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At least 991 records · Page 55
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NASA NTRS2008

Study of the Correlation between the Performances of Lunar Vehicle Wheels Predicted by the Nepean Wheeled Vehicle Performance Model and Test Data

This paper describes the results of a study of the correlation between the performances of wheels for lunar vehicles predicted using the Nepean wheeled vehicle performance model (NWVPM), developed under the auspices of Vehicle Systems Development Corporation, Ottawa, Canada, and the corresponding test data presented in Performance evaluation of wheels for lunar vehicles , Technical Report M-70-2, prepared for George C. Marshall Space Flight Center, National Aeronautics and Space Administration (NASA), USA, by the US Army Engineer Waterways Experiment Station (WES). The NWVPM was originally developed for design and performance evaluation of terrestrial off-road wheeled vehicles. The purpose of this study is to assess the potential of the NWVPM for evaluating wheel candidates for the new generation of extra-terrestrial vehicles. Two versions of a wire-mesh wheel and a hoop-spring wheel, which were considered as candidates for lunar roving vehicles for the NASA Apollo program in the late 1960s, together with a pneumatic wheel were examined in this study. The tractive performances of these wheels and of a 464 test vehicle with the pneumatic wheels on air-dry sand were predicted using the NWVPM and compared with the corresponding test data obtained under Earth s gravity and previously documented in the above-named report. While test data on wheel or vehicle performances obtained under Earth s gravity may not necessarily be representative of those on extra-terrestrial bodies, because of the differences in gravity and in environmental conditions, such as atmospheric pressure, it is still a valid approach to use test data obtained under Earth s gravity to evaluate the predictive capability of the NWVPM and its potential applications to predicting wheel or wheeled rover performances on extra-terrestrial bodies. Results of this study show that, using the ratio (P20/W) of the drawbar pull to normal load at 20 per cent slip as a performance indicator, there is a reasonable correlation between the predictions and experimental data. This indicates that the NWVPM has the potential as an engineering tool for evaluating wheel candidates for a future generation of extra-terrestrial vehicles, provided that appropriate input data are available.

Wong, J. Y.↗
NASA NTRS2008

Experimental and Numerical Characterization of High Heat Fluxes During Transient Blackbody Calibrations

High heat fluxes are encountered in numerous applications, such as hypersonic vehicles in flight, fires, and engines, Calibration of heat flux gages may be performed in a dual cavity cylindrical blackbody resulting in a transient calibration environment. To characterize the transient heat fluxes. experiments were performed on a dual cavity cylindrical blackbody at nominal temperatures varying from 800 C to 1900 C in increments of 100 C. Based on experiments, the optimum heat flux sensor insertion location as measured from the center partition was determined. The pre-insertion steady state axial temperature profile is compared experimentally, numerically, and analytically. The effect of convection in the blackbody cavity during the insertion is calculated and found to be less than 2 per cent. Also, an empirical correlation for predicting the emissivity of the blackbody is included. Detailed transient thermal models have been developed to simulate the heat flux calibration process at two extreme fluxes. The high (1MW/sq m) and relatively low (70 kw/sq m) fluxes are reported in this article. The transient models show the effect of inserting a heat flux gage at room temperature on the thermal equilibrium of the blackbody at 1800 C and 800 C nominal temperatures, respectively. Also, heat flux sensor outputs are derived from computed sensor temperature distributions and compared to experimental results.

Abdelmessih, Amanie N.↗
NASA NTRS2009

Timing of Crystallisation of the Lunar Magma Ocean Constrained by the Oldest Zircon

The presently favoured concept for the early evolution of the Moon involves consolidation of debris from a giant impact of a Mars sized body with Earth forming a primitive Moon with a thick global layer of melt referred to as the Lunar Magma Ocean1 . It is widely accepted that many significant features observed on the Moon today are the result of crystallisation of this magma ocean. However, controversy exists over the precise timing and duration of the crystallisation process. Resolution of this problem depends on the establishment of precise and robust key crystallisation time points. We report a 4417 6 Myr old zircon in lunar breccia sample 72215,195, which provides a precisely determined younger limit for the solidification of the Lunar Magma Ocean. A model based on these data, together with the age of the Moon forming giant impact, defines an exponential time frame for crystallisation and suggests formation of anorthositic crust after about 80-85% of the magma ocean was solidified. In combination with other zircon ages the 4417 +/- 6 Myr age also suggests that the very small (less than a few per cent) residual portion of the magma ocean continued to solidify during the following 300-500 m.y.

Nemchin, A.↗
NASA NTRS2010

Open Rotor Noise Prediction at NASA Langley - Capabilities, Research and Development

The high fuel prices of recent years have caused the operating cost of the airlines to soar. In an effort to bring down the fuel consumption, the major aircraft engine manufacturers are now taking a fresh look at open rotors for the propulsion of future airliners. Open rotors, also known as propfans or unducted fans, can offer up to 30 per cent improvement in efficiency compared to high bypass engines of 1980 vintage currently in use in most civilian aircraft. NASA Langley researchers have contributed significantly to the development of aeroacoustic technology of open rotors. This report discusses the current noise prediction technology at Langley and reviews the input data requirements, strengths and limitations of each method as well as the associated problems in need of attention by the researchers. We present a brief history of research on the aeroacoustics of rotating blade machinery at Langley Research Center. We then discuss the available noise prediction codes for open rotors developed at NASA Langley and their capabilities. In particular, we present the two useful formulations used for the computation of noise from subsonic and supersonic surfaces. Here we discuss the open rotor noise prediction codes ASSPIN and one based on Ffowcs Williams-Hawkings equation with penetrable data surface (FW - Hpds). The scattering of sound from surfaces near the rotor are calculated using the fast scattering code (FSC) which is also discussed in this report. Plans for further improvements of these codes are given.

Farassat, Fereidoun↗
NASA NTRS2011

Xenoliths in the CM2 Carbonaceous Chondrite LON 94101: Implications for Complex Mixing on the Asteroidal Parent Body

Xenoliths are foreign clasts that oc-cur in various classes of meteorites, e.g. [1,2,3]. A re-cent study reveals the presence of several distinct classes of xenoliths in regolith-bearing meteorites, in-cluding in over 20 different carbonaceous chondrites [4]. The most common types of xenoliths are fine-grained hydrous clasts, often referred to as C1 or CI clasts in the literature, although their mineralogy is actually more similar to hydrous micrometeorites [5,6]. Xenoliths in meteorites present an opportunity to study material not yet classified or available as separate meteorites, and can provide additional information on processes in the dynamic early history of the Solar Sys-tem. Here we have performed chemical and mineralogi-cal analyses of xenoliths in the CM2 carbonaceous chondrite LON 94101, using scanning electron micro-scopy (SEM) and transmission electron microscopy (TEM).

Lindgren, P.↗
NASA NTRS2011

The Herschel Multi-Tiered Extragalactic Survey: SPIRE-mm Photometric Redshifts

We investigate the potential of submm-mm and submm-mm-radio photometric red-shifts using a sample of mm-selected sources as seen at 250, 350 and 500 micrometers by the SPIRE instrument on Herschel. From a sample of 63 previously identified mm-sources with reliable radio identifications in the GOODS-N and Lockman Hole North fields 46 (73 per cent) are found to have detections in at least one SPIRE band. We explore the observed submm/mm colour evolution with redshift, finding that the colours of mm-sources are adequately described by a modified blackbody with constant optical depth Tau = (nu/nu(0))beta where beta = +1.8 and nu(0) = c/100 micrometers. We find a tight correlation between dust temperature and IR luminosity. Using a single model of the dust temperature and IR luminosity relation we derive photometric redshift estimates for the 46 SPIRE detected mm-sources. Testing against the 22 sources with known spectroscopic, or good quality optical/near-IR photometric, redshifts we find submm/mm photometric redshifts offer a redshift accuracy of |delta z|/(1+z) = 0.16 (less than |delta z| greater than = 0.51). Including constraints from the radio-far IR correlation the accuracy is improved to |delta z|/(1 + z) = 0.15 (less than |delta z| greater than = 0.45). We estimate the redshift distribution of mm-selected sources finding a significant excess at z greater than 3 when compared to 850 micrometer selected samples.

Roseboom, I. G.↗
NASA NTRS2011

The LBA Calibrator Survey of Southern Compact Extragalactic Radio Sources - LCS1

We present a catalogue of accurate positions and correlated flux densities for 410 flat-spectrum, compact extragalactic radio sources previously detected in the Australia Telescope 20 GHz (AT20G) survey. The catalogue spans the declination range [-90deg, -40deg] and was constructed from four 24-h very long baseline interferometry (VLBI) observing sessions with the Australian Long Baseline Array at 8.3 GHz. The VLBI detection rate in these experiments is 97 per cent, the median uncertainty of the source positions is 2.6 mas and the median correlated flux density on projected baselines longer than 1000 km is 0.14 Jy. The goals of this work are (1) to provide a pool of southern sources with positions accurate to a few milliarcsec, which can be used for phase-referencing observations, geodetic VLBI and space navigation; (2) to extend the complete flux-limited sample of compact extragalactic sources to the Southern hemisphere; and (3) to investigate the parsec-scale properties of high-frequency selected sources from the AT20G survey. As a result of this VLBI campaign, the number of compact radio sources south of declination -40deg which have measured VLBI correlated flux densities and positions known to milliarcsec accuracy has increased by a factor of 3.5.

Petrov, Leonid↗
NASA NTRS2012

Constraints on the Volatile Distribution Within Shackleton Crater at the Lunar South Pole

Shackleton crater is nearly coincident with the Moon's south pole. Its interior receives almost no direct sunlight and is a perennial cold trap, making Shackleton a promising candidate location in which to seek sequestered volatiles. However, previous orbital and Earth-based radar mapping and orbital optical imaging have yielded conflicting interpretations about the existence of volatiles. Here we present observations from the Lunar Orbiter Laser Altimeter on board the Lunar Reconnaissance Orbiter, revealing Shackleton to be an ancient, unusually well-preserved simple crater whose interior walls are fresher than its floor and rim. Shackleton floor deposits are nearly the same age as the rim, suggesting that little floor deposition has occurred since the crater formed more than three billion years ago. At a wavelength of 1,064 nanometres, the floor of Shackleton is brighter than the surrounding terrain and the interiors of nearby craters, but not as bright as the interior walls. The combined observations are explicable primarily by downslope movement of regolith on the walls exposing fresher underlying material. The relatively brighter crater floor is most simply explained by decreased space weathering due to shadowing, but a one-micrometre-thick layer containing about 20 per cent surficial ice is an alternative possibility.

Zuber, Maria T.↗
NASA NTRS2011

X-Ray Evidence for the Accretion Disc-Outflow Connection in 3C 111

We present the spectral analysis of three Suzaku X-ray Imaging Spectrometer observations of 3C III requested to monitor the predicted variability of its ultrafast outflow on approximately 7 d time-scales. We detect an ionized iron emission line in the first observation and a blueshifted absorption line in the second, when the flux is approximately 30 per cent higher. The location of the material is constrained at less than 0.006 pc from the variability. Detailed modelling supports an identification with ionized reflection off the accretion disc at approximately 20-100rg from the black hole and a highly ionized and massive ultrafast outflow with velocity approximately 0.1c, respectively. The outflow is most probably accelerated by radiation pressure, but additional magnetic thrust cannot be excluded. The measured high outflow rate and mechanical energy support the claims that disc outflows may have a significant feedback role. This work provides the first direct evidence for an accretion disc-outflow connection in a radio-loud active galactic nucleus, possibly linked also to the jet activity.

Tombesi, Frank↗
NASA NTRS2012

The Herschel Multi-Tiered Extragalactic Survey: SPIRE-mm Photometric Redshifts

We investigate the potential of submm-mm and submm-mm-radio photometric redshifts using a sample of mm-selected sources as seen at 250, 350 and 500 micron by the SPIRE instrument on Herschel. From a sample of 63 previously identified mm sources with reliable radio identifications in the Great Observatories Origins Deep Survey North and Lockman Hole North fields, 46 (73 per cent) are found to have detections in at least one SPIRE band. We explore the observed submm/mm color evolution with redshift, finding that the colors of mm sources are adequately described by a modified blackbody with constant optical depth Tau = (Nu/nu(sub 0))(exp Beta), where Beta = +1.8 and nu(sub 0) = c/100 micron. We find a tight correlation between dust temperature and IR luminosity. Using a single model of the dust temperature and IR luminosity relation, we derive photometric redshift estimates for the 46 SPIRE-detected mm sources. Testing against the 22 sources with known spectroscopic or good quality optical/near-IR photometric redshifts, we find submm/mm photometric redshifts offer a redshift accuracy of (absolute value of Delta sub (z))/(1 + z) = 0.16 (absolute value of Delta sub (z)) = 0.51). Including constraints from the radio-far-IR correlation, the accuracy is improved to (absolute value of Delta sub (z))/(1 + z) = 0.14 (((absolute value of Delta sub (z))) = 0.45). We estimate the redshift distribution of mm-selected sources finding a significant excess at Z > 3 when compared to approx 8S0 micron selected samples.

Roseboom, I. G.↗
NASA NTRS2008

Energy and Water Management

Energy efficiency isn't just a good idea; it's a necessity, both for cost reasons and to meet federal regulatory requirements. First, rising energy unit costs continue to erode NASA's mission budget. NASA spent roughly $156M on facility energy in FY 2007. Although that represents less than one per cent of NASA's overall annual budget, the upward trend in energy costs concerns the agency. While NASA reduced consumption 13%, energy unit costs have risen 63%. Energy cost increases counteract the effects of energy conservation, which results in NASA buying less yet spending more. The second factor is federal energy legislation. The National Energy Conservation Policy Act, as amended by the Energy Policy Act of 2005, Executive Order (EO) 13423 (January, 2007), and the Energy Independence and Security Act (December, 2007), mandates energy/water conservation goals for all federal agencies, including NASA. There are also reporting requirements associated with this legislation. The Energy/Water Management Task was created to support NASA Headquarters Environmental Management Division (HO EMD) in meeting these requirements. With assistance from TEERM, HQ EMD compiled and submitted the NASA Annual Report to the Department of Energy FY 2007. The report contains information on how NASA is meeting federally mandated energy and water management goals. TEERM monitored input for timeliness, errors, and conformity to the new energy/water reporting guidelines and helped compile the information into the final report. TEERM also assists NASA Energy/Water Management with proposal and award calls, updates to the energy/water management database, and facilitating communication within the energy/water management community. TEERM is also supporting NASA and the Interagency Working Group (IWG) on Hydrogen and Fuel Cells. Established shortly after the President announced the Hydrogen Fuel Initiative in 2003, this IWG serves as the mechanism for collaboration among the Federal agencies involved in hydrogen-related research, development, and demonstration. TEERM developed a matrix showing all Hydrogen and Fuel Cell activities from the various NASA centers to be included in the Group's extensive hydrogen research taxonomy of past, present, and future hydrogen activities of the Federal government.

Valek, Susan E.↗
NASA NTRS2013

New Brown Dwarf Discs in Upper Scorpius Observed with WISE

We present a census of the disc population for UKIDSS selected brown dwarfs in the 5-10 Myr old Upper Scorpius OB association. For 116 objects originally identified in UKIDSS, the majority of them not studied in previous publications, we obtain photometry from the Wide-Field Infrared Survey Explorer data base. The resulting colour magnitude and colour colour plots clearly show two separate populations of objects, interpreted as brown dwarfs with discs (class II) and without discs (class III). We identify 27 class II brown dwarfs, 14 of them not previously known. This disc fraction (27 out of 116, or 23%) among brown dwarfs was found to be similar to results for K/M stars in Upper Scorpius, suggesting that the lifetimes of discs are independent of the mass of the central object for low-mass stars and brown dwarfs. 5 out of 27 discs (19 per cent) lack excess at 3.4 and 4.6 microns and are potential transition discs (i.e. are in transition from class II to class III). The transition disc fraction is comparable to low-mass stars.We estimate that the time-scale for a typical transition from class II to class III is less than 0.4 Myr for brown dwarfs. These results suggest that the evolution of brown dwarf discs mirrors the behaviour of discs around low-mass stars, with disc lifetimes of the order of 5 10 Myr and a disc clearing time-scale significantly shorter than 1 Myr.

Dawson, P.↗
NASA NTRS2013

The Herschel* PEP-HERMES Luminosity Function- I. Probing the Evolution of PACS Selected Galaxies to z approx. equal to 4

We exploit the deep and extended far-IR data sets (at 70, 100 and 160 μm) of the Herschel Guaranteed Time Observation (GTO) PACS Evolutionary Probe (PEP) Survey, in combination with the Herschel Multi-tiered Extragalactic Survey data at 250, 350 and 500 μm, to derive the evolution of the rest-frame 35-, 60-, 90- and total infrared (IR) luminosity functions (LFs) up to z ∼ 4.We detect very strong luminosity evolution for the total IR LF (LIR ∝ (1 + z)(sup 3.55 +/- 0.10) up to z ∼ 2, and ∝ (1 + z)(sup 1.62 +/- 0.51) at 2 less than z less than approximately 4) combined with a density evolution (∝ (1 + z)(sup −0.57 +/- 0.22) up to z ∼ 1 and ∝ (1 + z)(sup −3.92 +/- 0.34) at 1 less than z less than approximately 4). In agreement with previous findings, the IR luminosity density (ρIR) increases steeply to z ∼ 1, then flattens between z ∼ 1 and z ∼ 3 to decrease at z greater than approximately 3. Galaxies with different spectral energy distributions, masses and specific star formation rates (SFRs) evolve in very different ways and this large and deep statistical sample is the first one allowing us to separately study the different evolutionary behaviours of the individual IR populations contributing to ρIR. Galaxies occupying the well-established SFR-stellar mass main sequence (MS) are found to dominate both the total IR LF and ρIR at all redshifts, with the contribution from off-MS sources (≥0.6 dex above MS) being nearly constant (∼20 per cent of the total ρIR) and showing no significant signs of increase with increasing z over the whole 0.8 < z <2.2 range. Sources with mass in the range 10 ≤ log(M/solar mass) ≤ 11 are found to dominate the total IR LF, with more massive galaxies prevailing at the bright end of the high-z (greater than approximately 2) LF. A two-fold evolutionary scheme for IR galaxies is envisaged: on the one hand, a starburst-dominated phase in which the Super Massive Black Holes (SMBH) grows and is obscured by dust (possibly triggered by a major merging event), is followed by an AGN-dominated phase, then evolving towards a local elliptical. On the other hand, moderately star-forming galaxies containing a low-luminosity AGN have various properties suggesting they are good candidates for systems in a transition phase preceding the formation of steady spiral galaxies.

Herschel↗
NASA NTRS2014

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalogue of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 and/or 218 GHz in the 2008 Southern survey. Flux densities span 14 -1700 mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two subpopulations: 167 radio galaxies powered by central active galactic nuclei (AGN) and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97 per cent of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogues. When combined with flux densities from the Australia Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148 GHz, with the trend continuing to 218 GHz. The ACT dust-dominated source population has a median spectral index, A(sub 148-218), of 3.7 (+0.62 or −0.86), and includes both local galaxies and sources with redshift around 6. Dusty sources with no counterpart in existing catalogues likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.

dusty star-forming galaxies (DSFGs)↗
NASA NTRS2014

Development Status of Adjustable X-Ray Optics with 0.5 Arcsecond Resolution

We report on the continuing development of adjustable, grazing incidence X-ray optics for 0.5 arcsec telescopes. Adjustable X-ray optics offer the potential for achieving sub-arcsecond imaging resolution while sufficiently thin and light-weight to constitute a mirror assembly with several square meters collecting area. The adjustable mirror concept employs a continuous thin film of piezoelectric material deposited on the back of the paraboloid and hyperboloid mirror segments. Individually addressable electrodes on the piezoelectric layer allow the introduction of deformations in localized "cells" which are used to correct mirror figure errors resulting from fabrication, mounting and aligning the thin mirrors, residual gravity release and temperature changes. We describe recent results of this development. These include improving cell yield to approx. 100 per cent, measurements of hysteresis and stability, comparisons of modeled and measured behavior, simulations of mirror performance, and the development and testing of conical Wolter- I mirror segments. We also present our plans going forward toward the eventual goal of achieving TRL 6 prior to the 2020 Decadal Review.

Reid, P. B.↗
NASA NTRS2014

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalogue of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 and/or 218 GHz in the 2008 Southern survey. Flux densities span 14 - 1700 mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two subpopulations: 167 radio galaxies powered by central active galactic nuclei (AGN) and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97 per cent of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogues. When combined with flux densities from the Australia Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148 GHz, with the trend continuing to 218 GHz. The ACT dust-dominated source population has a median spectral index, alpha(sub 148−218), of 3.7 +0.62/-0.86), and includes both local galaxies and sources with redshift around 6. Dusty sources with no counterpart in existing catalogues likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.

Telescope↗
NASA NTRS2015

Re-Evaluation of HSE DATA in Light of High P-T Partitioning Data: Late Chondritic Addition to Inner Solar System Bodies Not Always Required for HSE

Studies of terrestrial peridotite and martian and achondritic meteorites have led to the conclusion that addition of chondritic material to growing planets or planetesimals, after core formation, occurred on Earth, Moon, Mars, asteroid 4 Vesta, and the parent body of the angritic meteorites. One study even proposed that this was a common process in the final stages of growth. These conclusions are based al-most entirely on the 8 highly siderophile elements (HSE; Re, Au, Pt, Pd, Rh, Ru, Ir, Os), which have been used to argue for late accretion of chondritic material to the Earth after core formation was complete. This idea was originally proposed because the D(metal/silicate) values for the HSE are very high (greater than 10,000), yet their concentration in the terrestrial mantle is too high to be consistent with such high Ds. The HSE in the terrestrial mantle also are present in chondritic relative abundances and hence require similar Ds if this was the result of core-mantle equilibration. The conclusion that late chondritic additions are required for all five of these bodies is based on the chondritic relative abundances of the HSE, as well as their elevated concentrations in the samples. An easy solution is to call upon addition of chondritic material to the mantle of each body, just after core formation; however, in practice this means similar additions of chondritic materials to each body just after core formation which ranges from approximately 4-5 Ma after T(sub 0) for 4 Vesta and the angrites, to 10-25 Ma for Mars, to 35 to 60 Ma for Moon and perhaps the Earth. Since the work of there has been a realization that high PT conditions can lower the partition coefficients of many siderophile elements, indicating that high PT conditions (magma ocean stage) can potentially explain elevated siderophile element abundances. However, detailed high PT partitioning data have been lacking for many of the HSE to evaluate whether such ideas are viable for all four bodies. Re-cent partitioning studies have covered P, T, fO2, and compositional ranges that allow values to be predicted at conditions relevant to these five inner solar system bodies. Because the D(HSE) metal/silicate are lowered substantially at higher PT conditions and natural com-positions (FeNi metallic liquids and peridotites) it is natural to re-examine the role of core formation on the HSE patterns in a variety of inner solar system bodies. Here I will discuss other processes (including high PT core formation for Mars, Moon and Earth) that can produce the observed HSE patterns, and demonstrate that there are viable hypotheses other than the "one size fits all" hypothesis of late chondritic additions.

Righter, K.↗
NASA NTRS1961

A Study of the Free Oscillations of the Earth

Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

MacDonald, Gordon J. F.↗