Exploiting seismic waveforms of ambient noise and earthquakes

In this thesis, I apply detailed waveform modeling to study noise correlations in different environments, and earthquake waveforms for source parameters and velocity structure.

Green's functions from ambient noise correlations have primarily been used for travel-time measurement. In Part I of this thesis, by detailed waveform modeling of noise correlation functions, I retrieve both surface waves and crustal body waves from noise, and use them in improving earthquake centroid locations and regional crustal structures. I also present examples in which the noise correlations do not yield Green's functions, yet the results are still interesting and useful after case-by-case analyses, including non-uniform distribution of noise sources, spurious velocity changes, and noise correlations on the Amery Ice Shelf.

In Part II of this thesis, I study teleseismic body waves of earthquakes for source parameters or near-source structure. With the dense modern global network and improved methodologies, I obtain high-resolution earthquake locations, focal mechanisms and rupture processes, which provide critical insights to earthquake faulting processes in shallow and deep parts of subduction zones. Waveform modeling of relatively simple subduction zone events also displays new constraints on the structure of subducted slabs.

In summary, behind my approaches to the relatively independent problems, the philosophy is to bring observational insights from seismic waveforms in critical and simple ways.

Propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems

We investigate the propagation of an arbitrary elliptically polarized few-cycle ultrashort laser pulse in resonant two-level quantum systems using an iterative predictor-corrector finite-difference time-domain method. It is shown that when the initial effective area is equal to 2 pi, the effective area will remain invariant during the course of propagation, and a complete Rabi oscillation can be achieved. However, for an elliptically polarized few-cycle ultrashort laser pulse, polarization conversion can occur. Eventually, the laser pulse will evolve into two separate circularly polarized laser pulses with opposite helicities.

Propagation of a few-cycle laser pulse in a V-type three-level system

Propagation of a few-cycle laser pulse in a V-type three-level system (fine structure levels of rubidium) is investigated numerically. The full three-level Maxwell-Bloch equations without the rotating wave approximation and the standing slowly varying envelope approximation are solved by using a finite-difference time-domain method. It is shown that, when the usual unequal oscillator strengths are considered, self-induced transparency cannot be recovered and higher spectral components can be produced even for small-area pulses. (c) 2005 Pleiades Publishing, Inc.

Investigations of charge-carrier dynamics at semiconductor/liquid interfaces

Theoretical and experimental investigations of charge-carrier dynamics at semiconductor/liquid interfaces, specifically with respect to interfacial electron transfer and surface recombination, are presented.

Fermi's golden rule has been used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. The treatment allows comparison between charge-transfer kinetic data at metallic, semimetallic, and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been determined from experimental data for charge transfer at metallic electrodes. The maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10^-17-10^-16 cm⁴ s^-1, which is in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces.

Double-layer corrections have been evaluated for semiconductor electrodes in both depletion and accumulation conditions. In conjuction with the Gouy-Chapman-Stern model, a finite difference approach has been used to calculate potential drops at a representative solid/liquid interface. Under all conditions that were simulated, the correction to the driving force used to evaluate the interfacial rate constant was determined to be less than 2% of the uncorrected interfacial rate constant.

Photoconductivity decay lifetimes have been obtained for Si(111) in contact with solutions of CH₃OH or tetrahydrofuran containing one-electron oxidants. Silicon surfaces in contact with electrolyte solutions having Nernstian redox potentials > 0 V vs. SCE exhibited low effective surface recombination velocities regardless of the different surface chemistries. The formation of an inversion layer, and not a reduced density of electrical trap sites on the surface, is shown to be responsible for the long charge-carrier lifetimes observed for these systems. In addition, a method for preparing an air-stable, low surface recombination velocity Si surface through a two-step, chlorination/alkylation reaction is described.

2D modeling of lower mantle structure with WKM synthetics

The Earth is very heterogeneous, especially in the region close to the surface of the Earth, and in regions close to the core-mantle boundary (CMB). The lowermost mantle (bottom 300km of the mantle) is the place for fast anomaly (3% faster S velocity than PREM, modeled from Scd), for slow anomaly (-3% slower S velocity than PREM, modeled from S,ScS), for extreme anomalous structure (ultra-low velocity zone, 30% lower inS velocity, 10% lower in P velocity). Strong anomaly with larger dimension is also observed beneath Africa and Pacific, originally modeled from travel time of S, SKS and ScS. Given the heterogeneous nature of the earth, more accurate approach (than travel time) has to be applied to study the details of various anomalous structures, and matching waveform with synthetic seismograms has proven effective in constraining the velocity structures. However, it is difficult to make synthetic seismograms in more than 1D cases where no exact analytical solution is possible. Numerical methods like finite difference or finite elements are too time consuming in modeling body waveforms. We developed a 2D synthetic algorithm, which is extended from 1D generalized ray theory (GRT), to make synthetic seismograms efficiently (each seismogram per minutes). This 2D algorithm is related to WKB approximation, but is based on different principles, it is thus named to be WKM, i.e., WKB modified. WKM has been applied to study the variation of fast D" structure beneath the Caribbean sea, to study the plume beneath Africa. WKM is also applied to study PKP precursors which is a very important seismic phase in modeling lower mantle heterogeneity. By matching WKM synthetic seismograms with various data, we discovered and confirmed that (a) The D" beneath Caribbean varies laterally, and the variation is best revealed with Scd+Sab beyond 88 degree where Sed overruns Sab. (b) The low velocity structure beneath Africa is about 1500 km in height, at least 1000km in width, and features 3% reduced S velocity. The low velocity structure is a combination of a relatively thin, low velocity layer (200 km thick or less) beneath the Atlantic, then rising very sharply into mid mantle towards Africa. (c) At the edges of this huge Africa low velocity structures, ULVZs are found by modeling the large separation between S and ScS beyond 100 degree. The ULVZ to the eastern boundary was discovered with SKPdS data, and later is confirmed by PKP precursor data. This is the first time that ULVZ is verified with distinct seismic phase.

Polarization evolution of a few-cycle ultrashort laser pulse propagating in a degenerate three-level medium

The propagation of an arbitrary polarized few-cycle ultrashort laser pulse in a degenerate three-level medium is investigated by using an iterative predictor-corrector finite-difference time-domain method. It is found that the polarization evolution of the ultrashort laser pulse is dependent not only on the initial atomic coherence of the medium but also on the polarization condition of the incident laser pulse. When the initial effective area is equal to 2 pi, complete linear-to-circular and circular-to-linear polarization conversion of few-cycle ultrashort laser pulses can be achieved due to the quantum interference effects between the two different transition paths.

Discrete Modeling of Granular Media: A NURBS-based Approach

This dissertation is concerned with the development of a new discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). With NURBS, the new DEM is able to capture sphericity and angularity, the two particle morphological measures used in characterizing real grain geometries. By taking advantage of the parametric nature of NURBS, the Lipschitzian dividing rectangle (DIRECT) global optimization procedure is employed as a solution procedure to the closest-point projection problem, which enables the contact treatment of non-convex particles. A contact dynamics (CD) approach to the NURBS-based discrete method is also formulated. By combining particle shape flexibility, properties of implicit time-integration, and non-penetrating constraints, we target applications in which the classical DEM either performs poorly or simply fails, i.e., in granular systems composed of rigid or highly stiff angular particles and subjected to quasistatic or dynamic flow conditions. The CD implementation is made simple by adopting a variational framework, which enables the resulting discrete problem to be readily solved using off-the-shelf mathematical programming solvers. The capabilities of the NURBS-based DEM are demonstrated through 2D numerical examples that highlight the effects of particle morphology on the macroscopic response of granular assemblies under quasistatic and dynamic flow conditions, and a 3D characterization of material response in the shear band of a real triaxial specimen.

I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of, a high-density grating of 630 lines/mm (corresponding to d/lambda = 2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect. (c) 2006 Optical Society of America.

Talbot effect of a grating with different kinds of flaws

The Talbot effect of a grating with different kinds of flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging will also be distorted. Furthermore, we evaluate high-density gratings by detecting the near-field distribution with the scanning near-field optical microscopy technique. Experimental results are also given. (c) 2005 Optical Society of America.

Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

FDTD analysis of Talbot effect of a high density grating

Talbot effect of a grating with different flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging would also be distorted. Furthermore, we can evaluate high density gratings by detecting the near-field distribution.

Steady surface wave pattern in a shear flow

The subject under investigation concerns the steady surface wave patterns created by small concentrated disturbances acting on a non-uniform flow of a heavy fluid. The initial value problem of a point disturbance in a primary flow having an arbitrary velocity distribution (U(y), 0, 0) in a direction parallel to the undisturbed free surface is formulated. A geometric optics method and the classical integral transformation method are employed as two different methods of solution for this problem. Whenever necessary, the special case of linear shear (i.e. U(y) = 1+ϵy)) is chosen for the purpose of facilitating the final integration of the solution.

The asymptotic form of the solution obtained by the method of integral transforms agrees with the leading terms of the solution obtained by geometric optics when the latter is expanded in powers of small ϵ r.

The overall effect of the shear is to confine the wave field on the downstream side of the disturbance to a region which is smaller than the wave region in the case of uniform flows. If U(y) vanishes, and changes sign at a critical plane y = y_cr (e.g. ϵy_cr = -1 for the case of linear shear), then the boundary of this asymmetric wave field approaches this critical vertical plane. On this boundary the wave crests are all perpendicular to the x-axis, indicating that waves are reflected at this boundary.

Inside the wave field, as in the case of a point disturbance in a uniform primary flow, there exist two wave systems. The loci of constant phases (such as the crests or troughs) of these wave systems are not symmetric with respect to the x-axis. The geometric optics method and the integral transform method yield the same result of these loci for the special case of U(y) = U_o(1 + ϵy) and for large Kr (ϵr ˂˂ 1 ˂˂ Kr).

An expression for the variation of the amplitude of the waves in the wave field is obtained by the integral transform method. This is in the form of an expansion in small ϵr. The zeroth order is identical to the expression for the uniform stream case and is thus not applicable near the boundary of the wave region because it becomes infinite in that neighborhood. Throughout this investigation the viscous terms in the equations of motion are neglected, a reasonable assumption which can be justified when the wavelengths of the resulting waves are sufficiently large.

Phase interpretation for polarization-dependent near-field images of high-density gratings

It has been described that the near-field images of a high-density grating at the half self-imaging distance could be different for TE and TM polarization states. We propose that the phases of the diffraction orders play an important role in such polarization dependence. The view is verified through the coincidence of the numerical result of finite-difference time-domain method and the reconstructed results from the rigorous coupled-wave analysis. Field distributions of TE and TM polarizations are given numerically for a grating with period d = 2.3 lambda, which are verified through experiments with the scanning near-field optical microscopy technique. The concept of phase interpretation not only explains the polarization dependence at the half self-imaging distance of gratings with a physical view, but also, it could be widely used to describe the near-field diffraction of a variety of periodic diffractive optical elements whose feature size comparable to the wavelength. (C) 2008 Elsevier B.V. All rights reserved.

Detection of cryptosporidium oocysts in water and environmental concentrates

Whilst current methods for the isolation and enumeration of Cryptosporidium spp. oocysts in water have provided some insight into their occurrence and significance, they are regarded as being inefficient, variable and time-consuming, with much of the interpretation being left to the expertise of the analyst. Two expectations of novel developments are to reduce the variability and subjectivity associated with the isolation and identification of oocysts. Flocculation, immunomagnetisable and flow cytometric techniques, for concentrating oocysts from water samples, should prove more reliable than current methods, whilst the development of more avid and specific monoclonal antibodies in conjunction with the use of nuclear fluorochromes will aid identification. Further insight into the viability, taxonomy, species identification, infectivity and virulence of the parasite should be forthcoming through the use of techniques such as the polymerase chain reaction, in situ hybridisation and non-uniform alternating current electrical fields. Such information is necessary in order to enable microbiologists, epidemiologists, engineers, utility operators and regulators to assess the safety of a water supply, with respect to Cryptosporidium contamination, more effectively.