On the determination of the properties of a medium from its reflection coefficient

This thesis demonstrates how the parameters of a slightly non-homogeneous medium can be derived approximately from the reflection coefficient.

Two types of media are investigated. The first is described by the one-dimensional wave equation, the second by the more complex Timoshenko beam equation. In both cases, the media are assumed to be infinite in extent, with the media parameters becoming homogeneous as the space variable approaches positive or negative infinity.

Much effort is placed in deriving properties of the reflection coefficient for both cases. The wave equation is considered primarily to introduce the techniques used to investigate the more complex Timoshenko equation. In both cases, an approximation is derived for one of the medium parameters involving the reflection coefficient.

Reflection and refraction of light at the interface of a uniaxial bicrystal

This paper deals with a theoretical analysis of the reflection and refraction of light at the interface of a bicrystal by use of Maxwell's equations. For a general case, the formulas of Snell's Law and the four Fresnel coefficients for the reflection and refraction of extraordinary light at the interface of a uniaxial bicrystal are derived for the first time, as well as the Brewster angle value. The condition for total reflection is presented and the electromagnetic fields distributions at both sides of a bicrystal are presented when total reflection occurs.

Seismic structure above and below the core-mantle boundary

Seismic structure above and below the core-mantle boundary (CMB) has been studied through use of travel time and waveform analyses of several different seismic wave groups. Anomalous systematic trends in observables document mantle heterogeneity on both large and small scales. Analog and digital data has been utilized, and in many cases the analog data has been optically scanned and digitized prior to analysis.

Differential travel times of S - SKS are shown to be an excellent diagnostic of anomalous lower mantle shear velocity (V s) structure. Wavepath geometries beneath the central Pacific exhibit large S- SKS travel time residuals (up to 10 sec), and are consistent with a large scale 0(1000 km) slower than average V_s region (≥3%). S - SKS times for paths traversing this region exhibit smaller scale patterns and trends 0(100 km) indicating V_s perturbations on many scale lengths. These times are compared to predictions of three tomographically derived aspherical models: MDLSH of Tanimoto [1990], model SH12_WM13 of Suet al. [1992], and model SH.10c.17 of Masters et al. [1992]. Qualitative agreement between the tomographic model predictions and observations is encouraging, varying from fair to good. However, inconsistencies are present and suggest anomalies in the lower mantle of scale length smaller than the present 2000+ km scale resolution of tomographic models. 2-D wave propagation experiments show the importance of inhomogeneous raypaths when considering lateral heterogeneities in the lowermost mantle.

A dataset of waveforms and differential travel times of S, ScS, and the arrival from the D" layer, Scd, provides evidence for a laterally varying V_s velocity discontinuity at the base of the mantle. Two different localized D" regions beneath the central Pacific have been investigated. Predictions from a model having a V_s discontinuity 180 km above the CMB agree well with observations for an eastern mid-Pacific CMB region. This thickness differs from V_s discontinuity thicknesses found in other regions, such as a localized region beneath the western Pacific, which average near 280 km. The "sharpness" of the V_s jump at the top of D", i.e., the depth range over which the V_s increase occurs, is not resolved by our data, and our data can in fact may be modeled equally well by a lower mantle with the increase in V_s at the top of D" occurring over a 100 krn depth range. It is difficult at present to correlate D" thicknesses from this study to overall lower mantle heterogeneity, due to uncertainties in the 3-D models, as well as poor coverage in maps of D" discontinuity thicknesses.

P-wave velocity structure (V_p) at the base of the mantle is explored using the seismic phases SKS and SPdKS. SPdKS is formed when SKS waves at distances around 107° are incident upon the CMB with a slowness that allows for coupling with diffracted P-waves at the base of the mantle. The P-wave diffraction occurs at both the SKS entrance and exit locations of the outer core. SP_dKS arrives slightly later in time than SKS, having a wave path through the mantle and core very close to SKS. The difference time between SKS and SP_dKS strongly depends on V_p at the base of the mantle near SK Score entrance and exit points. Observations from deep focus Fiji-Tonga events recorded by North American stations, and South American events recorded by European and Eurasian stations exhibit anomalously large SP_dKS - SKS difference times. SKS and the later arriving SP_dKS phase are separated by several seconds more than predictions made by 1-D reference models, such as the global average PREM [Dziewonski and Anderson, 1981] model. Models having a pronounced low-velocity zone (5%) in V_p in the bottom 50-100 km of the mantle predict the size of the observed SP_dK S-SKS anomalies. Raypath perturbations from lower mantle V_s structure may also be contributing to the observed anomalies.

Outer core structure is investigated using the family of SmKS (m=2,3,4) seismic waves. SmKS are waves that travel as S-waves in the mantle, P-waves in the core, and reflect (m-1) times on the underside of the CMB, and are well-suited for constraining outermost core V_p structure. This is due to closeness of the mantle paths and also the shallow depth range these waves travel in the outermost core. S3KS - S2KS and S4KS - S3KS differential travel times were measured using the cross-correlation method and compared to those from reflectivity synthetics created from core models of past studies. High quality recordings from a deep focus Java Sea event which sample the outer core beneath the northern Pacific, the Arctic, and northwestern North America (spanning 1/8th of the core's surface area), have SmKS wavepaths that traverse regions where lower mantle heterogeneity is pre- dieted small, and are well-modeled by the PREM core model, with possibly a small V_p decrease (1.5%) in the outermost 50 km of the core. Such a reduction implies chemical stratification in this 50 km zone, though this model feature is not uniquely resolved. Data having wave paths through areas of known D" heterogeneity (±2% and greater), such as the source-side of SmKS lower mantle paths from Fiji-Tonga to Eurasia and Africa, exhibit systematic SmKS differential time anomalies of up to several seconds. 2-D wave propagation experiments demonstrate how large scale lower mantle velocity perturbations can explain long wavelength behavior of such anomalous SmKS times. When improperly accounted for, lower mantle heterogeneity maps directly into core structure. Raypaths departing from homogeneity play an important role in producing SmKS anomalies. The existence of outermost core heterogeneity is difficult to resolve at present due to uncertainties in global lower mantle structure. Resolving a one-dimensional chemically stratified outermost core also remains difficult due to the same uncertainties. Restricting study to higher multiples of SmKS (m=2,3,4) can help reduce the affect of mantle heterogeneity due to the closeness of the mantle legs of the wavepaths. SmKS waves are ideal in providing additional information on the details of lower mantle heterogeneity.

Structure of the earth's core and lowermost mantle from seismic PKP waves

This thesis addresses the fine structure, both radial and lateral, of compressional wave velocity and attenuation of the Earth's core and the lowermost mantle using waveforms, differential travel times and amplitudes of PKP waves, which penetrate the Earth's core.

The structure near the inner core boundary (ICB) is studied by analyzing waveforms of a regional sample. The waveform modeling approach is demonstrated to be an effective tool for constrainning the ICB structure. The best model features a sharp velocity jump of 0.78km/s at the ICB and a low velocity gradient at the lowermost outer core (indicating possible inhomogeneity) and high attenuation at the top of the inner core.

A spherically symmetric P-wave model of the core, is proposed from PKP differential times, waveforms and amplitudes. The ICB remains sharp with a velocity jump of 0. 78km/ s. A very low velocity gradient at the base of the fluid core is demonstrated to be a robust feature, indicating inhomogeneity is practically inevitable. The model also indicates that the attenuation in the inner core decreases with depth. The velocity at D" is smaller than PREM.

The inner core is confirmed to be very anisotropic, possessing a cylindrical symmetry around the Earth spin axis with the N-S direction 3% faster than the E-W direction. All of the N-S rays through the inner core were found to be faster than the E-W rays by 1.5 to 3.5s. Exhaustive data selection and efforts in insolating contributions from the region above ensure that this is an inner core feature.

The anisotropy at the very top of the inner core is found to be distinctly different from the deeper part. The top 60km of the inner core is not anisotropic. From 60km to 150km, there appears to be a transition from isotropy to anisotropy.

PKP differential travel times are used to study the P velocity structure in D". Systematic regional variations of up to 2s in AB-DF times were observed, attributed primarily to heterogeneities in the lower 500km of the mantle. However, direct comparisons with tomographic models are not successful.

Earthquakes of the Nepal Himalaya : towards a physical model of the seismic cycle

Home to hundreds of millions of souls and land of excessiveness, the Himalaya is also the locus of a unique seismicity whose scope and peculiarities still remain to this day somewhat mysterious. Having claimed the lives of kings, or turned ancient timeworn cities into heaps of rubbles and ruins, earthquakes eerily inhabit Nepalese folk tales with the fatalistic message that nothing lasts forever. From a scientific point of view as much as from a human perspective, solving the mysteries of Himalayan seismicity thus represents a challenge of prime importance. Documenting geodetic strain across the Nepal Himalaya with various GPS and leveling data, we show that unlike other subduction zones that exhibit a heterogeneous and patchy coupling pattern along strike, the last hundred kilometers of the Main Himalayan Thrust fault, or MHT, appear to be uniformly locked, devoid of any of the “creeping barriers” that traditionally ward off the propagation of large events. The approximately 20 mm/yr of reckoned convergence across the Himalaya matching previously established estimates of the secular deformation at the front of the arc, the slip accumulated at depth has to somehow elastically propagate all the way to the surface at some point. And yet, neither large events from the past nor currently recorded microseismicity nearly compensate for the massive moment deficit that quietly builds up under the giant mountains. Along with this large unbalanced moment deficit, the uncommonly homogeneous coupling pattern on the MHT raises the question of whether or not the locked portion of the MHT can rupture all at once in a giant earthquake. Univocally answering this question appears contingent on the still elusive estimate of the magnitude of the largest possible earthquake in the Himalaya, and requires tight constraints on local fault properties. What makes the Himalaya enigmatic also makes it the potential source of an incredible wealth of information, and we exploit some of the oddities of Himalayan seismicity in an effort to improve the understanding of earthquake physics and cipher out the properties of the MHT. Thanks to the Himalaya, the Indo-Gangetic plain is deluged each year under a tremendous amount of water during the annual summer monsoon that collects and bears down on the Indian plate enough to pull it away from the Eurasian plate slightly, temporarily relieving a small portion of the stress mounting on the MHT. As the rainwater evaporates in the dry winter season, the plate rebounds and tension is increased back on the fault. Interestingly, the mild waggle of stress induced by the monsoon rains is about the same size as that from solid-Earth tides which gently tug at the planets solid layers, but whereas changes in earthquake frequency correspond with the annually occurring monsoon, there is no such correlation with Earth tides, which oscillate back-and-forth twice a day. We therefore investigate the general response of the creeping and seismogenic parts of MHT to periodic stresses in order to link these observations to physical parameters. First, the response of the creeping part of the MHT is analyzed with a simple spring-and-slider system bearing rate-strengthening rheology, and we show that at the transition with the locked zone, where the friction becomes near velocity neutral, the response of the slip rate may be amplified at some periods, which values are analytically related to the physical parameters of the problem. Such predictions therefore hold the potential of constraining fault properties on the MHT, but still await observational counterparts to be applied, as nothing indicates that the variations of seismicity rate on the locked part of the MHT are the direct expressions of variations of the slip rate on its creeping part, and no variations of the slip rate have been singled out from the GPS measurements to this day. When shifting to the locked seismogenic part of the MHT, spring-and-slider models with rate-weakening rheology are insufficient to explain the contrasted responses of the seismicity to the periodic loads that tides and monsoon both place on the MHT. Instead, we resort to numerical simulations using the Boundary Integral CYCLes of Earthquakes algorithm and examine the response of a 2D finite fault embedded with a rate-weakening patch to harmonic stress perturbations of various periods. We show that such simulations are able to reproduce results consistent with a gradual amplification of sensitivity as the perturbing period get larger, up to a critical period corresponding to the characteristic time of evolution of the seismicity in response to a step-like perturbation of stress. This increase of sensitivity was not reproduced by simple 1D-spring-slider systems, probably because of the complexity of the nucleation process, reproduced only by 2D-fault models. When the nucleation zone is close to its critical unstable size, its growth becomes highly sensitive to any external perturbations and the timings of produced events may therefore find themselves highly affected. A fully analytical framework has yet to be developed and further work is needed to fully describe the behavior of the fault in terms of physical parameters, which will likely provide the keys to deduce constitutive properties of the MHT from seismological observations.

Effect of nonuniform seismic input on arch dams

Standard earthquake analyses of civil engineering structures use uniform ground motions even though considerable variations in both amplitude and phase can occur along the foundation interface for long-span bridges and large dams. The objective of this thesis is to quantify the effect that these nonuniformities have on the structural response.

The nonuniform, free-field motions of the foundation interface are assumed to be caused by incident plane body waves. The medium in which these waves travel is a linear, elastic half-space containing a canyon of uniform cross section in which the structure is placed. The solutions for the free-field motions that are due to incident SH, P and SV waves are calculated using the boundary element method.

An analysis of Pacoima (arch) dam located near Los Angeles, California, is performed for both uniform and nonuniform excitations. The important effect of nonuniformities in the free-field motions, sometimes leading to a decrease in the dam response and sometimes to an increase, is quantified.

Characterization of diverse megathrust fault behavior related to seismic supercycles, Mentawai Islands, Sumatra

Long paleoseismic histories are necessary for understanding the full range of behavior of faults, as the most destructive events often have recurrence intervals longer than local recorded history. The Sunda megathrust, the interface along which the Australian plate subducts beneath Southeast Asia, provides an ideal natural laboratory for determining a detailed paleoseismic history over many seismic cycles. The outer-arc islands above the seismogenic portion of the megathrust cyclically rise and subside in response to processes on the underlying megathrust, providing uncommonly good illumination of megathrust behavior. Furthermore, the growth histories of coral microatolls, which record tectonic uplift and subsidence via relative sea level, can be used to investigate the detailed coseismic and interseismic deformation patterns. One particularly interesting area is the Mentawai segment of the megathrust, which has been shown to characteristically fail in a series of ruptures over decades, rather than a single end-to-end rupture. This behavior has been termed a seismic “supercycle.” Prior to the current rupture sequence, which began in 2007, the segment previously ruptured during the 14th century, the late 16th to late 17th century, and most recently during historical earthquakes in 1797 and 1833. In this study, we examine each of these previous supercycles in turn.

First, we expand upon previous analysis of the 1797–1833 rupture sequence with a comprehensive review of previously published coral microatoll data and the addition of a significant amount of new data. We present detailed maps of coseismic uplift during the two great earthquakes and of interseismic deformation during the periods 1755–1833 and 1950–1997 and models of the corresponding slip and coupling on the underlying megathrust. We derive magnitudes of Mw 8.7–9.0 for the two historical earthquakes, and determine that the 1797 earthquake fundamentally changed the state of coupling on the fault for decades afterward. We conclude that while major earthquakes generally do not involve rupture of the entire Mentawai segment, they undoubtedly influence the progression of subsequent ruptures, even beyond their own rupture area. This concept is of vital importance for monitoring and forecasting the progression of the modern rupture sequence.

Turning our attention to the 14th century, we present evidence of a shallow slip event in approximately A.D. 1314, which preceded the “conventional” megathrust rupture sequence. We calculate a suite of slip models, slightly deeper and/or larger than the 2010 Pagai Islands earthquake, that are consistent with the large amount of subsidence recorded at our study site. Sea-level records from older coral microatolls suggest that these events occur at least once every millennium, but likely far less frequently than their great downdip neighbors. The revelation that shallow slip events are important contributors to the seismic cycle of the Mentawai segment further complicates our understanding of this subduction megathrust and our assessment of the region’s exposure to seismic and tsunami hazards.

Finally, we present an outline of the complex intervening rupture sequence that took place in the 16th and 17th centuries, which involved at least five distinct uplift events. We conclude that each of the supercycles had unique features, and all of the types of fault behavior we observe are consistent with highly heterogeneous frictional properties of the megathrust beneath the south-central Mentawai Islands. We conclude that the heterogeneous distribution of asperities produces terminations and overlap zones between fault ruptures, resulting in the seismic “supercycle” phenomenon.

Control of single attosecond pulse generation from the reflection of a synthesized relativistic laser pulse on a solid surface

The influence of the carrier-envelope phase (CEP) of the driving laser pulse on the generation of single attosecond (as) pulses from surface harmonics by using the polarization gating technique is investigated in detail. It is found that the modulation depth of the high-order harmonic spectrum depends on the CEP, and a strong single 68 as pulse can be generated when the CEP is stable and has the proper value. The physical origin of the influence of the CEP is explained in terms of the oscillating mirror model. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2997342]

Planar reflection of gaseous detonations

Pipes containing flammable gaseous mixtures may be subjected to internal detonation. When the detonation normally impinges on a closed end, a reflected shock wave is created to bring the flow back to rest. This study built on the work of Karnesky (2010) and examined deformation of thin-walled stainless steel tubes subjected to internal reflected gaseous detonations. A ripple pattern was observed in the tube wall for certain fill pressures, and a criterion was developed that predicted when the ripple pattern would form. A two-dimensional finite element analysis was performed using Johnson-Cook material properties; the pressure loading created by reflected gaseous detonations was accounted for with a previously developed pressure model. The residual plastic strain between experiments and computations was in good agreement.

During the examination of detonation-driven deformation, discrepancies were discovered in our understanding of reflected gaseous detonation behavior. Previous models did not accurately describe the nature of the reflected shock wave, which motivated further experiments in a detonation tube with optical access. Pressure sensors and schlieren images were used to examine reflected shock behavior, and it was determined that the discrepancies were related to the reaction zone thickness extant behind the detonation front. During these experiments reflected shock bifurcation did not appear to occur, but the unfocused visualization system made certainty impossible. This prompted construction of a focused schlieren system that investigated possible shock wave-boundary layer interaction, and heat-flux gauges analyzed the boundary layer behind the detonation front. Using these data with an analytical boundary layer solution, it was determined that the strong thermal boundary layer present behind the detonation front inhibits the development of reflected shock wave bifurcation.

Cloud computing services for seismic networks

This thesis describes a compositional framework for developing situation awareness applications: applications that provide ongoing information about a user's changing environment. The thesis describes how the framework is used to develop a situation awareness application for earthquakes. The applications are implemented as Cloud computing services connected to sensors and actuators. The architecture and design of the Cloud services are described and measurements of performance metrics are provided. The thesis includes results of experiments on earthquake monitoring conducted over a year. The applications developed by the framework are (1) the CSN --- the Community Seismic Network --- which uses relatively low-cost sensors deployed by members of the community, and (2) SAF --- the Situation Awareness Framework --- which integrates data from multiple sources, including the CSN, CISN --- the California Integrated Seismic Network, a network consisting of high-quality seismometers deployed carefully by professionals in the CISN organization and spread across Southern California --- and prototypes of multi-sensor platforms that include carbon monoxide, methane, dust and radiation sensors.

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.

Methods of multiparameter inversion of seismic data using the acoustic and elastic born approximations

This thesis presents two different forms of the Born approximations for acoustic and elastic wavefields and discusses their application to the inversion of seismic data. The Born approximation is valid for small amplitude heterogeneities superimposed over a slowly varying background. The first method is related to frequency-wavenumber migration methods. It is shown to properly recover two independent acoustic parameters within the bandpass of the source time function of the experiment for contrasts of about 5 percent from data generated using an exact theory for flat interfaces. The independent determination of two parameters is shown to depend on the angle coverage of the medium. For surface data, the impedance profile is well recovered.

The second method explored is mathematically similar to iterative tomographic methods recently introduced in the geophysical literature. Its basis is an integral relation between the scattered wavefield and the medium parameters obtained after applying a far-field approximation to the first-order Born approximation. The Davidon-Fletcher-Powell algorithm is used since it converges faster than the steepest descent method. It consists essentially of successive backprojections of the recorded wavefield, with angular and propagation weighing coefficients for density and bulk modulus. After each backprojection, the forward problem is computed and the residual evaluated. Each backprojection is similar to a before-stack Kirchhoff migration and is therefore readily applicable to seismic data. Several examples of reconstruction for simple point scatterer models are performed. Recovery of the amplitudes of the anomalies are improved with successive iterations. Iterations also improve the sharpness of the images.

The elastic Born approximation, with the addition of a far-field approximation is shown to correspond physically to a sum of WKBJ-asymptotic scattered rays. Four types of scattered rays enter in the sum, corresponding to P-P, P-S, S-P and S-S pairs of incident-scattered rays. Incident rays propagate in the background medium, interacting only once with the scatterers. Scattered rays propagate as if in the background medium, with no interaction with the scatterers. An example of P-wave impedance inversion is performed on a VSP data set consisting of three offsets recorded in two wells.

Travel time tomographic studies of seismic structures around subducted lithospheric slabs

The nature of the subducted lithospheric slab is investigated seismologically by tomographic inversions of ISC residual travel times. The slab, in which nearly all deep earthquakes occur, is fast in the seismic images because it is much cooler than the ambient mantle. High resolution three-dimensional P and S wave models in the NW Pacific are obtained using regional data, while inversion for the SW Pacific slabs includes teleseismic arrivals. Resolution and noise estimations show the models are generally well-resolved.

The slab anomalies in these models, as inferred from the seismicity, are generally coherent in the upper mantle and become contorted and decrease in amplitude with depth. Fast slabs are surrounded by slow regions shallower than 350 km depth. Slab fingering, including segmentation and spreading, is indicated near the bottom of the upper mantle. The fast anomalies associated with the Japan, Izu-Bonin, Mariana and Kermadec subduction zones tend to flatten to sub-horizontal at depth, while downward spreading may occur under parts of the Mariana and Kuril arcs. The Tonga slab appears to end around 550 km depth, but is underlain by a fast band at 750-1000 km depths.

The NW Pacific model combined with the Clayton-Comer mantle model predicts many observed residual sphere patterns. The predictions indicate that the near-source anomalies affect the residual spheres less than the teleseismic contributions. The teleseismic contributions may be removed either by using a mantle model, or using teleseismic station averages of residuals from only regional events. The slab-like fast bands in the corrected residual spheres are are consistent with seismicity trends under the Mariana Tzu-Bonin and Japan trenches, but are inconsistent for the Kuril events.

The comparison of the tomographic models with earthquake focal mechanisms shows that deep compression axes and fast velocity slab anomalies are in consistent alignment, even when the slab is contorted or flattened. Abnormal stress patterns are seen at major junctions of the arcs. The depth boundary between tension and compression in the central parts of these arcs appears to depend on the dip and topology of the slab.