Using Earth Deformation Caused by Surface Mass Loading to Constrain the Elastic Structure of the Crust and Mantle

Surface mass loads come in many different varieties, including the oceans, atmosphere, rivers, lakes, glaciers, ice caps, and snow fields. The loads migrate over Earth's surface on time scales that range from less than a day to many thousand years. The weights of the shifting loads exert normal forces on Earth's surface. Since the Earth is not perfectly rigid, the applied pressure deforms the shape of the solid Earth in a manner controlled by the material properties of Earth's interior. One of the most prominent types of surface mass loading, ocean tidal loading (OTL), comes from the periodic rise and fall in sea-surface height due to the gravitational influence of celestial objects, such as the moon and sun. Depending on geographic location, the surface displacements induced by OTL typically range from millimeters to several centimeters in amplitude, which may be inferred from Global Navigation and Satellite System (GNSS) measurements with sub-millimeter precision. Spatiotemporal characteristics of observed OTL-induced surface displacements may therefore be exploited to probe Earth structure. In this thesis, I present descriptions of contemporary observational and modeling techniques used to explore Earth's deformation response to OTL and other varieties of surface mass loading. With the aim to extract information about Earth's density and elastic structure from observations of the response to OTL, I investigate the sensitivity of OTL-induced surface displacements to perturbations in the material structure. As a case study, I compute and compare the observed and predicted OTL-induced surface displacements for a network of GNSS receivers across South America. The residuals in three distinct and dominant tidal bands are sub-millimeter in amplitude, indicating that modern ocean-tide and elastic-Earth models well predict the observed displacement response in that region. Nevertheless, the sub-millimeter residuals exhibit regional spatial coherency that cannot be explained entirely by random observational uncertainties and that suggests deficiencies in the forward-model assumptions. In particular, the discrepancies may reveal sensitivities to deviations from spherically symmetric, non-rotating, elastic, and isotropic (SNREI) Earth structure due to the presence of the South American craton.

Liquid silicate equation of state : using shock waves to understand the properties of the deep Earth

The equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe₂SiO₄ (fayalite), Mg₂SiO₄ (forsterite), CaFeSi₂O₆ (hedenbergite), an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆ (anorthite-hedenbergite), and an equimolar mixture of CaAl₂Si₂O₈-CaFeSi₂O₆-CaMgSi₂O₆(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi₂O₆ (diopside), CaAl₂Si₂O₈ (anorthite), and MgSiO₃ (enstatite), which were previously determined by shock wave methods, are also presented.

The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al₂O₃-SiO₂-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.

The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar X_Fe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

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.

Constraints on the carbon cycle and climate during the early evolution of animals

One of the greatest challenges in science lies in disentangling causality in complex, coupled systems. This is illustrated no better than in the dynamic interplay between the Earth and life. The early evolution and diversification of animals occurred within a backdrop of global change, yet reconstructing the potential role of the environment in this evolutionary transition is challenging. In the 200 million years from the end-Cryogenian to the Ordovician, enigmatic Ediacaran fauna explored body plans, animals diversified and began to biomineralize, forever changing the ocean's chemical cycles, and the biological community in shallow marine ecosystems transitioned from a microbial one to an animal one.

In the following dissertation, a multi-faceted approach combining macro- and micro-scale analyses is presented that draws on the sedimentology, geochemistry and paleontology of the rocks that span this transition to better constrain the potential environmental changes during this interval.

In Chapter 1, the potential of clumped isotope thermometry in deep time is explored by assessing the importance of burial and diagenesis on the thermometer. Eocene- to Precambrian-aged carbonates from the Sultanate of Oman were analyzed from current burial depths of 350-5850 meters. Two end-member styles of diagenesis independent of burial depth were observed.

Chapters 2, 3 and 4 explore the fallibility of the Ediacaran carbon isotope record and aspects of the sedimentology and geochemistry of the rocks preserving the largest negative carbon isotope excursion on record---the Shuram Excursion. Chapter 2 documents the importance of temperature, fluid composition and mineralogy on the delta 18-O min record and interrogates the bulk trace metal signal. Chapter 3 explores the spatial variability in delta 13-C recorded in the transgressive Johnnie Oolite and finds a north-to-south trend recording the onset of the excursion. Chapter 4 investigates the nature of seafloor precipitation during this excursion and more broadly. We document the potential importance of microbial respiratory reactions on the carbonate chemistry of the sediment-water interface through time.

Chapter 5 investigates the latest Precambrian sedimentary record in carbonates from the Sultanate of Oman, including how delta 13-C and delta 34-S CAS vary across depositional and depth gradients. A new model for the correlation of the Buah and Ara formations across Oman is presented. Isotopic results indicate delta 13-C varies with relative eustatic change and delta 34-S CAS may vary in absolute magnitude across Oman.

Chapter 6 investigates the secular rise in delta 18-Omin in the early Paleozoic by using clumped isotope geochemistry on calcitic and phosphatic fossils from the Cambrian and Ordovician. Results do not indicate extreme delta 18-O seawater depletion and instead suggest warmer equatorial temperatures across the early Paleozoic.

I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering

This dissertation consists of two parts. The first part presents an explicit procedure for applying multi-Regge theory to production processes. As an illustrative example, the case of three body final states is developed in detail, both with respect to kinematics and multi-Regge dynamics. Next, the experimental consistency of the multi-Regge hypothesis is tested in a specific high energy reaction; the hypothesis is shown to provide a good qualitative fit to the data. In addition, the results demonstrate a severe suppression of double Pomeranchon exchange, and show the coupling of two "Reggeons" to an external particle to be strongly damped as the particle's mass increases. Finally, with the use of two body Regge parameters, order of magnitude estimates of the multi-Regge cross section for various reactions are given.

The second part presents a diffraction model for high energy proton-proton scattering. This model developed by Chou and Yang assumes high energy elastic scattering results from absorption of the incident wave into the many available inelastic channels, with the absorption proportional to the amount of interpenetrating hadronic matter. The assumption that the hadronic matter distribution is proportional to the charge distribution relates the scattering amplitude for pp scattering to the proton form factor. The Chou-Yang model with the empirical proton form factor as input is then applied to calculate a high energy, fixed momentum transfer limit for the scattering cross section, This limiting cross section exhibits the same "dip" or "break" structure indicated in present experiments, but falls significantly below them in magnitude. Finally, possible spin dependence is introduced through a weak spin-orbit type term which gives rather good agreement with pp polarization data.

Part I. A study of the velocity structure of the earth by the use of core phases. Part II. The 1971 San Fernando earthquake series focal mechanisms and tectonics

The initial objective of Part I was to determine the nature of upper mantle discontinuities, the average velocities through the mantle, and differences between mantle structure under continents and oceans by the use of P'dP', the seismic core phase P'P' (PKPPKP) that reflects at depth d in the mantle. In order to accomplish this, it was found necessary to also investigate core phases themselves and their inferences on core structure. P'dP' at both single stations and at the LASA array in Montana indicates that the following zones are candidates for discontinuities with varying degrees of confidence: 800-950 km, weak; 630-670 km, strongest; 500-600 km, strong but interpretation in doubt; 350-415 km, fair; 280-300 km, strong, varying in depth; 100-200 km, strong, varying in depth, may be the bottom of the low-velocity zone. It is estimated that a single station cannot easily discriminate between asymmetric P'P' and P'dP' for lead times of about 30 sec from the main P'P' phase, but the LASA array reduces this uncertainty range to less than 10 sec. The problems of scatter of P'P' main-phase times, mainly due to asymmetric P'P', incorrect identification of the branch, and lack of the proper velocity structure at the velocity point, are avoided and the analysis shows that one-way travel of P waves through oceanic mantle is delayed by 0.65 to 0.95 sec relative to United States mid-continental mantle.

A new P-wave velocity core model is constructed from observed times, dt/dΔ's, and relative amplitudes of P'; the observed times of SKS, SKKS, and PKiKP; and a new mantle-velocity determination by Jordan and Anderson. The new core model is smooth except for a discontinuity at the inner-core boundary determined to be at a radius of 1215 km. Short-period amplitude data do not require the inner core Q to be significantly lower than that of the outer core. Several lines of evidence show that most, if not all, of the arrivals preceding the DF branch of P' at distances shorter than 143° are due to scattering as proposed by Haddon and not due to spherically symmetric discontinuities just above the inner core as previously believed. Calculation of the travel-time distribution of scattered phases and comparison with published data show that the strongest scattering takes place at or near the core-mantle boundary close to the seismic station.

In Part II, the largest events in the San Fernando earthquake series, initiated by the main shock at 14 00 41.8 GMT on February 9, 1971, were chosen for analysis from the first three months of activity, 87 events in all. The initial rupture location coincides with the lower, northernmost edge of the main north-dipping thrust fault and the aftershock distribution. The best focal mechanism fit to the main shock P-wave first motions constrains the fault plane parameters to: strike, N 67° (± 6°) W; dip, 52° (± 3°) NE; rake, 72° (67°-95°) left lateral. Focal mechanisms of the aftershocks clearly outline a downstep of the western edge of the main thrust fault surface along a northeast-trending flexure. Faulting on this downstep is left-lateral strike-slip and dominates the strain release of the aftershock series, which indicates that the downstep limited the main event rupture on the west. The main thrust fault surface dips at about 35° to the northeast at shallow depths and probably steepens to 50° below a depth of 8 km. This steep dip at depth is a characteristic of other thrust faults in the Transverse Ranges and indicates the presence at depth of laterally-varying vertical forces that are probably due to buckling or overriding that causes some upward redirection of a dominant north-south horizontal compression. Two sets of events exhibit normal dip-slip motion with shallow hypocenters and correlate with areas of ground subsidence deduced from gravity data. Several lines of evidence indicate that a horizontal compressional stress in a north or north-northwest direction was added to the stresses in the aftershock area 12 days after the main shock. After this change, events were contained in bursts along the downstep and sequencing within the bursts provides evidence for an earthquake-triggering phenomenon that propagates with speeds of 5 to 15 km/day. Seismicity before the San Fernando series and the mapped structure of the area suggest that the downstep of the main fault surface is not a localized discontinuity but is part of a zone of weakness extending from Point Dume, near Malibu, to Palmdale on the San Andreas fault. This zone is interpreted as a decoupling boundary between crustal blocks that permits them to deform separately in the prevalent crustal-shortening mode of the Transverse Ranges region.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

Establishing the C. elegans uterine seam cell (utse) as a novel model for studying cell behavior

The molecular inputs necessary for cell behavior are vital to our understanding of development and disease. Proper cell behavior is necessary for processes ranging from creating one’s face (neural crest migration) to spreading cancer from one tissue to another (invasive metastatic cancers). Identifying the genes and tissues involved in cell behavior not only increases our understanding of biology but also has the potential to create targeted therapies in diseases hallmarked by aberrant cell behavior.

A well-characterized model system is key to determining the molecular and spatial inputs necessary for cell behavior. In this work I present the C. elegans uterine seam cell (utse) as an ideal model for studying cell outgrowth and shape change. The utse is an H-shaped cell within the hermaphrodite uterus that functions in attaching the uterus to the body wall. Over L4 larval stage, the utse grows bidirectionally along the anterior-posterior axis, changing from an ellipsoidal shape to an elongated H-shape. Spatially, the utse requires the presence of the uterine toroid cells, sex muscles, and the anchor cell nucleus in order to properly grow outward. Several gene families are involved in utse development, including Trio, Nav, Rab GTPases, Arp2/3, as well as 54 other genes found from a candidate RNAi screen. The utse can be used as a model system for studying metastatic cancer. Meprin proteases are involved in promoting invasiveness of metastatic cancers and the meprin-likw genes nas-21, nas-22, and toh-1 act similarly within the utse. Studying nas-21 activity has also led to the discovery of novel upstream inhibitors and activators as well as targets of nas-21, some of which have been characterized to affect meprin activity. This illustrates that the utse can be used as an in vivo model for learning more about meprins, as well as various other proteins involved in metastasis.

Solar System Small-Body Demographics with the Palomar Transient Factory Survey

Observational studies of our solar system's small-body populations (asteroids and comets) offer insight into the history of our planetary system, as these minor planets represent the left-over building blocks from its formation. The Palomar Transient Factory (PTF) survey began in 2009 as the latest wide-field sky-survey program to be conducted on the 1.2-meter Samuel Oschin telescope at Palomar Observatory. Though its main science program has been the discovery of high-energy extragalactic sources (such as supernovae), during its first five years PTF has collected nearly five million observations of over half a million unique solar system small bodies. This thesis begins to analyze this vast data set to address key population-level science topics, including: the detection rates of rare main-belt comets and small near-Earth asteroids, the spin and shape properties of asteroids as inferred from their lightcurves, the applicability of this visible light data to the interpretation of ultraviolet asteroid observations, and a comparison of the physical properties of main-belt and Jovian Trojan asteroids. Future sky-surveys would benefit from application of the analytical techniques presented herein, which include novel modeling methods and unique applications of machine-learning classification. The PTF asteroid small-body data produced in the course of this thesis work should remain a fertile source of solar system science and discovery for years to come.

Regional variations in upper mantle structure beneath North America

Several types of seismological data, including surface wave group and phase velocities, travel times from large explosions, and teleseismic travel time anomalies, have indicated that there are significant regional variations in the upper few hundred kilometers of the mantle beneath continental areas. Body wave travel times and amplitudes from large chemical and nuclear explosions are used in this study to delineate the details of these variations beneath North America.

As a preliminary step in this study, theoretical P wave travel times, apparent velocities, and amplitudes have been calculated for a number of proposed upper mantle models, those of Gutenberg, Jeffreys, Lehman, and Lukk and Nersesov. These quantities have been calculated for both P and S waves for model CIT11GB, which is derived from surface wave dispersion data. First arrival times for all the models except that of Lukk and Nersesov are in close agreement, but the travel time curves for later arrivals are both qualitatively and quantitatively very different. For model CIT11GB, there are two large, overlapping regions of triplication of the travel time curve, produced by regions of rapid velocity increase near depths of 400 and 600 km. Throughout the distance range from 10 to 40 degrees, the later arrivals produced by these discontinuities have larger amplitudes than the first arrivals. The amplitudes of body waves, in fact, are extremely sensitive to small variations in the velocity structure, and provide a powerful tool for studying structural details.

Most of eastern North America, including the Canadian Shield has a Pn velocity of about 8.1 km/sec, with a nearly abrupt increase in compressional velocity by ~ 0.3 km/sec near at a depth varying regionally between 60 and 90 km. Variations in the structure of this part of the mantle are significant even within the Canadian Shield. The low-velocity zone is a minor feature in eastern North America and is subject to pronounced regional variations. It is 30 to 50 km thick, and occurs somewhere in the depth range from 80 to 160 km. The velocity decrease is less than 0.2 km/sec.

Consideration of the absolute amplitudes indicates that the attenuation due to anelasticity is negligible for 2 hz waves in the upper 200 km along the southeastern and southwestern margins of the Canadian Shield. For compressional waves the average Q for this region is > 3000. The amplitudes also indicate that the velocity gradient is at least 2 x 10^-3 both above and below the low-velocity zone, implying that the temperature gradient is < 4.8°C/km if the regions are chemically homogeneous.

In western North America, the low-velocity zone is a pronounced feature, extending to the base of the crust and having minimum velocities of 7.7 to 7.8 km/sec. Beneath the Colorado Plateau and Southern Rocky Mountains provinces, there is a rapid velocity increase of about 0.3 km/sec, similar to that observed in eastern North America, but near a depth of 100 km.

Complicated travel time curves observed on profiles with stations in both eastern and western North America can be explained in detail by a model taking into account the lateral variations in the structure of the low-velocity zone. These variations involve primarily the velocity within the zone and the depth to the top of the zone; the depth to the bottom is, for both regions, between 140 and 160 km.

The depth to the transition zone near 400 km also varies regionally, by about 30-40 km. These differences imply variations of 250 °C in the temperature or 6 % in the iron content of the mantle, if the phase transformation of olivine to the spinel structure is assumed responsible. The structural variations at this depth are not correlated with those at shallower depths, and follow no obvious simple pattern.

The computer programs used in this study are described in the Appendices. The program TTINV (Appendix IV) fits spherically symmetric earth models to observed travel time data. The method, described in Appendix III, resembles conventional least-square fitting, using partial derivatives of the travel time with respect to the model parameters to perturb an initial model. The usual ill-conditioned nature of least-squares techniques is avoided by a technique which minimizes both the travel time residuals and the model perturbations.

Spherically symmetric earth models, however, have been found inadequate to explain most of the observed travel times in this study. TVT4, a computer program that performs ray theory calculations for a laterally inhomogeneous earth model, is described in Appendix II. Appendix I gives a derivation of seismic ray theory for an arbitrarily inhomogeneous earth model.

An investigation of the three-body reaction He^3(He^3, 2p)He^4

Reactions produced by the He³ bombardment of the He³ have been investigated for bombarding energies from 1 to 20 MeV using a tandem Van de Graaff accelerator. Proton spectra from the three-body reaction He³(He³, 2p)He⁴ have been measured with a counter telescope at 13 angles for 9 bombarding energies between 3 and 18 MeV. The results are compared with a model for the reaction which includes a strong p-He⁴ final-state interaction. Alpha-particle spectra have been obtained at 12 and 18 MeV for forward angles with a magnetic spectrometer. These spectra indicate a strongly forward-peaked mechanism involving the ¹S₀ p-p interaction in addition to the p-He⁴ interaction. Measurements of p-He⁴ and p-p coincidence spectra at 10 MeV confirm these features of the reaction mechanism. Deuteron spectra from the reaction of He³(He³, d)pHe³ have been measured at 18 MeV. A triton spectrum from the reaction He³(He³, t)3p at 20 MeV and 4⁰ is interpreted in terms of a sequential decay through an excited state of the alpha particle at 20.0 MeV. No effects are observed which would indicate an interaction in the residual (3p) system. Below 3 MeV the He³(He³, 2p)He⁴ reaction mechanism is observed to be changing and further measurements are suggested in view of the importance of this reaction in stellar interiors.

Studies of noble gases in meteorites and in the earth

The isotopic and elemental abundances of noble gases in the solar system are investigated, using simple mixing models and mass-spectrometric measurements of the noble gases in meteorites and terrestrial rocks and minerals.

Primordial neon is modeled by two isotopically distinct components from the interstellar gas and dust. Neon from the gas dominates solar neon, which contains about ten times more ²⁰Ne than ²²Ne. Neon from the dust is represented in meteorites by neon-E, with ²⁰Ne/²²Ne less than 0.6. Isotopic variations in meteorites require neon from both dust and gas to be present. Mixing dust and gas without neon loss generates linear correlation lines on three-isotope and composition-concentration diagrams. A model for solar wind implantation predicts small deviations from linear mixing, due to preferential sputtering of the lighter neon isotopes.

Neon in meteorites consists of galactic cosmic ray spallation neon and at least two primordial components, neon-E and neon-S. Neon was measured in several meteorites to investigate these end- members. Cosmogenic neon produced from sodium is found to be strongly enriched in ²²Ne. Neon measurements on sodium-rich samples must be interpreted with care so not to confuse this source of ²²Ne with neon-E, which is also rich in ²²Ne.

Neon data for the carbonaceous chondrite Mokoia show that the end member composition of neon-Si in meteorites is ²⁰Ne/²²Ne = 13.7, the same as the present solar wind. The solar wind composition evidently has remained constant since before the compaction of Mokoia.

Ca, Al-rich inclusions from the Allende meteorite were examined for correlation between neon-E and oxygen or magnesium isotopic anomalies. ²²Ne and ³⁶Ar enrichments found in some inclusions are attributed to cosmic- ray-induced reactions on Na and Cl, not to a primordial component. Neon-E is not detectably enriched in Allende.

Measurements were made to determine the noble gas contents of various terrestrial rocks and minerals, and to investigate the cycling of noble gases between different terrestrial reservoirs. Beryl crystals contain a characteristic suite of magmatic gases including nucleogenic ²¹Ne and ²²Ne from (α,n) reactions, radiogenic ⁴⁰Ar, and fissiogenic ^131-136Xe from the decay of K and U in the continental crust. Significant concentrations of atmospheric noble gases are also present in beryl.

Both juvenile and atmospheric noble gases are found in rocks from the Skaergaard intrusion. The ratio ⁴⁰Ar/³⁶Ar (corrected for in situ decay of ⁴⁰K) correlates with δ¹⁸O in plagioclase. Atmospheric argon has been introduced into samples that have experienced oxygen-isotope exchange with circulating meteoric hydrothermal fluids. Unexchanged samples contain juvenile argon with ⁴⁰Ar/³⁶Ar greater than 6000 that was trapped from the Skaergaard magma.

Juvenile and atmospheric gases have been measured in the glassy rims of mid-ocean ridge (MOR) pillow basalts. Evidence is presented that three samples contain excess radiogenic ¹²⁹Xe and fission xenon, in addition to the excess radiogenic ⁴⁰Ar found in all samples. These juvenile gases are being outgassed from the upper-mantle source region of the MOR magma. No isotopic evidence has been found here for juvenile primordial noble gases accompanying the juvenile radiogenic gases in the MOR glasses. Large argon isotopic variations in a single specimen provide a clear indication of the late-stage addition of atmospheric argon, probably from seawater.

The Skaergaard data demonstrate that atmospheric noble gases dissolved in ground water can be transferred into crustal rocks. Subduction of oceanic crust altered by seawater can transport atmospheric noble gases into the upper mantle. A substantial portion of the noble gases in mantle derived rocks may represent subducted gases, not a primordial component as is often assumed.