency-wavenumber domain and in the frequency-slowness domain are very powerful approaches, still there was a need of studying the effects of the change of scale from geophysical applications to geotechnical ones. Indeed because of the peculiar properties of Rayleigh waves, surface testing is strongly affected by the distance travelled by the analysed wave. The numerical simulations performed in the research show that the phase velocity obtained using multistation methods with a limited number of receivers close to the source is not a modal value as it is for geophysical applications, but an apparent phase velocity arising from modal superposition. The experimental tests showed the good performances of multistation methods when compared to the SASW method. In particular some drawbacks of the latter method, due essentially to its two-station nature, are avoided and the field-testing appears to be very promising for future applications. In particular the application of the frequency-wavenumber domain analysis can lead to much faster and more stable estimates of the experimental dispersion curve and the process is easily automated, with a great saving of time and less requirement for subjective decisions. Another important advantage is given by the stability with respect to a near field effects that lead to a better reconstruction of the dispersion curve for the low frequencies and hence to a deeper characterization. The necessity of a new method for the simultaneous determination of surface wave dispersion and attenuation curves is linked to the strong coupling existing between the two. Such coupling is extremely important for the subsequent inversion process, in a consistent method leading from the field measurements to the stiffness and damping profiles. The proposed method uses a new testing configuration, designed to measure the experimental transfer function. Successively a regression process of the complex quantity with the corresponding expression obtained modelling soil as a linear viscoelastic layered system leads to the experimental dispersion and attenuation curves. Some preliminary results are reported showing very encouraging results, also if a more extensively testing programme is required for the complete validation of the metho