Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.

I. Foehn winds of southern California. II. Foehn wind cyclo-genesis. III. Weather conditions associated with the Akron disaster. IV. The Los Angeles storm of December 30, 1933 to January 1, 1934

I. Foehn winds of southern California.
An investigation of the hot, dry and dust laden winds occurring in the late fall and early winter in the Los Angeles Basin and attributed in the past to the influences of the desert regions to the north revealed that these currents were of a foehn nature. Their properties were found to be entirely due to dynamical heating produced in the descent from the high level areas in the interior to the lower Los Angeles Basin. Any dust associated with the phenomenon was found to be acquired from the Los Angeles area rather than transported from the desert. It was found that the frequency of occurrence of a mild type foehn of this nature during this season was sufficient to warrant its classification as a winter monsoon. This results from the topography of the Los Angeles region which allows an easy entrance to the air from the interior by virtue of the low level mountain passes north of the area. This monsoon provides the mild winter climate of southern California since temperatures associated with the foehn currents are far higher than those experienced when maritime air from the adjacent Pacific Ocean occupies the region.

II. Foehn wind cyclo-genesis.
Intense anticyclones frequently build up over the high level regions of the Great Basin and Columbia Plateau which lie between the Sierra Nevada and Cascade Mountains to the west and the Rocky Mountains to the east. The outflow from these anticyclones produce extensive foehns east of the Rockies in the comparatively low level areas of the middle west and the Canadian provinces of Alberta and Saskatchewan. Normally at this season of the year very cold polar continental air masses are present over this territory and with the occurrence of these foehns marked discontinuity surfaces arise between the warm foehn current, which is obliged to slide over a colder mass, and the Pc air to the east. Cyclones are easily produced from this phenomenon and take the form of unstable waves which propagate along the discontinuity surface between the two dissimilar masses. A continual series of such cyclones was found to occur as long as the Great Basin anticyclone is maintained with undiminished intensity.

III. Weather conditions associated with the Akron disaster.
This situation illustrates the speedy development and propagation of young disturbances in the eastern United States during the spring of the year under the influence of the conditionally unstable tropical maritime air masses which characterise the region. It also furnishes an excellent example of the superiority of air mass and frontal methods of weather prediction for aircraft operation over the older methods based upon pressure distribution.

IV. The Los Angeles storm of December 30, 1933 to January 1, 1934.
This discussion points out some of the fundamental interactions occurring between air masses of the North Pacific Ocean in connection with Pacific Coast storms and the value of topographic and aerological considerations in predicting them. Estimates of rainfall intensity and duration from analyses of this type may be made and would prove very valuable in the Los Angeles area in connection with flood control problems.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

The Pacoima Area

The Pacoima area consists of Miocene (sediments and basalts) rocks underlain by a quartz diorite basement complex of Jurassic age. The stratigranhic units range from 25 feet to more than 600 feet in thickness. The lower sediments are arkosic land- laid deposits while the Modelo formation, shallow marine in origin, consists of thinly bedded sandstones, shales, volcanic ash and calcareous members. An andesitic mass, possibly a volcanic plug, outcrops near the summit of one of the hills.

An anticline, and possibly an associated syncline, has been developed by compressional folding. Small scale contortion is locally exposed. Regional dip is northward, decreasing from south to north in the area. Faulting is common, most faults trending nearly north-south. Movement along these faults ranges from a few feet to several hundred feet.

There are no important mineral deposits in the area. Quarrying of the basement rocks has been abandoned.

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.