Venus gravity and topography: 60th degree and order model

NASA Technical Reports Server (NTRS)

Konopliv, A. S.; Borderies, N. J.; Chodas, P. W.; Christensen, E. J.; Sjogren, W. L.; Williams, B. G.; Balmino, G.; Barriot, J. P.

1993-01-01

We have combined the most recent Pioneer Venus Orbiter (PVO) and Magellan (MGN) data with the earlier 1978-1982 PVO data set to obtain a new 60th degree and order spherical harmonic gravity model and a 120th degree and order spherical harmonic topography model. Free-air gravity maps are shown over regions where the most marked improvement has been obtained (Ishtar-Terra, Alpha, Bell and Artemis). Gravity versus topography relationships are presented as correlations per degree and axes orientation.

Venus spherical harmonic gravity model to degree and order 60

NASA Technical Reports Server (NTRS)

Konopliv, Alex S.; Sjogren, William L.

1994-01-01

The Magellan and Pioneer Venus Orbiter radiometric tracking data sets have been combined to produce a 60th degree and order spherical harmonic gravity field. The Magellan data include the high-precision X-band gravity tracking from September 1992 to May 1993 and post-aerobraking data up to January 5, 1994. Gravity models are presented from the application of Kaula's power rule for Venus and an alternative a priori method using surface accelerations. Results are given as vertical gravity acceleration at the reference surface, geoid, vertical Bouguer, and vertical isostatic maps with errors for the vertical gravity and geoid maps included. Correlation of the gravity with topography for the different models is also discussed.

Jupiter’s atmospheric jet streams extend thousands of kilometres deep

NASA Astrophysics Data System (ADS)

Kaspi, Y.; Galanti, E.; Hubbard, W. B.; Stevenson, D. J.; Bolton, S. J.; Iess, L.; Guillot, T.; Bloxham, J.; Connerney, J. E. P.; Cao, H.; Durante, D.; Folkner, W. M.; Helled, R.; Ingersoll, A. P.; Levin, S. M.; Lunine, J. I.; Miguel, Y.; Militzer, B.; Parisi, M.; Wahl, S. M.

2018-03-01

The depth to which Jupiter’s observed east–west jet streams extend has been a long-standing question. Resolving this puzzle has been a primary goal for the Juno spacecraft, which has been in orbit around the gas giant since July 2016. Juno’s gravitational measurements have revealed that Jupiter’s gravitational field is north–south asymmetric, which is a signature of the planet’s atmospheric and interior flows. Here we report that the measured odd gravitational harmonics J3, J5, J7 and J9 indicate that the observed jet streams, as they appear at the cloud level, extend down to depths of thousands of kilometres beneath the cloud level, probably to the region of magnetic dissipation at a depth of about 3,000  kilometres. By inverting the measured gravity values into a wind field, we calculate the most likely vertical profile of the deep atmospheric and interior flow, and the latitudinal dependence of its depth. Furthermore, the even gravity harmonics J8 and J10 resulting from this flow profile also match the measurements, when taking into account the contribution of the interior structure. These results indicate that the mass of the dynamical atmosphere is about one per cent of Jupiter’s total mass.

Fast calculation of low altitude disturbing gravity for ballistics

NASA Astrophysics Data System (ADS)

Wang, Jianqiang; Wang, Fanghao; Tian, Shasha

2018-03-01

Fast calculation of disturbing gravity is a key technology in ballistics while spherical cap harmonic(SCH) theory can be used to solve this problem. By using adjusted spherical cap harmonic(ASCH) methods, the spherical cap coordinates are projected into a global coordinates, then the non-integer associated Legendre functions(ALF) of SCH are replaced by integer ALF of spherical harmonics(SH). This new method is called virtual spherical harmonics(VSH) and some numerical experiment were done to test the effect of VSH. The results of earth's gravity model were set as the theoretical observation, and the model of regional gravity field was constructed by the new method. Simulation results show that the approximated errors are less than 5mGal in the low altitude range of the central region. In addition, numerical experiments were conducted to compare the calculation speed of SH model, SCH model and VSH model, and the results show that the calculation speed of the VSH model is raised one order magnitude in a small scope.

Time-variable and static gravity field of Mars from MGS, Mars Odyssey, and MRO

NASA Astrophysics Data System (ADS)

Genova, Antonio; Goossens, Sander; Lemoine, Frank G.; Mazarico, Erwan; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.

2016-04-01

The Mars Global Surveyor (MGS), Mars Odyssey (ODY), and Mars Reconnaissance Orbiter (MRO) missions have significantly contributed to the determination of global high-resolution global gravity fields of Mars for the last 16 years. All three spacecraft were located in sun-synchronous, near-circular polar mapping orbits for their primary mission phases at different altitudes and Local Solar Time (LST). X-Band tracking data have been acquired from the NASA Deep Space Network (DSN) providing information on the time-variable and static gravity field of Mars. MGS operated between 1999 and 2006 at 390 km altitude. ODY and MRO are still orbiting Mars with periapsis altitudes of 400 km and 255 km, respectively. Before entering these mapping phases, all three spacecraft collected radio tracking data at lower altitudes (˜170-200 km) that help improve the resolution of the gravity field of Mars in specific regions. We analyzed the entire MGS radio tracking data set, and ODY and MRO radio data until 2015. These observations were processed using a batch least-squares filter through the NASA GSFC GEODYN II software. We combined all 2- and 3-way range rate data to estimate the global gravity field of Mars to degree and order 120, the seasonal variations of gravity harmonic coefficients C20, C30, C40 and C50 and the Love number k2. The gravity contribution of Mars atmospheric pressures on the surface of the planet has been discerned from the time-varying and static gravity harmonic coefficients. Surface pressure grids computed using the Mars-GRAM 2010 atmospheric model, with 2.5° x2.5° spatial and 2-h resolution, are converted into gravity spherical harmonic coefficients. Consequently, the estimated gravity and tides provide direct information on the solid planet. We will present the new Goddard Mars Model (GMM-3) of Mars gravity field in spherical harmonics to degree and order 120. The solution includes the Love number k2 and the 3-frequencies (annual, semi-annual, and tri-annual) time-variable coefficients of the gravity zonal harmonics C20, C30, C40 and C50. The seasonal gravity coefficients led us to determine the inter-annual mass exchange between the polar caps over ˜11 years from October 2002 to November 2014.

Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution and terrain correction: An attempt of global numerical computations

NASA Technical Reports Server (NTRS)

Wang, Y. M.

1989-01-01

The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere-at least to the ellipsoid. The goal is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g sub 1 term). The terrain correction was also computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. The fast Fourier transformation was applied to the computations.

Harmonic analysis of the DTU10 global gravity anomalies

NASA Astrophysics Data System (ADS)

Abrykosov, O.; Förste, Ch.; Gruber, Ch.; Shako, R.; Barthelmes, F.

2012-04-01

We have computed the Earth's gravity models to degree/order 5400 and 10800 (in terms of the ellipsoidal and spherical harmonics) from a rigorous integration of the 2'x2' and 1'x1' global grids of gravity anomalies provided by the Danish Technical University (DTU). The gravity signal recovered from the DTU10 data shows 1) a strong dependency on the truncation of the EGM2008 gravity model which were used to fill-in land areas in the DTU10 grids and 2) an irregular behaviour at frequencies behind the resolution of the EGM2008. We discuss the gravity signal and its accuracy estimation computed from the complete DTU10 grids as well as separately from the data over land and ocean areas.

The Dawn Gravity Investigation at Vesta and Ceres

NASA Technical Reports Server (NTRS)

Konopliv, A. S.; Asmar, S.W.; Bills, B. G.; Mastrodemos, N.; Park, R. S.; Raymond, C. A.; Smith, D. E.; Zuber, M. T.

2011-01-01

The objective of the Dawn gravity investigation is to use high precision X-band Doppler tracking and landmark tracking from optical images to measure the gravity fields of Vesta and Ceres to a half-wavelength surface resolution better than 90-km and 300-km, respectively. Depending on the Doppler tracking assumptions, the gravity field will be determined to somewhere between harmonic degrees 15 and 25 for Vesta and about degree 10 for Ceres. The gravity fields together with shape models determined from Dawn's framing camera constrain models of the interior from the core to the crust. The gravity field is determined jointly with the spin pole location. The second degree harmonics together with assumptions on obliquity or hydrostatic equilibrium may determine the moments of inertia.

A suppression of differential rotation in Jupiter’s deep interior

NASA Astrophysics Data System (ADS)

Guillot, T.; Miguel, Y.; Militzer, B.; Hubbard, W. B.; Kaspi, Y.; Galanti, E.; Cao, H.; Helled, R.; Wahl, S. M.; Iess, L.; Folkner, W. M.; Stevenson, D. J.; Lunine, J. I.; Reese, D. R.; Biekman, A.; Parisi, M.; Durante, D.; Connerney, J. E. P.; Levin, S. M.; Bolton, S. J.

2018-03-01

Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown, limiting our ability to probe the structure and composition of the planet. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric and the determination of its non-zero odd gravitational harmonics J3, J5, J7 and J9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops. Here we report an analysis of Jupiter’s even gravitational harmonics J4, J6, J8 and J10 as observed by Juno and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.

Can even-order laser harmonics exhibited by Bohmian trajectories in symmetric potentials be observed?

PubMed

Peatross, J; Johansen, J

2014-01-13

Strong-field laser-atom interactions provide extreme conditions that may be useful for investigating the de Broglie-Bohm quantum interpretation. Bohmian trajectories representing bound electrons in individual atoms exhibit both even and odd harmonic motion when subjected to a strong external laser field. The phases of the even harmonics depend on the random initial positions of the trajectories within the wave function, making the even harmonics incoherent. In contrast, the phases of odd harmonics remain for the most part coherent regardless of initial position. Under the conjecture that a Bohmian point particle plays the role of emitter, this suggests an experiment to determine whether both even and odd harmonics are produced at the atomic level. Estimates suggest that incoherent emission of even harmonics may be detectable out the side of an intense laser focus interacting with a large number of atoms.

Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies

NASA Astrophysics Data System (ADS)

Balmino, G.; Vales, N.; Bonvalot, S.; Briais, A.

2012-07-01

The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth's topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid's surface to the Earth's surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1' × 1' equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth's topography-bathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical harmonic coefficients were computed up to the third degree of the altitude, and the harmonics of the other, smaller parts up to the second degree. Their sum constitutes what we call ETOPG1, the Earth's TOPography derived Gravity model at 1' resolution (half-wavelength). The EGM2008 gravity field model and ETOPG1 were then used to rigorously compute 1' × 1' point values of surface gravity anomalies and disturbances, respectively, worldwide, at the real Earth's surface, i.e. at the lower limit of the atmosphere. The disturbance grid is the most interesting product of this study and can be used in various contexts. The surface gravity anomaly grid is an accurate product associated with EGM2008 and ETOPO1, but its gravity information contents are those of EGM2008. Our method was validated by comparison with a direct numerical integration approach applied to a test area in Morocco-South of Spain (Kuhn, private communication 2011) and the agreement was satisfactory. Finally isostatic corrections according to the Airy model, but in spherical geometry, with harmonic coefficients derived from the sets of the ETOPO1 different parts, were computed with a uniform depth of compensation of 30 km. The new world Bouguer and isostatic gravity maps and grids here produced will be made available through the Commission for the Geological Map of the World. Since gravity values are those of the EGM2008 model, geophysical interpretation from these products should not be done for spatial scales below 5 arc minutes (half-wavelength).

Harmonic multiplication using resonant tunneling

NASA Technical Reports Server (NTRS)

Sollner, T. C. L. G.; Brown, E. R.; Goodhue, W. D.; Correa, C. A.

1988-01-01

This paper demonstrates the use of resonant-tunneling diodes as varistors for harmonic multiplication. It is shown that efficient odd-harmonic conversion is possible and that even harmonics do not appear because of the antisymmetry of the current-voltage (I-V) curve. It is also shown that, with the proper choice of resonant-tunneling structure and pump amplitude, most of the harmonic output power can be confined to a single odd-harmonic frequency. Fifth-harmonic multiplication was demonstrated with an output at 21.75 GHz and a power conversion efficiency of 0.5 percent, and a fifth-harmonic efficiency of 2.7 percent was achieved in a circuit simulation using an improved I-V curve.

Quasi-phase-matching of only even-order high harmonics.

PubMed

Diskin, Tzvi; Cohen, Oren

2014-03-24

High harmonic spectrum of a quasi-monochromatic pump that interacts with isotropic media consists of only odd-order harmonics. Addition of a secondary pump, e.g. a static field or the second harmonic of the primary pump, can results with generation of both odd and even harmonics of the primary pump. We propose a method for quasi-phase matching of only the even-order harmonics of the primary pump. We formulate a theory for this process and demonstrate it numerically. We also show that it leads to attosecond pulse trains with constant carrier envelop phase and high repetition rate.

Spectral analysis of the gravity and topography of Mars

NASA Technical Reports Server (NTRS)

Bills, Bruce G.; Frey, Herbert V.; Kiefer, Walter S.; Nerem, R. Steven; Zuber, Maria T.

1993-01-01

New spherical harmonic models of the gravity and topography of Mars place important constraints on the structure and dynamics of the interior. The gravity and topography models are significantly phase coherent for harmonic degrees n less than 30 (wavelengths greater than 700 km). Loss of coherence below that wavelength is presumably due to inadequacies of the models, rather than a change in behavior of the planet. The gravity/topography admittance reveals two very different spectral domains: for n greater than 4, a simple Airy compensation model, with mean depth of 100 km, faithfully represents the observed pattern; for degrees 2 and 3, the effective compensation depths are 1400 and 550 km, respectively, strongly arguing for dynamic compensation at those wavelengths. The gravity model has been derived from a reanalysis of the tracking data for Mariner 9 and the Viking Orbiters, The topography model was derived by harmonic analysis of the USGS digital elevation model of Mars. Before comparing gravity and topography for internal structure inferences, we must ensure that both are consistently referenced to a hydrostatic datum. For the gravity, this involves removal of hydrostatic components of the even degree zonal coefficients. For the topography, it involves adding the degree 4 equipotential reference surface, to get spherically referenced values, and then subtracting the full degree 50 equipotential. Variance spectra and phase coherence of orthometric heights and gravity anomalies are addressed.

Use of videos for students to see the effect of changing gravity on harmonic oscillators

NASA Astrophysics Data System (ADS)

Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber

2010-03-01

In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.

Venus - Global gravity and topography

NASA Technical Reports Server (NTRS)

Mcnamee, J. B.; Borderies, N. J.; Sjogren, W. L.

1993-01-01

A new gravity field determination that has been produced combines both the Pioneer Venus Orbiter (PVO) and the Magellan Doppler radio data. Comparisonsbetween this estimate, a spherical harmonic model of degree and order 21, and previous models show that significant improvements have been made. Results are displayed as gravity contours overlaying a topographic map. We also calculate a new spherical harmonic model of topography based on Magellan altimetry, with PVO altimetry included where gaps exist in the Magellan data. This model is also of degree and order 21, so in conjunction with the gravity model, Bouguer and isostatic anomaly maps can be produced. These results are very consistent with previous results, but reveal more spatial resolution in the higher latitudes.

Normal Gravity Fields and Equipotential Ellipsoids of Small Objects in the Solar System: A Closed-form Solution in Ellipsoidal Harmonics up to the Second Degree

NASA Astrophysics Data System (ADS)

Hu, Xuanyu

2017-11-01

We propose a definition for the normal gravity fields and normal figures of small objects in the solar system, such as asteroids, cometary nuclei, and planetary moons. Their gravity fields are represented as series of ellipsoidal harmonics, ensuring more robust field evaluation in the proximity of an arbitrary, convex shape than using spherical harmonics. The normal gravity field, approximate to the actual field, can be described by a finite series of three terms, that is, degree zero, and the zonal and sectoral harmonics of degree two. The normal gravity is that of an equipotential ellipsoid, defined as the normal ellipsoid of the body. The normal ellipsoid may be distinct from the actual figure. We present a rationale for specifying and a numerical method for determining the parameters of the normal ellipsoid. The definition presented here generalizes the convention of the normal spheroid of a large, hydrostatically equilibrated planet, such as Earth. Modeling the normal gravity and the normal ellipsoid is relevant to studying the formation of the “rubble pile” objects, which may have been accreted, or reorganized after disruption, under self-gravitation. While the proposed methodology applies to convex, approximately ellipsoidal objects, those bi-lobed objects can be treated as contact binaries comprising individual convex subunits. We study an exemplary case of the nearly ellipsoidal Martian moon, Phobos, subject to strong tidal influence in its present orbit around Mars. The results allude to the formation of Phobos via gravitational accretion at some further distance from Mars.

Teaching Physics from a Reduced Gravity Environment

NASA Astrophysics Data System (ADS)

Benge, Raymond D.; Young, C.; Davis, S.; Worley, A.; Smith, L.; Gell, A.

2010-01-01

This poster reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. Typical homework problems for introductory physics classes ask questions such as "What would be the period of oscillation if this experiment were performed on the Moon or Mars?” This gives students a chance to actually see the effects predicted by the equations. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms in both college and high school physics classes.

Experimental and simulation studies on the behavior of signal harmonics in magnetic particle imaging.

PubMed

Murase, Kenya; Konishi, Takashi; Takeuchi, Yuki; Takata, Hiroshige; Saito, Shigeyoshi

2013-07-01

Our purpose in this study was to investigate the behavior of signal harmonics in magnetic particle imaging (MPI) by experimental and simulation studies. In the experimental studies, we made an apparatus for MPI in which both a drive magnetic field (DMF) and a selection magnetic field (SMF) were generated with a Maxwell coil pair. The MPI signals from magnetic nanoparticles (MNPs) were detected with a solenoid coil. The odd- and even-numbered harmonics were calculated by Fourier transformation with or without background subtraction. The particle size of the MNPs was measured by transmission electron microscopy (TEM), dynamic light-scattering, and X-ray diffraction methods. In the simulation studies, the magnetization and particle size distribution of MNPs were assumed to obey the Langevin theory of paramagnetism and a log-normal distribution, respectively. The odd- and even-numbered harmonics were calculated by Fourier transformation under various conditions of DMF and SMF and for three different particle sizes. The behavior of the harmonics largely depended on the size of the MNPs. When we used the particle size obtained from the TEM image, the simulation results were most similar to the experimental results. The similarity between the experimental and simulation results for the even-numbered harmonics was better than that for the odd-numbered harmonics. This was considered to be due to the fact that the odd-numbered harmonics were more sensitive to background subtraction than were the even-numbered harmonics. This study will be useful for a better understanding, optimization, and development of MPI and for designing MNPs appropriate for MPI.

Validity of the "Laplace Swindle" in Calculation of Giant-Planet Gravity Fields

NASA Astrophysics Data System (ADS)

Hubbard, William B.

2014-11-01

Jupiter and Saturn have large rotation-induced distortions, providing an opportunity to constrain interior structure via precise measurement of external gravity. Anticipated high-precision gravity measurements close to the surfaces of Jupiter (Juno spacecraft) and Saturn (Cassini spacecraft), possibly detecting zonal harmonics to J10 and beyond, will place unprecedented requirements on gravitational modeling via the theory of figures (TOF). It is not widely appreciated that the traditional TOF employs a formally nonconvergent expansion attributed to Laplace. This suspect expansion is intimately related to the standard zonal harmonic (J-coefficient) expansion of the external gravity potential. It can be shown (Hubbard, Schubert, Kong, and Zhang: Icarus, in press) that both Jupiter and Saturn are in the domain where Laplace's "swindle" works exactly, or at least as well as necessary. More highly-distorted objects such as rapidly spinning asteroids may not be in this domain, however. I present a numerical test for the validity and precision of TOF via polar "audit points". I extend the audit-point test to objects rotating differentially on cylinders, obtaining zonal harmonics to J20 and beyond. Models with only low-order differential rotation do not exhibit dramatic effects in the shape of the zonal harmonic spectrum. However, a model with Jupiter-like zonal winds exhibits a break in the zonal harmonic spectrum above about J10, and generally follows the more shallow Kaula power rule at higher orders. This confirms an earlier result obtained by a different method (Hubbard: Icarus 137, 357-359, 1999).

Annual, Seasonal, and Secular Changes in Time-Variable Gravity from GRACE

NASA Astrophysics Data System (ADS)

Lemoine, F. G.; Luthcke, S. B.; Klosko, S. M.; Rowlands, D. D.; Chinn, D. S.; McCarthy, J. J.; Ray, R. D.; Boy, J.

2007-12-01

The NASA/DLR GRACE mission, launched in 2002, has now operated for more than five years, producing monthly and ten-day snapshots of the variations of the gravity field of the Earth. The available solutions, either from spherical harmonics or from mascons, allow us new insights into the variations of surface gravity on the Earth at annual, inter-annual, and secular time scales. Our baseline time series, based on GGM02C, NCEP Atmospheric Gravity with IB, and GOT00 tides now is extended to July 2007, spanning four+ years, and we analyze both mascon and spherical harmonic solutions from this time series with respect to global hydrology variations. Our 4degx4deg mascon solutions are extended to cover all continental regions of the globe. Comparisons with hydrology (land-surface) models can offer insights into how these models might be improved. We compare our baseline time series, with new time series that include an updated Goddard Ocean Tide (GOT) model, ECMWF- 3hr atmosphere de-aliasing data, and the MOG-2D ocean dealiasing product. Finally, we intercompare the spherical harmonic solutions at low degree from GRACE from the various product centers (e.g., GFZ, CSR, GRGS), and look for secular signals in both the GSFC mascon and spherical harmonic solutions, taking care to compare the results for secular gravity field change with independent solutions developed over 25 years of independent tracking to geodetic satellites by Satellite Laser Ranging (SLR) and DORIS.

The warm, rich sound of valve guitar amplifiers

NASA Astrophysics Data System (ADS)

Keeports, David

2017-03-01

Practical solid state diodes and transistors have made glass valve technology nearly obsolete. Nevertheless, valves survive largely because electric guitar players much prefer the sound of valve amplifiers to the sound of transistor amplifiers. This paper discusses the introductory-level physics behind that preference. Overdriving an amplifier adds harmonics to an input sound. While a moderately overdriven valve amplifier produces strong even harmonics that enhance a sound, an overdriven transistor amplifier creates strong odd harmonics that can cause dissonance. The functioning of a triode valve explains its creation of even and odd harmonics. Music production software enables the examination of both the wave shape and the harmonic content of amplified sounds.

A harmonic analysis of lunar topography

NASA Technical Reports Server (NTRS)

Bills, B. G.; Ferrari, A. J.

1977-01-01

A global lunar topographic map has been derived from existing earth-based and orbital observations supplemented in areas without data by a linear autocovariance predictor. Of 2592 bins, each 5 deg square, 1380 (64.7% by area) contain at least one measurement. A spherical harmonic analysis to degree 12 yields a mean radius of 1737.53 plus or minus 0.03 km (formal standard error) and an offset of the center of figure of 1.98 plus or minus 0.06 km toward (19 plus or minus 2) deg S, (194 plus or minus 1) deg E. A Bouguer gravity map, derived from a 12-degree free-air gravity model and the present topography data, is presented for an elevation of 100 km above the mean surface. It is confirmed that the low-degree gravity harmonics are determined primarily by surface height variations and only secondarily by lateral density variations.

High-resolution Local Gravity Model of the South Pole of the Moon from GRAIL Extended Mission Data

NASA Technical Reports Server (NTRS)

Goossens, Sander Johannes; Sabaka, Terence J.; Nicholas, Joseph B.; Lemoine, Frank G.; Rowlands, David D.; Mazarico, Erwan; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.

2014-01-01

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6deg by 1/6deg (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40deg. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

A new method for gravity field recovery based on frequency analysis of spherical harmonics

NASA Astrophysics Data System (ADS)

Cai, Lin; Zhou, Zebing

2017-04-01

All existing methods for gravity field recovery are mostly based on the space-wise and time-wise approach, whose core processes are constructing the observation equations and solving them by the least square method. It's should be pointed that the least square method means the approximation. On the other hand, we can directly and precisely obtain the coefficients of harmonics by computing the Fast Fourier Transform (FFT) when we do 1-D data (time series) analysis. So the question whether we directly and precisely obtain the coefficients of spherical harmonic by computing 2-D FFT of measurements of satellite gravity mission is of great significance, since this may guide us to a new understanding of the signal components of gravity field and make us determine it quickly by taking advantage of FFT. Like the 1-D data analysis, the 2-D FFT of measurements of satellite can be computed rapidly. If we can determine the relationship between spherical harmonics and 2-D Fourier frequencies and the transfer function from measurements to spherical coefficients, the question mentioned above can be solved. So the objective of this research project is to establish a new method based on frequency analysis of spherical harmonic, which directly compute the confidents of spherical harmonic of gravity field, which is differ from recovery by least squares. There is a one to one correspondence between frequency spectrum and the time series in 1-D FFT. The 2-D FFT has a similar relationship to 1-D FFT. Owing to the fact that any degree or order (higher than one) of spherical function has multi frequencies and these frequencies may be aliased. Fortunately, the elements and ratio of these frequencies of spherical function can be determined, and we can compute the coefficients of spherical function from 2-D FFT. This relationship can be written as equations and equivalent to a matrix, which is solid and can be derived in advance. Until now the relationship has be determined. Some preliminary results, which only compute lower degree spherical harmonics, indicates that the difference between the input (EGM2008) and output (coefficients from recovery) is smaller than 5E-17, while the minimal precision of computer software (Matlab) is 2.2204E-16.

Venus Gravity: 180th Degree and Order Model

NASA Technical Reports Server (NTRS)

Konopliv, A. S.; Banerdt, W. B.; Sjogren, W. L.

1998-01-01

The Megallan Doppler radiometric tracking data provides unprecedented precision for spacecraft based gravity measurements with the maximum resolution approaching spherical harmonic degree and order 180 in selected equatorial regions.

Deconstructing the shallow internal structure of the Moon using GRAIL gravity and LOLA topography

NASA Astrophysics Data System (ADS)

Zuber, M. T.

2015-12-01

Globally-distributed, high-resolution gravity and topography observations of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission and Lunar Orbiter Laser Altimeter (LOLA) instrument aboard the Lunar Reconnaissance Orbiter (LRO) spacecraft afford the unprecedented opportunity to explore the shallow internal structure of the Moon. Gravity and topography can be combined to produce Bouguer gravity that reveals the distribution of mass in the subsurface, with high degrees in the spherical harmonic expansion of the Bouguer anomalies sensitive to shallowest structure. For isolated regions of the lunar highlands and several basins we have deconstructed the gravity field and mapped the subsurface distribution of density anomalies. While specified spherical harmonic degree ranges can be used to estimate contributions at different depths, such analyses require considerable caution in interpretation. A comparison of filtered Bouguer gravity with forward models of disk masses with plausible densities illustrates the interdependencies of the gravitational power of density anomalies with depth and spatial scale. The results have implications regarding the limits of interpretation of lunar subsurface structure.

The Size of Mars' Fluid Core From Mars k2 Love Number Obtained From Analysis of MGS Doppler Tracking.

NASA Astrophysics Data System (ADS)

Yoder, C. F.; Konopliv, A. S.; Yuan, D. N.; Standish, E. M.; Folkner, W. M.

2002-12-01

The solar tidal deformation of Mars, measured by its k2 potential Love number, has been obtained from analysis of MGS radio tracking. The observed k2 =0.164+-0.016 is large enough to rule out a solid iron core. The inferred core radius Rc (1600km

Attosecond control of orbital parity mix interferences and the relative phase of even and odd harmonics in an attosecond pulse train.

PubMed

Laurent, G; Cao, W; Li, H; Wang, Z; Ben-Itzhak, I; Cocke, C L

2012-08-24

We experimentally demonstrate that atomic orbital parity mix interferences can be temporally controlled on an attosecond time scale. Electron wave packets are formed by ionizing argon gas with a comb of odd and even high-order harmonics, in the presence of a weak infrared field. Consequently, a mix of energy-degenerate even and odd parity states is fed in the continuum by one- and two-photon transitions. These interfere, leading to an asymmetric electron emission along the polarization vector. The direction of the emission can be controlled by varying the time delay between the comb and infrared field pulses. We show that such asymmetric emission provides information on the relative phase of consecutive odd and even order harmonics in the attosecond pulse train.

A new approach for estimating the Jupiter and Saturn gravity fields using Juno and Cassini measurements, trajectory estimation analysis, and a dynamical wind model optimization

NASA Astrophysics Data System (ADS)

Galanti, Eli; Durante, Daniele; Iess, Luciano; Kaspi, Yohai

2017-04-01

The ongoing Juno spacecraft measurements are improving our knowledge of Jupiter's gravity field. Similarly, the Cassini Grand Finale will improve the gravity estimate of Saturn. The analysis of the Juno and Cassini Doppler data will provide a very accurate reconstruction of spacial gravity variations, but these measurements will be very accurate only over a limited latitudinal range. In order to deduce the full gravity fields of Jupiter and Saturn, additional information needs to be incorporated into the analysis, especially with regards to the planets' wind structures. In this work we propose a new iterative approach for the estimation of Jupiter and Saturn gravity fields, using simulated measurements, a trajectory estimation model, and an adjoint based inverse thermal wind model. Beginning with an artificial gravitational field, the trajectory estimation model is used to obtain the gravitational moments. The solution from the trajectory model is then used as an initial guess for the thermal wind model, and together with an optimization method, the likely penetration depth of the winds is computed, and its uncertainty is evaluated. As a final step, the gravity harmonics solution from the thermal wind model is given back to the trajectory model, along with an estimate of their uncertainties, to be used as a priori for a new calculation of the gravity field. We test this method both for zonal harmonics only and with a full gravity field including tesseral harmonics. The results show that by using this method some of the gravitational moments are fitted better to the `observed' ones, mainly due to the added information from the dynamical model which includes the wind structure and its depth. Thus, it is suggested that the method presented here has the potential of improving the accuracy of the expected gravity moments estimated from the Juno and Cassini radio science experiments.

Harmonic generation with a dual frequency pulse.

PubMed

Keravnou, Christina P; Averkiou, Michalakis A

2014-05-01

Nonlinear imaging was implemented in commercial ultrasound systems over the last 15 years offering major advantages in many clinical applications. In this work, pulsing schemes coupled with a dual frequency pulse are presented. The pulsing schemes considered were pulse inversion, power modulation, and power modulated pulse inversion. The pulse contains a fundamental frequency f and a specified amount of its second harmonic 2f. The advantages and limitations of this method were evaluated with both acoustic measurements of harmonic generation and theoretical simulations based on the KZK equation. The use of two frequencies in a pulse results in the generation of the sum and difference frequency components in addition to the other harmonic components. While with single frequency pulses, only power modulation and power modulated pulse inversion contained odd harmonic components, with the dual frequency pulse, pulse inversion now also contains odd harmonic components.

Development of Gravity Acceleration Measurement Using Simple Harmonic Motion Pendulum Method Based on Digital Technology and Photogate Sensor

NASA Astrophysics Data System (ADS)

Yulkifli; Afandi, Zurian; Yohandri

2018-04-01

Development of gravitation acceleration measurement using simple harmonic motion pendulum method, digital technology and photogate sensor has been done. Digital technology is more practical and optimizes the time of experimentation. The pendulum method is a method of calculating the acceleration of gravity using a solid ball that connected to a rope attached to a stative pole. The pendulum is swung at a small angle resulted a simple harmonic motion. The measurement system consists of a power supply, Photogate sensors, Arduino pro mini and seven segments. The Arduino pro mini receives digital data from the photogate sensor and processes the digital data into the timing data of the pendulum oscillation. The calculation result of the pendulum oscillation time is displayed on seven segments. Based on measured data, the accuracy and precision of the experiment system are 98.76% and 99.81%, respectively. Based on experiment data, the system can be operated in physics experiment especially in determination of the gravity acceleration.

Low-degree gravity change from GPS data of COSMIC and GRACE satellite missions

NASA Astrophysics Data System (ADS)

Lin, Tingjung; Hwang, Cheinway; Tseng, Tzu-Pang; Chao, B. F.

2012-01-01

This paper demonstrates estimation of time-varying gravity harmonic coefficients from GPS data of COSMIC and GRACE satellite missions. The kinematic orbits of COSMIC and GRACE are determined to the cm-level accuracy. The NASA Goddard's GEODYN II software is used to model the orbit dynamics of COSMIC and GRACE, including the effect of a static gravity field. The surface forces are estimated per one orbital period. Residual orbits generated from kinematic and reference orbits serve as observables to determine the harmonic coefficients in the weighted-constraint least-squares. The monthly COSMIC and GRACE GPS data from September 2006 to December 2007 (16 months) are processed to estimate harmonic coefficients to degree 5. The geoid variations from the GPS and CSR RL04 (GRACE) solutions show consistent patterns over space and time, especially in regions of active hydrological changes. The monthly GPS-derived second zonal coefficient closely resembles the SLR-derived and CSR RL04 values, and third and fourth zonal coefficients resemble the CSR RL04 values.

Convergence and divergence in spherical harmonic series of the gravitational field generated by high-resolution planetary topography—A case study for the Moon

NASA Astrophysics Data System (ADS)

Hirt, Christian; Kuhn, Michael

2017-08-01

Theoretically, spherical harmonic (SH) series expansions of the external gravitational potential are guaranteed to converge outside the Brillouin sphere enclosing all field-generating masses. Inside that sphere, the series may be convergent or may be divergent. The series convergence behavior is a highly unstable quantity that is little studied for high-resolution mass distributions. Here we shed light on the behavior of SH series expansions of the gravitational potential of the Moon. We present a set of systematic numerical experiments where the gravity field generated by the topographic masses is forward-modeled in spherical harmonics and with numerical integration techniques at various heights and different levels of resolution, increasing from harmonic degree 90 to 2160 ( 61 to 2.5 km scales). The numerical integration is free from any divergence issues and therefore suitable to reliably assess convergence versus divergence of the SH series. Our experiments provide unprecedented detailed insights into the divergence issue. We show that the SH gravity field of degree-180 topography is convergent anywhere in free space. When the resolution of the topographic mass model is increased to degree 360, divergence starts to affect very high degree gravity signals over regions deep inside the Brillouin sphere. For degree 2160 topography/gravity models, severe divergence (with several 1000 mGal amplitudes) prohibits accurate gravity modeling over most of the topography. As a key result, we formulate a new hypothesis to predict divergence: if the potential degree variances show a minimum, then the SH series expansions diverge somewhere inside the Brillouin sphere and modeling of the internal potential becomes relevant.

A harmonic analysis of lunar gravity

NASA Technical Reports Server (NTRS)

Bills, B. G.; Ferrari, A. J.

1980-01-01

An improved model of lunar global gravity has been obtained by fitting a sixteenth-degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface. To compensate for the irregular selenographic distribution of these data, the solution algorithm has also incorporated a semi-empirical a priori covariance function. Maps of the free-air gravity disturbance and its formal error are presented, as are free-air anomaly and Bouguer anomaly maps. The lunar gravitational variance spectrum has the form V(G; n) = O(n to the -4th power), as do the corresponding terrestrial and martian spectra. The variance spectra of the Bouguer corrections (topography converted to equivalent gravity) for these bodies have the same basic form as the observed gravity; and, in fact, the spectral ratios are nearly constant throughout the observed spectral range for each body. Despite this spectral compatibility, the correlation between gravity and topography is generally quite poor on a global scale.

The orbits of the uranian satellites and rings, the gravity field of the uranian system, and the orientation of the pole of Uranus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jacobson, R. A., E-mail: robert.jacobson@jpl.nasa.gov

2014-11-01

French et al. determined the orbits of the Uranian rings, the orientation of the pole of Uranus, and the gravity harmonics of Uranus from Earth-based and Voyager ring occultations. Jacobson et al. determined the orbits of the Uranian satellites and the masses of Uranus and its satellites from Earth-based astrometry and observations acquired with the Voyager 2 spacecraft; they used the gravity harmonics and pole from French et al. Jacobson and Rush reconstructed the Voyager 2 trajectory and redetermined the Uranian system gravity parameters, satellite orbits, and ring orbits in a combined analysis of the data used previously augmented withmore » additional Earth-based astrometry. Here we report on an extension of that work that incorporates additional astrometry and ring occultations together with improved data processing techniques.« less

Hearing the transformation of conical to closed-pipe resonances

NASA Astrophysics Data System (ADS)

Ruiz, Michael J.

2017-05-01

The harmonics for an open cone with slant length L are the same as the harmonics for an open pipe with length L . When the cone is transformed through phases of closed-open conical frusta into a cylinder of length L closed at one end, the fundamental halves and only odd harmonics remain. A simple approach using boundary conditions is presented in order to understand this remarkable fact. A new free interactive HMTL5 application is provided which enables the user to hear the resonances of a complete cone transform into the pitches of a conical frustum closed at the small end, and eventually into the odd harmonics of a closed cylindrical pipe.

The relationship between mean anomaly block sizes and spherical harmonic representations. [of earth gravity

NASA Technical Reports Server (NTRS)

Rapp, R. H.

1977-01-01

The frequently used rule specifying the relationship between a mean gravity anomaly in a block whose side length is theta degrees and a spherical harmonic representation of these data to degree l-bar is examined in light of the smoothing parameter used by Pellinen (1966). It is found that if the smoothing parameter is not considered, mean anomalies computed from potential coefficients can be in error by about 30% of the rms anomaly value. It is suggested that the above mentioned rule should be considered only a crude approximation.

Non-Newtonian gravity or gravity anomalies?

NASA Technical Reports Server (NTRS)

Rubincam, David P.; Chao, B. Fong; Schatten, Kenneth H.; Sager, William W.

1988-01-01

Geophysical measurements of G differ from laboratory values, indicating that gravity may be non-Newtonian. A spherical harmonic formulation is presented for the variation of (Newtonian) gravity inside the Earth. Using the GEM-10B Earth Gravitational Field Model, it is shown that long-wavelength gravity anomalies, if not corrected, may masquerade as non-Newtonian gravity by providing significant influences on experimental observation of delta g/delta r and G. An apparent contradiction in other studies is also resolved: i.e., local densities appear in equations when average densities of layers seem to be called for.

Fluid core size of Mars from detection of the solar tide

NASA Technical Reports Server (NTRS)

Yoder, C. F.; Konopliv, A. S.; Yuan, D. N.; Standish, E. M.; Folkner, W. M.

2003-01-01

The solar tidal deformation of Mars, measured by its k2 potential Love number, has been obtained from an analysis of Mars Global Surveyor radio tracking. The observed k2 of 0.153 +/- 0.017 is large enough to rule out a solid iron core and so indicates that at least the outer part of the core is liquid. The inferred core radius is between 1520 and 1840 kilometers and is independent of many interior properties, although partial melt of the mantle is one factor that could reduce core size. Ice-cap mass changes can be deduced from the seasonal variations in air pressure and the odd gravity harmonic J3, given knowledge of cap mass distribution with latitude. The south cap seasonal mass change is about 30 to 40% larger than that of the north cap.

Fluid Core Size of Mars from Detection of the Solar Tide

NASA Astrophysics Data System (ADS)

Yoder, C. F.; Konopliv, A. S.; Yuan, D. N.; Standish, E. M.; Folkner, W. M.

2003-04-01

The solar tidal deformation of Mars, measured by its k2 potential Love number, has been obtained from an analysis of Mars Global Surveyor radio tracking. The observed k2 of 0.153 +/- 0.017 is large enough to rule out a solid iron core and so indicates that at least the outer part of the core is liquid. The inferred core radius is between 1520 and 1840 kilometers and is independent of many interior properties, although partial melt of the mantle is one factor that could reduce core size. Ice-cap mass changes can be deduced from the seasonal variations in air pressure and the odd gravity harmonic J3, given knowledge of cap mass distribution with latitude. The south cap seasonal mass change is about 30 to 40% larger than that of the north cap.

Analysis of harmonic spline gravity models for Venus and Mars

NASA Technical Reports Server (NTRS)

Bowin, Carl

1986-01-01

Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.

Mid-infrared-to-mid-ultraviolet supercontinuum enhanced by third-to-fifteenth odd harmonics.

PubMed

Mitrofanov, A V; Voronin, A A; Mitryukovskiy, S I; Sidorov-Biryukov, D A; Pugžlys, A; Andriukaitis, G; Flöry, T; Stepanov, E A; Fedotov, A B; Baltuška, A; Zheltikov, A M

2015-05-01

A high-energy supercontinuum spanning 4.7 octaves, from 250 to 6500 nm, is generated using a 0.3-TW, 3.9-μm output of a mid-infrared optical parametric chirped-pulse amplifier as a driver inducing a laser filament in the air. The high-frequency wing of the supercontinuum spectrum is enhanced by odd-order optical harmonics of the mid-infrared driver. Optical harmonics up to the 15th order are observed in supercontinuum spectra as overlapping, yet well-resolved peaks broadened, as verified by numerical modeling, due to spatially nonuniform ionization-induced blue shift.

High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data.

PubMed

Goossens, Sander; Sabaka, Terence J; Nicholas, Joseph B; Lemoine, Frank G; Rowlands, David D; Mazarico, Erwan; Neumann, Gregory A; Smith, David E; Zuber, Maria T

2014-05-28

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models. We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models.

High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data

PubMed Central

Goossens, Sander; Sabaka, Terence J; Nicholas, Joseph B; Lemoine, Frank G; Rowlands, David D; Mazarico, Erwan; Neumann, Gregory A; Smith, David E; Zuber, Maria T

2014-01-01

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models. Key Points We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models PMID:26074637

On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.

2004-01-01

The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.

Antarctic Rebound and the Time-Dependence of the Earth's Shape

NASA Technical Reports Server (NTRS)

Ivins, Erik R.; James, Thomas S.

2000-01-01

Great strides have been made during the past 30 years in refining models of the last global glaciation. The refinements draw upon a vastly expanded relative sea level and sedimentary core record. Furthermore, we now possess a sharpened understanding of the mechanisms that drive climate changes associated with deglaciation. Some 15 years ago, using only 5.5 years of ranging data, analyses of the drift in LAGEOS I node acceleration was used to infer that postglacial rebound was responsible for a secular change in the Earth's ellipsoidal shape (Yoder et al., .1983]. Today there exists a wealth of geodynamics satellite orbit data that constrain the secular time-dependence of the Earth's shape and low order gravity field, which includes mass redistribution from present-day glacier and great ice sheet imbalance and from postglacial rebound. We have shown that an unambiguous determination of the secular variation in the Earth's pear shaped harmonic (l = 3, m = 0) might provide information that bears on the present-day mass balance of Antarctica. This issue is revisited in light of new constraints on glacial loading during the late-Pleistocene and Holocene. An especially critical issue for the interpretation of secular odd degree zonal harmonics, l = 3 to 7, is the timing and magnitude of the deglaciation of Antarctica from Last Glacial Maximum. We explore ways in which the recovery of secular variation in both zonal and non-zonal harmonics for l = 2 through 7 can improve constraints on both rebound and present-day ice sheet balance.

Spatial properties of odd and even low order harmonics generated in gas.

PubMed

Lambert, G; Andreev, A; Gautier, J; Giannessi, L; Malka, V; Petralia, A; Sebban, S; Stremoukhov, S; Tissandier, F; Vodungbo, B; Zeitoun, Ph

2015-01-14

High harmonic generation in gases is developing rapidly as a soft X-ray femtosecond light-source for applications. This requires control over all the harmonics characteristics and in particular, spatial properties have to be kept very good. In previous literature, measurements have always included several harmonics contrary to applications, especially spectroscopic applications, which usually require a single harmonic. To fill this gap, we present here for the first time a detailed study of completely isolated harmonics. The contribution of the surrounding harmonics has been totally suppressed using interferential filtering which is available for low harmonic orders. In addition, this allows to clearly identify behaviors of standard odd orders from even orders obtained by frequency-mixing of a fundamental laser and of its second harmonic. Comparisons of the spatial intensity profiles, of the spatial coherence and of the wavefront aberration level of 5ω at 160 nm and 6ω at 135 nm have then been performed. We have established that the fundamental laser beam aberrations can cause the appearance of a non-homogenous donut-shape in the 6ω spatial intensity distribution. This undesirable effect can be easily controlled. We finally conclude that the spatial quality of an even harmonic can be as excellent as in standard generation.

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction. M.S. Thesis

NASA Technical Reports Server (NTRS)

Davis, John H.

1993-01-01

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

Long period nodal motion of sun synchronous orbits

NASA Technical Reports Server (NTRS)

Duck, K. I.

1975-01-01

An approximative model is formulated for assessing these perturbations that significantly affect long term modal motion of sun synchronous orbits. Computer simulations with several independent computer programs consider zonal and tesseral gravitational harmonics, third body gravitational disturbances induced by the sun and the moon, and atmospheric drag. A pendulum model consisting of evenzonal harmonics through order 4 and solar gravity dominated nodal motion approximation. This pendulum motion results from solar gravity inducing an inclination oscillation which couples into the nodal precession induced by the earth's oblateness. The pendulum model correlated well with simulations observed flight data.

Low degree Earth's gravity coefficients determined from different space geodetic observations and climate models

NASA Astrophysics Data System (ADS)

Wińska, Małgorzata; Nastula, Jolanta

2017-04-01

Large scale mass redistribution and its transport within the Earth system causes changes in the Earth's rotation in space, gravity field and Earth's ellipsoid shape. These changes are observed in the ΔC21, ΔS21, and ΔC20 spherical harmonics gravity coefficients, which are proportional to the mass load-induced Earth rotational excitations. In this study, linear trend, decadal, inter-annual, and seasonal variations of low degree spherical harmonics coefficients of Earth's gravity field, determined from different space geodetic techniques, Gravity Recovery and Climate Experiment (GRACE), satellite laser ranging (SLR), Global Navigation Satellite System (GNSS), Earth rotation, and climate models, are examined. In this way, the contribution of each measurement technique to interpreting the low degree surface mass density of the Earth is shown. Especially, we evaluate an usefulness of several climate models from the Coupled Model Intercomparison Project phase 5 (CMIP5) to determine the low degree Earth's gravity coefficients using GRACE satellite observations. To do that, Terrestrial Water Storage (TWS) changes from several CMIP5 climate models are determined and then these simulated data are compared with the GRACE observations. Spherical harmonics ΔC21, ΔS21, and ΔC20 changes are calculated as the sum of atmosphere and ocean mass effect (GAC values) taken from GRACE and a land surface hydrological estimate from the selected CMIP5 climate models. Low degree Stokes coefficients of the surface mass density determined from GRACE, SLR, GNSS, Earth rotation measurements and climate models are compared to each other in order to assess their consistency. The comparison is done by using different types of statistical and signal processing methods.

A high resolution gravity model for Venus - GVM-1

NASA Technical Reports Server (NTRS)

Nerem, R. S.; Bills, B. G.; Mcnamee, J. B.

1993-01-01

A spherical harmonic model of the gravitational field of Venus complete to degree and order 50 has been developed using the S-band Doppler tracking data of the Pioneer Venus Orbiter (PVO) collected between 1979 and 1982. The short wavelengths of this model could only be resolved near the PVO periapse location (about 14 deg N latitude), therefore a priori constraints were applied to the model to bias poorly observed coefficients towards zero. The resulting model has a half-wavelength resolution of 400 km near the PVO periapse location, but the resolution degrades to greater than 1000 km near the poles. This gravity model correlates well with a degree 50 spherical harmonic expansion of the Venus topography derived from a combination of Magellan and PVO data. New tracking data from Magellan's gravity mission should provide some improvement to this model, although a complete model of the Venusian gravity field will depend on tracking of Magellan after the circularization of its orbit using aerobraking.

The ITSG-Grace2014 Gravity Field Model

NASA Astrophysics Data System (ADS)

Kvas, Andreas; Mayer-Gürr, Torsten; Zehenter, Norbert; Klinger, Beate

2015-04-01

The ITSG-Grace2014 GRACE-only gravity field model consists of a high resolution unconstrained static model (up to degree 200) with trend and annual signal, monthly unconstrained solutions with different spatial resolutions as well as daily snapshots derived by using a Kalman smoother. Apart from the estimated spherical harmonic coefficients, full variance-covariance matrices for the monthly solutions and the static gravity field component are provided. Compared to the previous release, multiple improvements in the processing chain are implemented: updated background models, better ionospheric modeling for GPS observations, an improved satellite attitude by combination of star camera and angular accelerations, estimation of K-band antenna center variations within the gravity field recovery process as well as error covariance function determination. Furthermore, daily gravity field variations have been modeled in the adjustment process to reduce errors caused by temporal leakage. This combined estimation of daily gravity variations field variations together with the static gravity field component represents a computational challenge due to the significantly increased parameter count. The modeling of daily variations up to a spherical harmonic degree of 40 for the whole GRACE observation period results in a system of linear equations with over 6 million unknown gravity field parameters. A least squares adjustment of this size is not solvable in a sensible time frame, therefore measures to reduce the problem size have to be taken. The ITSG-Grace2014 release is presented and selected parts of the processing chain and their effect on the estimated gravity field solutions are discussed.

Earth Gravitational Model 2020

NASA Astrophysics Data System (ADS)

Barnes, Daniel; Holmes, Simon; Factor, John; Ingalls, Sarah; Presicci, Manny; Beale, James

2017-04-01

The National Geospatial-Intelligence Agency [NGA], in conjunction with its U.S. and international partners, has begun preliminary work on its next Earth Gravitational Model, to replace EGM2008. The new 'Earth Gravitational Model 2020' [EGM2020] has an expected public release date of 2020, and will likely retain the same harmonic basis and resolution as EGM2008. As such, EGM2020 will be essentially an ellipsoidal harmonic model up to degree (n) and order (m) 2159, but will be released as a spherical harmonic model to degree 2190 and order 2159. EGM2020 will benefit from new data sources and procedures. Updated satellite gravity information from the GOCE and GRACE mission, will better support the lower harmonics, globally. Multiple new acquisitions (terrestrial, airborne and ship borne) of gravimetric data over specific geographical areas, will provide improved global coverage and resolution over the land, as well as for coastal and some ocean areas. Ongoing accumulation of satellite altimetry data as well as improvements in the treatment of this data, will better define the marine gravity field, most notably in polar and near-coastal regions. NGA and partners are evaluating different approaches for optimally combining the new GOCE/GRACE satellite gravity models with the terrestrial data. These include the latest methods employing a full covariance adjustment. NGA is also working to assess systematically the quality of its entire gravimetry database, towards correcting biases and other egregious errors where possible, and generating improved error models that will inform the final combination with the latest satellite gravity models. Outdated data gridding procedures have been replaced with improved approaches. For EGM2020, NGA intends to extract maximum value from the proprietary data that overlaps geographically with unrestricted data, whilst also making sure to respect and honor its proprietary agreements with its data-sharing partners. Approved for Public Release, 15-564

Earth Gravitational Model 2020

NASA Astrophysics Data System (ADS)

Barnes, D.; Factor, J. K.; Holmes, S. A.; Ingalls, S.; Presicci, M. R.; Beale, J.; Fecher, T.

2015-12-01

The National Geospatial-Intelligence Agency [NGA], in conjunction with its U.S. and international partners, has begun preliminary work on its next Earth Gravitational Model, to replace EGM2008. The new 'Earth Gravitational Model 2020' [EGM2020] has an expected public release date of 2020, and will likely retain the same harmonic basis and resolution as EGM2008. As such, EGM2020 will be essentially an ellipsoidal harmonic model up to degree (n) and order (m) 2159, but will be released as a spherical harmonic model to degree 2190 and order 2159. EGM2020 will benefit from new data sources and procedures. Updated satellite gravity information from the GOCE and GRACE mission, will better support the lower harmonics, globally. Multiple new acquisitions (terrestrial, airborne and shipborne) of gravimetric data over specific geographical areas, will provide improved global coverage and resolution over the land, as well as for coastal and some ocean areas. Ongoing accumulation of satellite altimetry data as well as improvements in the treatment of this data, will better define the marine gravity field, most notably in polar and near-coastal regions. NGA and partners are evaluating different approaches for optimally combining the new GOCE/GRACE satellite gravity models with the terrestrial data. These include the latest methods employing a full covariance adjustment. NGA is also working to assess systematically the quality of its entire gravimetry database, towards correcting biases and other egregious errors where possible, and generating improved error models that will inform the final combination with the latest satellite gravity models. Outdated data gridding procedures have been replaced with improved approaches. For EGM2020, NGA intends to extract maximum value from the proprietary data that overlaps geographically with unrestricted data, whilst also making sure to respect and honor its proprietary agreements with its data-sharing partners.

Harmonic Series Meets Fibonacci Sequence

ERIC Educational Resources Information Center

Chen, Hongwei; Kennedy, Chris

2012-01-01

The terms of a conditionally convergent series may be rearranged to converge to any prescribed real value. What if the harmonic series is grouped into Fibonacci length blocks? Or the harmonic series is arranged in alternating Fibonacci length blocks? Or rearranged and alternated into separate blocks of even and odd terms of Fibonacci length?

Theory of a refined earth model

NASA Technical Reports Server (NTRS)

Krause, H. G. L.

1968-01-01

Refined equations are derived relating the variations of the earths gravity and radius as functions of longitude and latitude. They particularly relate the oblateness coefficients of the old harmonics and the difference of the polar radii /respectively, ellipticities and polar gravity accelerations/ in the Northern and Southern Hemispheres.

Modeling of the Earth's gravity field using the New Global Earth Model (NEWGEM)

NASA Technical Reports Server (NTRS)

Kim, Yeong E.; Braswell, W. Danny

1989-01-01

Traditionally, the global gravity field was described by representations based on the spherical harmonics (SH) expansion of the geopotential. The SH expansion coefficients were determined by fitting the Earth's gravity data as measured by many different methods including the use of artificial satellites. As gravity data have accumulated with increasingly better accuracies, more of the higher order SH expansion coefficients were determined. The SH representation is useful for describing the gravity field exterior to the Earth but is theoretically invalid on the Earth's surface and in the Earth's interior. A new global Earth model (NEWGEM) (KIM, 1987 and 1988a) was recently proposed to provide a unified description of the Earth's gravity field inside, on, and outside the Earth's surface using the Earth's mass density profile as deduced from seismic studies, elevation and bathymetric information, and local and global gravity data. Using NEWGEM, it is possible to determine the constraints on the mass distribution of the Earth imposed by gravity, topography, and seismic data. NEWGEM is useful in investigating a variety of geophysical phenomena. It is currently being utilized to develop a geophysical interpretation of Kaula's rule. The zeroth order NEWGEM is being used to numerically integrate spherical harmonic expansion coefficients and simultaneously determine the contribution of each layer in the model to a given coefficient. The numerically determined SH expansion coefficients are also being used to test the validity of SH expansions at the surface of the Earth by comparing the resulting SH expansion gravity model with exact calculations of the gravity at the Earth's surface.

Interannual Variations in Earth's Low-Degree Gravity Field and the Connections With Geophysical/Climatic Changes

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Cox, Christopher M.

2004-01-01

Long-wavelength time-variable gravity recently derived from satellite laser ranging (SLR) analysis have focused to a large extent on the effects of the recent (since 1998) large anomalous change in J2, or the Earth's oblateness, and the potential causes. However, it is relatively more difficult to determine whether there are corresponding signals in the shorter wavelength zonal harmonics from the existing SLR-derived time variable gravity results, although it appears that geophysical fluid mass transport is being observed. For example, the recovered J3 time series shows remarkable agreement with NCEP-derived estimates of atmospheric gravity variations. Likewise, some of the non-zonal spherical harmonic components have significant interannual signal that appears to be related to mass transport. The non-zonal degree-2 components show reasonable temporal correlation with atmospheric signals, as well as climatic effects such as El Nino Southern Oscillation. We will present recent updates on the J2 evolution, as well as a look at other low-degree components of the interannual variations of gravity, complete through degree 4. We will examine the possible geophysical and climatic causes of these low-degree time-variable gravity related to oceanic and hydrological mass transports, for example some anomalous but prominent signals found in the extratropic Pacific ocean related to the Pacific Decadal Oscillation.

An Improved 360 Degree and Order Model of Venus Topography

NASA Technical Reports Server (NTRS)

Rappaport, Nicole J.; Konopliv, Alex S.; Kucinskas, Algis B.; Ford, Peter G.

1999-01-01

We present an improved 360 degree and order spherical harmonic solution for Venus' topography. The new model uses the most recent set of Venus altimetry data with spacecraft positions derived from a recent high resolution gravity model. Geometric analysis indicates that the offset between the center of mass and center of figure of Venus is about 10 times smaller than that for the Earth, the Moon, or Mars. Statistical analyses confirm that the RMS topography follows a power law over the central part of the spectrum. Compared to the previous topography model, the new model is more highly correlated with Venus' harmonic gravity field.

High intensity single bunch operation with heavy periodic transient beam loading in wide band rf cavities

NASA Astrophysics Data System (ADS)

Tamura, Fumihiko; Hotchi, Hideaki; Schnase, Alexander; Yoshii, Masahito; Yamamoto, Masanobu; Ohmori, Chihiro; Nomura, Masahiro; Toda, Makoto; Shimada, Taihei; Hasegawa, Katsushi; Hara, Keigo

2015-09-01

The rapid cycling synchrotron (RCS) in the Japan Proton Accelerator Research Complex (J-PARC) was originally designed to accelerate two high intensity bunches, while some of neutron experiments in the materials and life science experimental facility and a muon experiment using main ring beams require a single bunch operation mode, in which one of the two rf buckets is filled and the other is empty. The beam intensity in the single bunch operation has been limited by longitudinal beam losses due to the rf bucket distortions by the wake voltage of the odd harmonics (h =1 ,3 ,5 ) in the wide band magnetic alloy cavities. We installed an additional rf feedforward system to compensate the wake voltages of the odd harmonics (h =1 ,3 ,5 ). The additional system has a similar structure as the existing feedforward system for the even harmonics (h =2 ,4 ,6 ). We describe the function of the feedforward system for the odd harmonics, the commissioning methodology, and the commissioning results. The longitudinal beam losses during the single bunch acceleration disappeared with feedforward for the odd harmonics. We also confirmed that the beam quality in the single bunch acceleration are similar to that of the normal operation with two bunches. Thus, high intensity single bunch acceleration at the intensity of 2.3 ×1013 protons per bunch has been achieved in the J-PARC RCS. This article is a follow-up of our previous article, Phys. Rev. ST Accel. Beams 14, 051004 (2011). The feedforward system extension for single bunch operation was successful.

The Mystery of the Mars North Polar Gravity-Topography Correlation(Or Lack Thereof)

NASA Technical Reports Server (NTRS)

Phillips, R. J.; Sjogren, W. L.; Johnson, C. L.

1999-01-01

Maps of moderately high resolution gravity data obtained from the Mars Global Surveyor (MGS) gravity calibration orbit campaign and high precision topography obtained from the Mars Orbiter Laser Altimeter (MOLA) experiment reveal relationships between gravity and topography in high northern latitudes of Mars. Figure 1 shows the results of a JPL spherical harmonic gravity model bandpass filtered between degrees 6 and 50 contoured over a MOLA topographic image. A positive gravity anomaly exists over the main North Polar cap, but there are at least six additional positive gravity anomalies, as well as a number of smaller negative anomalies, with no obvious correlation to topography. Additional information is contained in the original extended abstract.

Enhancement of high harmonics from plasmas using two-color pump and chirp variation of 1 kHz Ti:sapphire laser pulses.

PubMed

Ganeev, R A; Hutchison, C; Zaïr, A; Witting, T; Frank, F; Okell, W A; Tisch, J W G; Marangos, J P

2012-01-02

We have investigated resonance effects in high-order harmonic generation (HHG) within laser-produced plasmas. We demonstrate a significantly improved harmonic yield by using two-color pump-induced enhancement and a 1 kHz pulse repetition rate. Together with an increased HHG output, the even harmonics in the cutoff region were enhanced with respect to odd harmonics. We report the observation of a resonance-induced growth in intensity of 20th harmonic in silver plasma (2×), 26th harmonic in vanadium plasma (4×), and 28th harmonic in chromium plasma (5×).

(abstract) Venus Gravity Field

NASA Technical Reports Server (NTRS)

Konopliv, A. S.; Sjogren, W. L.

1995-01-01

A global gravity field model of Venus to degree and order 75 (5772 spherical harmonic coefficients) has been estimated from Doppler radio tracking of the orbiting spacecraft Pioneer Venus Orbiter (1979-1992) and Magellan (1990-1994). After the successful aerobraking of Magellan, a near circular polar orbit was attained and relatively uniform gravity field resolution (approximately 200 km) was obtained with formal uncertainties of a few milligals. Detailed gravity for several highland features are displayed as gravity contours overlaying colored topography. The positive correlation of typography with gravity is very high being unlike that of the Earth, Moon, and Mars. The amplitudes are Earth-like, but have significantly different gravity-topography ratios for different features. Global gravity, geoid, and isostatic anomaly maps as well as the admittance function are displayed.

2017 Updates: Earth Gravitational Model 2020

NASA Astrophysics Data System (ADS)

Barnes, D. E.; Holmes, S. A.; Ingalls, S.; Beale, J.; Presicci, M. R.; Minter, C.

2017-12-01

The National Geospatial-Intelligence Agency [NGA], in conjunction with its U.S. and international partners, has begun preliminary work on its next Earth Gravitational Model, to replace EGM2008. The new `Earth Gravitational Model 2020' [EGM2020] has an expected public release date of 2020, and will retain the same harmonic basis and resolution as EGM2008. As such, EGM2020 will be essentially an ellipsoidal harmonic model up to degree (n) and order (m) 2159, but will be released as a spherical harmonic model to degree 2190 and order 2159. EGM2020 will benefit from new data sources and procedures. Updated satellite gravity information from the GOCE and GRACE mission, will better support the lower harmonics, globally. Multiple new acquisitions (terrestrial, airborne and shipborne) of gravimetric data over specific geographical areas (Antarctica, Greenland …), will provide improved global coverage and resolution over the land, as well as for coastal and some ocean areas. Ongoing accumulation of satellite altimetry data as well as improvements in the treatment of this data, will better define the marine gravity field, most notably in polar and near-coastal regions. NGA and partners are evaluating different approaches for optimally combining the new GOCE/GRACE satellite gravity models with the terrestrial data. These include the latest methods employing a full covariance adjustment. NGA is also working to assess systematically the quality of its entire gravimetry database, towards correcting biases and other egregious errors. Public release number 15-564

Gravity field of Venus at constant altitude and comparison with earth

NASA Technical Reports Server (NTRS)

Bowin, C.; Abers, G.; Shure, L.

1985-01-01

The gravity field of Venus is characterized in gravity-anomaly and geoid-undulation maps produced by applying the harmonic-spline technique (Shure et al., 1982 and 1983; Parker and Shure, 1982) to Pioneer Venus Orbiter line-of-sight data. A positive correlation between Venusian topographic features and gravity anomalies is observed, in contrast to the noncorrelation seen on earth, and attributed to the thicker crust of Venus (70-80 vs 5-40 km for earth), crustal loading by recent volcanism, and possible regional elevation due to deep heating and thermal expansion.

Hearing the Transformation of Conical to Closed-Pipe Resonances

ERIC Educational Resources Information Center

Ruiz, Michael J.

2017-01-01

The harmonics for an open cone with slant length "L" are the same as the harmonics for an open pipe with length "L." When the cone is transformed through phases of closed-open conical frusta into a cylinder of length "L" closed at one end, the fundamental halves and only odd harmonics remain. A simple approach using…

On the Retrieval of Geocenter Motion from Gravity Data

NASA Astrophysics Data System (ADS)

Rosat, S.; Mémin, A.; Boy, J. P.; Rogister, Y. J. G.

2017-12-01

The center of mass of the whole Earth, the so-called geocenter, is moving with respect to the Center of Mass of the solid Earth because of the loading exerted by the Earth's fluid layers on the solid crust. Space geodetic techniques tying satellites and ground stations (e.g. GNSS, SLR and DORIS) have been widely employed to estimate the geocenter motion. Harmonic degree-1 variations of the gravity field are associated to the geocenter displacement. We show that ground records of time-varying gravity from Superconducting Gravimeters (SGs) can be used to constrain the geocenter motion. Two major difficulties have to be tackled: (1) the sensitivity of surface gravimetric measurements to local mass changes, and in particular hydrological and atmospheric variabilities; (2) the spatial aliasing (spectral leakage) of spherical harmonic degrees higher than 1 induced by the under-sampling of station distribution. The largest gravity variations can be removed from the SG data by subtracting solid and oceanic tides as well as atmospheric and hydrologic effects using global models. However some hydrological signal may still remain. Since surface water content is well-modelled using GRACE observations, we investigate how the spatial aliasing in SG data can be reduced by employing GRACE solutions when retrieving geocenter motion. We show synthetic simulations using complete surface loading models together with GRACE solutions computed at SG stations. In order to retrieve the degree-one gravity variations that are associated with the geocenter motion, we use a multi-station stacking method that performs better than a classical spherical harmonic stacking when the station distribution is inhomogeneous. We also test the influence of the network configuration on the estimate of the geocenter motion. An inversion using SG and GRACE observations is finally presented and the results are compared with previous geocenter estimates.

Orbital Disturbance Analysis due to the Lunar Gravitational Potential and Deviation Minimization through the Trajectory Control in Closed Loop

NASA Astrophysics Data System (ADS)

Gonçalves, L. D.; Rocco, E. M.; de Moraes, R. V.

2013-10-01

A study evaluating the influence due to the lunar gravitational potential, modeled by spherical harmonics, on the gravity acceleration is accomplished according to the model presented in Konopliv (2001). This model provides the components x, y and z for the gravity acceleration at each moment of time along the artificial satellite orbit and it enables to consider the spherical harmonic degree and order up to100. Through a comparison between the gravity acceleration from a central field and the gravity acceleration provided by Konopliv's model, it is obtained the disturbing velocity increment applied to the vehicle. Then, through the inverse problem, the Keplerian elements of perturbed orbit of the satellite are calculated allowing the orbital motion analysis. Transfer maneuvers and orbital correction of lunar satellites are simulated considering the disturbance due to non-uniform gravitational potential of the Moon, utilizing continuous thrust and trajectory control in closed loop. The simulations are performed using the Spacecraft Trajectory Simulator-STRS, Rocco (2008), which evaluate the behavior of the orbital elements, fuel consumption and thrust applied to the satellite over the time.

Short and long periodic atmospheric variations between 25 and 200 km

NASA Technical Reports Server (NTRS)

Justus, C. G.; Woodrum, A.

1973-01-01

Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analyzed by a daily difference method and results on the distribution statistics, magnitude, and spatial structure of gravity wave and planetary wave atmospheric variations are presented. Time structure of the gravity wave variations were determined by the analysis of residuals from harmonic analysis of time series data. Planetary wave contributions in the 25-85 km range were discovered and found to have significant height and latitudinal variation. Long period planetary waves, and seasonal variations were also computed by harmonic analysis. Revised height variations of the gravity wave contributions in the 25 to 85 km height range were computed. An engineering method and design values for gravity wave magnitudes and wave lengths are given to be used for such tasks as evaluating the effects on the dynamical heating, stability and control of spacecraft such as the space shuttle vehicle in launch or reentry trajectories.

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

NASA Astrophysics Data System (ADS)

Balajany, Hamideh; Mehrafarin, Mohammad

2018-05-01

By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis-Riesenfeld phase.

Gravity field of Jupiter’s moon Amalthea and the implication on a spacecraft trajectory

NASA Astrophysics Data System (ADS)

Weinwurm, Gudrun

2006-01-01

Before its final plunge into Jupiter in September 2003, GALILEO made a last 'visit' to one of Jupiter's moons - Amalthea. This final flyby of the spacecraft's successful mission occurred on November 5, 2002. In order to analyse the spacecraft data with respect to Amalthea's gravity field, interior models of the moon had to be provided. The method used for this approach is based on the numerical integration of infinitesimal volume elements of a three-axial ellipsoid in elliptic coordinates. To derive the gravity field coefficients of the body, the second method of Neumann was applied. Based on the spacecraft trajectory data provided by the Jet Propulsion Laboratory, GALILEO's velocity perturbations at closest approach could be calculated. The harmonic coefficients of Amalthea's gravity field have been derived up to degree and order six, for both homogeneous and reasonable heterogeneous cases. Founded on these numbers the impact on the trajectory of GALILEO was calculated and compared to existing Doppler data. Furthermore, predictions for future spacecraft flybys were derived. No two-way Doppler-data was available during the flyby and the harmonic coefficients of the gravity field are buried in the one-way Doppler-noise. Nevertheless, the generated gravity field models reflect the most likely interior structure of the moon and can be a basis for further exploration of the Jovian system.

High-resolution regional gravity field modelling in a mountainous area from terrestrial gravity data

NASA Astrophysics Data System (ADS)

Bucha, Blažej; Janák, Juraj; Papčo, Juraj; Bezděk, Aleš

2016-11-01

We develop a high-resolution regional gravity field model by a combination of spherical harmonics, band-limited spherical radial basis functions (SRBFs) and the residual terrain model (RTM) technique. As the main input data set, we employ a dense terrestrial gravity database (3-6 stations km-2), which enables gravity field modelling up to very short spatial scales. The approach is based on the remove-compute-restore methodology in which all the parts of the signal that can be modelled are removed prior to the least-squares adjustment in order to smooth the input gravity data. To this end, we utilize degree-2159 spherical harmonic models and the RTM technique using topographic models at 2 arcsec resolution. The residual short-scale gravity signal is modelled via the band-limited Shannon SRBF expanded up to degree 21 600, which corresponds to a spatial resolution of 30 arcsec. The combined model is validated against GNSS/levelling-based height anomalies, independent surface gravity data, deflections of the vertical and terrestrial vertical gravity gradients achieving an accuracy of 2.7 cm, 0.53 mGal, 0.39 arcsec and 279 E in terms of the RMS error, respectively. A key aspect of the combined approach, especially in mountainous areas, is the quality of the RTM. We therefore compare the performance of two RTM techniques within the innermost zone, the tesseroids and the polyhedron. It is shown that the polyhedron-based approach should be preferred in rugged terrain if a high-quality RTM is required. In addition, we deal with the RTM computations at points located below the reference surface of the residual terrain which is known to be a rather delicate issue.

Earth System Data Records of Mass Transport from Time-Variable Gravity Data

NASA Astrophysics Data System (ADS)

Zlotnicki, V.; Talpe, M.; Nerem, R. S.; Landerer, F. W.; Watkins, M. M.

2014-12-01

Satellite measurements of time variable gravity have revolutionized the study of Earth, by measuring the ice losses of Greenland, Antarctica and land glaciers, changes in groundwater including unsustainable losses due to extraction of groundwater, the mass and currents of the oceans and their redistribution during El Niño events, among other findings. Satellite measurements of gravity have been made primarily by four techniques: satellite tracking from land stations using either lasers or Doppler radio systems, satellite positioning by GNSS/GPS, satellite to satellite tracking over distances of a few hundred km using microwaves, and through a gravity gradiometer (radar altimeters also measure the gravity field, but over the oceans only). We discuss the challenges in the measurement of gravity by different instruments, especially time-variable gravity. A special concern is how to bridge a possible gap in time between the end of life of the current GRACE satellite pair, launched in 2002, and a future GRACE Follow-On pair to be launched in 2017. One challenge in combining data from different measurement systems consists of their different spatial and temporal resolutions and the different ways in which they alias short time scale signals. Typically satellite measurements of gravity are expressed in spherical harmonic coefficients (although expansions in terms of 'mascons', the masses of small spherical caps, has certain advantages). Taking advantage of correlations among spherical harmonic coefficients described by empirical orthogonal functions and derived from GRACE data it is possible to localize the otherwise coarse spatial resolution of the laser and Doppler derived gravity models. This presentation discusses the issues facing a climate data record of time variable mass flux using these different data sources, including its validation.

Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.

Gravity research at Cottrell observatory

NASA Technical Reports Server (NTRS)

Tuman, V. S.; Anderson, J. D.; Lau, E. L.

1977-01-01

The Cottrell gravity research observatory and work in progress are described. Equipment in place and equipment to be installed, the cryogenic gravity meter (CGM), concrete pads to support the vertical seismometer, CGM, and guest experiments, techniques of data analysis, and improvements needed in the CGM are discussed. Harmonic earth eigenvibrations with multipole moments are examined and their compatibility with a fictitious black hole binary system (of which the primary central mass is assigned a value one million solar masses) located 400 light-years away is shown by calculations.

Solution of the Quantum Harmonic Oscillator Plus a Delta-Function Potential at the Origin: The "Oddness" of Its Even-Parity Solutions

ERIC Educational Resources Information Center

Viana-Gomes, J.; Peres, N. M. R.

2011-01-01

We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…

A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation.

PubMed

Tie, Junbo; Cao, Juliang; Chang, Lubing; Cai, Shaokun; Wu, Meiping; Lian, Junxiang

2018-03-16

Compensation of gravity disturbance can improve the precision of inertial navigation, but the effect of compensation will decrease due to the accelerometer bias, and estimation of the accelerometer bias is a crucial issue in gravity disturbance compensation. This paper first investigates the effect of accelerometer bias on gravity disturbance compensation, and the situation in which the accelerometer bias should be estimated is established. The accelerometer bias is estimated from the gravity vector measurement, and a model of measurement noise in gravity vector measurement is built. Based on this model, accelerometer bias is separated from the gravity vector measurement error by the method of least squares. Horizontal gravity disturbances are calculated through EGM2008 spherical harmonic model to build the simulation scene, and the simulation results indicate that precise estimations of the accelerometer bias can be obtained with the proposed method.

A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation

PubMed Central

Cao, Juliang; Cai, Shaokun; Wu, Meiping; Lian, Junxiang

2018-01-01

Compensation of gravity disturbance can improve the precision of inertial navigation, but the effect of compensation will decrease due to the accelerometer bias, and estimation of the accelerometer bias is a crucial issue in gravity disturbance compensation. This paper first investigates the effect of accelerometer bias on gravity disturbance compensation, and the situation in which the accelerometer bias should be estimated is established. The accelerometer bias is estimated from the gravity vector measurement, and a model of measurement noise in gravity vector measurement is built. Based on this model, accelerometer bias is separated from the gravity vector measurement error by the method of least squares. Horizontal gravity disturbances are calculated through EGM2008 spherical harmonic model to build the simulation scene, and the simulation results indicate that precise estimations of the accelerometer bias can be obtained with the proposed method. PMID:29547552

Mars topography harmonics and geophysical implications

NASA Technical Reports Server (NTRS)

Bills, B. G.; Ferrari, A. J.

1978-01-01

The paper describes an improved model of Martian global topography which has been obtained by fitting a sixteenth-degree harmonic series to occultation, radar, spectral, and photogrammetric measurements. Empirical elevation data based on photographic data are used to supplement the observations in areas without data. Values for the mean radius, the mean density, and the displacement of the center of the figure from the center of mass are presented. The reported geometric flattening is too great and the reported dynamic flattening is too small for Mars to be homogeneous and hydrostatic. Maps of the data distribution, global topography, and Bouguer gravity anomaly are interpreted in terms of a crustal thickness map which is consistent with gravity, topography, and recent preliminary Viking seismic results.

The harmonic development of the Earth tide generating potential due to the direct effect of the planets

NASA Astrophysics Data System (ADS)

Hartmann, Torsten; Wenzel, Hans-Georg

1994-09-01

The time-harmonic development of the Earth tide generating potential due to the direct effect of the planets Venus, Jupiter, Mars, Mercury and Saturn has been computed. The catalog of the fully normalized potential coefficients contains 1483 waves. It is based on the DE102 numerical ephemeris of the planets between years 1900 and 2200. Gravity tides due to the planets computed from the catalog at the surface of the Earth have an accuracy of about 0.027 pm/sq s (1 pm/sq s = 10(exp -12) m/sq s = 0.1 ngal) rms and 0.160 / 0.008 pm/sq s at maximum in time / frequency domain using the new benchmark tidal gravity series (Wenzel 1994).

Global accuracy estimates of point and mean undulation differences obtained from gravity disturbances, gravity anomalies and potential coefficients

NASA Technical Reports Server (NTRS)

Jekeli, C.

1979-01-01

Through the method of truncation functions, the oceanic geoid undulation is divided into two constituents: an inner zone contribution expressed as an integral of surface gravity disturbances over a spherical cap; and an outer zone contribution derived from a finite set of potential harmonic coefficients. Global, average error estimates are formulated for undulation differences, thereby providing accuracies for a relative geoid. The error analysis focuses on the outer zone contribution for which the potential coefficient errors are modeled. The method of computing undulations based on gravity disturbance data for the inner zone is compared to the similar, conventional method which presupposes gravity anomaly data within this zone.

Lunar gravity derived from long-period satellite motion, a proposed method

NASA Technical Reports Server (NTRS)

Ferrari, A. J.

1971-01-01

A method was devised to determine the spherical harmonic coefficients of the lunar gravity field. The method consists of a two-step data reduction and estimation process. Pseudo-Doppler data were generated simulating two different lunar orbits. The analysis included the perturbing effects of the L1 lunar gravity field, the earth, the sun, and solar radiation pressure. Orbit determinations were performed on these data and long-period orbital elements were obtained. The Kepler element rates from these solutions were used to recover L1 lunar gravity coefficients. Overall results of the experiment show that lunar gravity coefficients can be accurately determined and that the method is dynamically consistent with long-period perturbation theory.

ARISTOTELES: A European approach for an Earth gravity field recovery mission

NASA Technical Reports Server (NTRS)

Benz, R.; Faulks, H.; Langemann, M.

1989-01-01

Under contract of the European Space Agency a system study for a spaceborne gravity field recovery mission was performed, covering as a secondary mission objective geodetic point positioning in the cm range as well. It was demonstrated that under the given programmatic constraints including dual launch and a very tight development schedule, a six months gravity field mission in a 200 km near polar, dawn-dusk orbit is adequate to determine gravity anomalies to better than 5 mgal with a spatial resolution of 100 x 100 km half wavelength. This will enable scientists to determine improved spherical harmonic coefficients of the Earth gravity field equation to the order and degree of 180 or better.

Mass change from GRACE: a simulated comparison of Level-1B analysis techniques

NASA Astrophysics Data System (ADS)

Andrews, Stuart B.; Moore, Philip; King, Matt. A.

2015-01-01

Spherical harmonic and mascon parameters have both been successfully applied in the recovery of time-varying gravity fields from Gravity Recovery and Climate Experiment (GRACE). However, direct comparison of any mass flux is difficult with solutions generated by different groups using different codes and algorithms. It is therefore opportune to compare these methodologies, within a common software base, to understand potential limitations associated with each technique. Here we use simulations to recover a known monthly surface mass distribution from GRACE KBRR data. The ability of spherical harmonic and mascon parameters to resolve basin-level mass change is quantified with an assessment of how the noise and errors, inherent in GRACE solutions, are handled. Recovery of a noise and error free GLDAS anomaly revealed no quantifiable difference between spherical harmonic and mascon parameters. Expansion of the GLDAS anomaly to degree and order 120 shows that both spherical harmonic and mascon parameters are affected by comparable omission errors. However, the inclusion of realistic KBRR noise and errors in the simulations reveals the advantage of the mascon parameters over spherical harmonics at reducing noise and errors in the higher degree and order harmonics with an rms (cm of EWH) to the GLDAS anomaly of 10.0 for the spherical harmonic solution and 8.8 (8.6) for the 4°(2°) mascon solutions. The introduction of a constraint matrix in the mascon solution based on parameters that share geophysical similarities is shown to further reduce the signal lost at all degrees. The recovery of a simulated Antarctic mass loss signal shows that the mascon methodology is superior to spherical harmonics for this region with an rms (cm of EWH) of 8.7 for the 2° mascon solution compared to 10.0 for the spherical harmonic solution. Investigating the noise and errors for a month when the satellites were in resonance revealed both the spherical harmonic and mascon methodologies are able to recover the GLDAS and Antarctic mass loss signal with either a comparable (spherical harmonic) or improved (mascon) rms compared to non-resonance periods.

Development and analysis of a twelfth degree and order gravity model for Mars

NASA Technical Reports Server (NTRS)

Christensen, E. J.; Balmino, G.

1979-01-01

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Simultaneous solution of the geoid and the surface density anomalies

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Safari, A.; Karimi, R.; AllahTavakoli, Y.

2012-04-01

The main application of the land gravity data in geodesy is "local geoid" or "local gravity field" modeling, whereas the same data could play a vital role for the anomalous mass-density modeling in geophysical explorations. In the realm of local geoid computations based on Geodetic Boundary Value Problems (GBVP), it is needed that the effect of the topographic (or residual terrain) masses be removed via application of the Newton integral in order to perform the downward continuation in a harmonic space. However, harmonization of the downward continuation domain may not be perfectly possible unless accurate information about the mass-density of the topographic masses be available. On the other hand, from the exploration point of view the unwanted topographical masses within the aforementioned procedure could be regarded as the signal. In order to overcome the effect of the remaining masses within the remove step of the GBVP, which cause uncertainties in mathematical modeling of the problem, here we are proposing a methodology for simultaneous solution of the geoid and residual surface density modeling In other words, a new mathematical model will be offered which both provides the needed harmonic space for downward continuation and at the same time accounts for the non-harmonic terms of gravitational field and makes use of it for residual mass density modeling within the topographic region. The presented new model enjoys from uniqueness of the solution, opposite to the inverse application of the Newton integral for mass density modeling which is non-unique, and only needs regularization to remove its instability problem. In this way, the solution of the model provides both the incremental harmonic gravitational potential on surface of the reference ellipsoid as the gravity field model and the lateral surface mass-density variations via the second derivatives of the non harmonic terms of gravitational field. As the case study and accuracy verification, the proposed methodology is applied for identification of the salt geological structures as well as geoid computations within the northern coasts of Persian Gulf.

A distinguishing gravitational property for gravitational equation in higher dimensions

NASA Astrophysics Data System (ADS)

Dadhich, Naresh

2016-03-01

It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d=2N+1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions.

Geodesy and gravity experiment in earth orbit using a superconducting gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1985-01-01

A superconducting gravity gradiometer is under development with NASA support for space application. It is planned that a sensitive three-axis gravity gradiometer will be flown in a low-altitude (about 160 km) polar orbit in the 1990's for the purpose of obtaining a high-resolution gravity map of the earth. The large twice-an-orbit term in the harmonic expansion of gravity coming from the oblateness of the earth can be analyzed to obtain a precision test of the inverse square law at a distance of 100-1000 km. In this paper, the design, operating principle, and performance of the superconducting gravity gradiometer are described. The concept of a gravity-gradiometer mission (GGM), which is in an initial stage of development is discussed. In particular, requirements that such a mission imposes on the design of the cryogenic spacecraft will be addressed.

Gravity Field of Venus and Comparison with Earth

NASA Technical Reports Server (NTRS)

Bowin, C.

1985-01-01

The acceleration (gravity) anomaly estimates by spacecraft tracking, determined from Doppler residuals, are components of the gravity field directed along the spacecraft Earth line of sight (LOS). These data constitute a set of vector components of a planet's gravity field, the specific component depending upon where the Earth happened to be at the time of each measurement, and they are at varying altitudes above the planet surface. From this data set the gravity field vector components were derived using the method of harmonic splines which imposes a smoothness criterion to select a gravity model compatible with the LOS data. Given the piecewise model it is now possible to upward and downward continue the field quantities desired with a few parameters unlike some other methods which must return to the full dataset for each desired calculation.

Gravity field models from kinematic orbits of CHAMP, GRACE and GOCE satellites

NASA Astrophysics Data System (ADS)

Bezděk, Aleš; Sebera, Josef; Klokočník, Jaroslav; Kostelecký, Jan

2014-02-01

The aim of our work is to generate Earth's gravity field models from GPS positions of low Earth orbiters. Our inversion method is based on Newton's second law, which relates the observed acceleration of the satellite with forces acting on it. The observed acceleration is obtained as numerical second derivative of kinematic positions. Observation equations are formulated using the gradient of the spherical harmonic expansion of the geopotential. Other forces are either modelled (lunisolar perturbations, tides) or provided by onboard measurements (nongravitational perturbations). From this linear regression model the geopotential harmonic coefficients are obtained. To this basic scheme of the acceleration approach we added some original elements, which may be useful in other inversion techniques as well. We tried to develop simple, straightforward and still statistically correct model of observations. (i) The model is linear in the harmonic coefficients, no a priori gravity field model is needed, no regularization is applied. (ii) We use the generalized least squares to successfully mitigate the strong amplification of noise due to numerical second derivative. (iii) The number of other fitted parameters is very small, in fact we use only daily biases, thus we can monitor their behaviour. (iv) GPS positions have correlated errors. The sample autocorrelation function and especially the partial autocorrelation function indicate suitability of an autoregressive model to represent the correlation structure. The decorrelation of residuals improved the accuracy of harmonic coefficients by a factor of 2-3. (v) We found it better to compute separate solutions in the three local reference frame directions than to compute them together at the same time; having obtained separate solutions for along-track, cross-track and radial components, we combine them using the normal matrices. Relative contribution of the along-track component to the combined solution is 50 percent on average. (vi) The computations were performed on an ordinary PC up to maximum degree and order 120. We applied the presented method to orbits of CHAMP and GRACE spanning seven years (2003-2009) and to two months of GOCE (Nov/Dec 2009). The obtained long-term static gravity field models are of similar or better quality compared to other published solutions. We also tried to extract the time-variable gravity signal from CHAMP and GRACE orbits. The acquired average annual signal shows clearly the continental areas with important and known hydrological variations.

Nonlinear optical effects of opening a gap in graphene

NASA Astrophysics Data System (ADS)

Carvalho, David N.; Biancalana, Fabio; Marini, Andrea

2018-05-01

Graphene possesses remarkable electronic, optical, and mechanical properties that have taken the research of two-dimensional relativistic condensed matter systems to prolific levels. However, the understanding of how its nonlinear optical properties are affected by relativisticlike effects has been broadly uncharted. It has been recently shown that highly nontrivial currents can be generated in free-standing samples, notably leading to the generation of even harmonics. Since graphene monolayers are centrosymmetric media, for which such harmonic generation at normal incidence is deemed inaccessible, this light-driven phenomenon is both startling and promising. More realistically, graphene samples are often deposited on a dielectric substrate, leading to additional intricate interactions. Here, we present a treatment to study this instance by gapping the spectrum and we show this leads to the appearance of a Berry phase in the carrier dynamics. We analyze the role of such a phase in the generated nonlinear current and conclude that it suppresses odd-harmonic generation. The pump energy can be tuned to the energy gap to yield interference among odd harmonics mediated by interband transitions, allowing even harmonics to be generated. Our results and general methodology pave the way for understanding the role of gap opening in the nonlinear optics of two-dimensional lattices.

High-harmonic generation from an atomically thin semiconductor [Observation of high harmonics from an atomically thin semiconductor

DOE PAGES

Liu, Hanzhe; Li, Yilei; You, Yong Sing; ...

2016-11-14

High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales. The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands. Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process, including different symmetries, access to individual valleys and enhanced many-body interactions. Here we demonstrate non-perturbative HHG from a monolayer MoS 2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatiblemore » with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. In conclusion, the combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.« less

Mercury's Interior from MESSENGER Radio Science Data

NASA Astrophysics Data System (ADS)

Genova, A.; Mazarico, E.; Goossens, S. J.; Lemoine, F. G.; Neumann, G. A.; Smith, D. E.; Zuber, M. T.

2017-12-01

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft provided precise radio tracking data in orbit about Mercury for more than 4 years, from March 2011 to April 2015. These geodetic measurements enable us to investigate the interior structure of the planet from the inner core to the crust. The first three years of radio data allowed us to determine the gravity field of Mercury with a resolution of 150 km in the northern hemisphere (degree and order 50 in spherical harmonics) since the periapsis was located at higher latitudes (>65˚N) and 200-500 km altitudes. The comparison of this gravity solution with Mercury's topography, which was retrieved by using over 25 million individual measurements of the Mercury Laser Altimeter (MLA), resulted in a preliminary map of the crustal thickness of the planet. However, those results were limited by the resolution of the gravity field since the topography was defined in spherical harmonics up to degree and order 125. The last year of the MESSENGER extended mission was dedicated to a low-altitude campaign, where the spacecraft periapsis was maintained at altitudes between 25 and 100 km. The radio data collected during this mission phase allowed us to significantly improve the resolution of the gravity field locally in the northern hemisphere up to degree and order 100 in spherical harmonics. We present the gravity anomalies and crustal thickness maps that lead to a better understanding on the formation and evolution of specific regions. We present our estimated orientation model, which slightly differs from the solutions that were obtained by using Earth-based radar measurements and the co-registration of MESSENGER imaging and altimetry data. These previous estimates provide a direct measurement of the surface response, whereas the orientation model from gravity is more sensitive to the inner and outer core. A discrepancy between core and surface obliquities may provide fundamental information on the status of the outer core and the presence of a solid inner core. We also present the latest solution of the tidal Love number k2 that enables us to constrain the basal temperature and rigidity of the outer molten core.

Refinements in the Combined Adjustment of Satellite Altimetry and Gravity Anomaly Data

DTIC Science & Technology

1977-07-12

observations. - 151 UM Uj&liiäUäBä&immeä*,*^^ ^«^V^.^.v.rf ffM ’* ^.,/-=:jfcfe^te:^*ä*di 9.2 Spherical Harmonic Resolution The number of spherical harmonic...depend on the point mass parameters, 185 —--■ ^* p^^!?8!^ Bpp ^pg(p|SP!|p|g| we can write dr 1 dN 1 and use (9.44a). The presence of the state

Spherical harmonic analysis of a harmonic function given on a spheroid

NASA Astrophysics Data System (ADS)

Claessens, S. J.

2016-07-01

A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

Gravity fields of the solar system

NASA Technical Reports Server (NTRS)

Zendell, A.; Brown, R. D.; Vincent, S.

1975-01-01

The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

One-impulse targeting strategy for longitudinal drift control of geosynchronous spacecraft subject to tesseral harmonics and luni-solar gravity perturbations

NASA Technical Reports Server (NTRS)

Kechichian, J. A.

1984-01-01

Kamel's (1973) East-West Stationkeeping Analysis is extended and an algorithm is presented that targets the geosynchronous spacecraft to the ideal initial conditions starting from any given relative longitude deviation within a given tolerance deadband in order to repeat the ideal longitudinal drift cycle that results in the longest possible period of time between maneuvers. The motion description takes into account the perturbations introduced by earth's tesseral harmonics and by the luni-solar gravity, assuming a near-circular orbit that requires only the control of orbital energy to repeat the ideal drift cycle via a single impulsive velocity change. The location of the maneuver along the orbit is such that the post-Delta-V eccentricity is always minimized.

Superconducting tensor gravity gradiometer

NASA Technical Reports Server (NTRS)

Paik, H. J.

1981-01-01

The employment of superconductivity and other material properties at cryogenic temperatures to fabricate sensitive, low-drift, gravity gradiometer is described. The device yields a reduction of noise of four orders of magnitude over room temperature gradiometers, and direct summation and subtraction of signals from accelerometers in varying orientations are possible with superconducting circuitry. Additional circuits permit determination of the linear and angular acceleration vectors independent of the measurement of the gravity gradient tensor. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting tensor gravity gradiometer for the NASA Geodynamics Program is intended for a LEO polar trajectory to measure the harmonic expansion coefficients of the earth's gravity field up to order 300.

Tunneling ionization and harmonic generation in two-color fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kondo, K.; Kobayashi, Y.; Sagisaka, A.

1996-02-01

Tunneling ionization and harmonic generation in two-color fields were studied with a fundamental beam ({omega}) and its harmonics (2{omega},3{omega}), which were generated by a 100-fs Ti:sapphire laser. Ion yields of atoms and molecules were successfully controlled by means of a change in the relative phase between {omega} and 3{omega} pulses. Two-color interference was clearly observed in photoelectron spectra and harmonic spectra. In the {omega}{endash}2{omega} field even-order harmonics were observed in which the intensity was almost equal to that of the odd harmonics because of an asymmetric optical field. These results were compared with the quasi-static model for ionization and withmore » the quantum theory for harmonic generation. {copyright} {ital 1996 Optical Society of America.}« less

Evaluation of GOCE-based global gravity field models over Japan after the full mission using free-air gravity anomalies and geoid undulations

NASA Astrophysics Data System (ADS)

Odera, Patroba Achola; Fukuda, Yoichi

2017-09-01

The performance of Gravity field and steady-state Ocean Circulation Explorer (GOCE) global gravity field models (GGMs), at the end of GOCE mission covering 42 months, is evaluated using geoid undulations and free-air gravity anomalies over Japan, including six sub-regions (Hokkaido, north Honshu, central Honshu, west Honshu, Shikoku and Kyushu). Seventeen GOCE-based GGMs are evaluated and compared with EGM2008. The evaluations are carried out at 150, 180, 210, 240 and 270 spherical harmonics degrees. Results show that EGM2008 performs better than GOCE and related GGMs in Japan and three sub-regions (Hokkaido, central Honshu and Kyushu). However, GOCE and related GGMs perform better than EGM2008 in north Honshu, west Honshu and Shikoku up to degree 240. This means that GOCE data can improve geoid model over half of Japan. The improvement is only evident between degrees 150 and 240 beyond which EGM2008 performs better than GOCE GGMs in all the six regions. In general, the latest GOCE GGMs (releases 4 and 5) perform better than the earlier GOCE GGMs (releases 1, 2 and 3), indicating the contribution of data collected by GOCE in the last months before the mission ended on 11 November 2013. The results indicate that a more accurate geoid model over Japan is achievable, based on a combination of GOCE, EGM2008 and terrestrial gravity data sets. [Figure not available: see fulltext. Caption: Standard deviations of the differences between observed and GGMs implied ( a) free-air gravity anomalies over Japan, ( b) geoid undulations over Japan. n represents the spherical harmonic degrees

Time-Variable Gravity from Satellite Laser-Ranging: The Low-Degree Components and Their Connections with Geophysical/Climatic Changes

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Cox, Christopher M.

2004-01-01

Satellite laser-ranging (SLR) has been observing the tiny variations in Earth s global gravity for over 2 decades. The oblateness of the Earth's gravity field, J2, has been observed to undergo a secular decrease of J2 due mainly to the post-glacial rebound of the mantle. Sometime around 1998 this trend reversed quite suddenly. This reversal persisted until 2001, at which point the atmosphere-corrected time series appears to have reversed yet again towards normal. This anomaly signifies a large interannual change in global mass distribution. A number of possible causes have been considered, with oceanic mass redistribution as the leading candidate although other effects, such as glacial melting and core effects may be contributing. In fact, a strong correlation has been found between the J2 variability and the Pacific decadal oscillation. It is relatively more difficult to solve for corresponding signals in the shorter wavelength harmonics from the existing SLR-derived time variable gravity results, although it appears that geophysical fluid mass transport is being observed. For example, the recovered J3 time series shows remarkable agreement with NCEP-derived estimates of atmospheric gravity variations. Likewise, some of the non-zonal harmonic components have significant interannual signal that appears to be related to mass transport related to climatic effects such as El Nino Southern Oscillation. We will present recent updates on the J2 evolution, as well as a monthly time sequence of low-degree component map of the time-variable gravity complete through degree 4, and examine possible geophysical/climatic causes.

Implications of postseismic gravity change following the great 2004 Sumatra-Andaman earthquake from the regional harmonic analysis of GRACE intersatellite tracking data

USGS Publications Warehouse

Han, S.-C.; Sauber, J.; Luthcke, S.B.; Ji, C.; Pollitz., F. F.

2008-01-01

We report Gravity Recovery and Climate Experiment (GRACE) satellite observations of coseismic displacements and postseismic transients from the great Sumatra-Andaman Islands (thrust event; Mw ???9.2) earthquake in December 2004. Instead of using global spherical harmonic solutions of monthly gravity fields, we estimated the gravity changes directly using intersatellite range-rate data with regionally concentrated spherical Slepian basis functions every 15-day interval. We found significant step-like (coseismic) and exponential-like (postseismic) behavior in the time series of estimated coefficients (from May 2003 to April 2007) for the spherical Slepian function's. After deriving coseismic slip estimates from seismic and geodetic data that spanned different time intervals, we estimated and evaluated postseismic relaxation mechanisms with alternate asthenosphere viscosity models. The large spatial coverage and uniform accuracy of our GRACE solution enabled us to clearly delineate a postseismic transient signal in the first 2 years of postearthquake GRACE data. Our preferred interpretation of the long-wavelength components of the postseismic avity change is biviscous viscoelastic flow. We estimated a transient viscosity of 5 ??17 Pa s and a steady state viscosity of 5 ?? 1018 - 1019 Pa s. Additional years of the GRACE observations should provide improved steady state viscosity estimates. In contrast to our interpretation of coseismic gravity change, the prominent postearthquake positive gravity change around the Nicobar Islands is accounted for by seafloor uplift with less postseismic perturbation in intrinsic density in the region surrounding the earthquake. Copyright 2008 by the American Geophysical Union.

Time-Variable Gravity from Space: Quarter Century of Observations, Mysteries, and Prospects

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.

2003-01-01

Any large mass transport in the Earth system produces changes in the gravity field. Via the space geodetic technique of satellite-laser ranging in the last quarter century, the Earth s dynamic oblateness J2 (the lowest-degree harmonic component of the gravity field) has been observed to undergo a slight decrease - until around 1998, when it switched quite suddenly to an increase trend which has continued to date. The secular decrease in J2 has long been attributed primarily to the post-glacial rebound in the mantle; the present increase signifies an even larger change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound, at least over interannual timescales. Intriguing evidences have been found in the ocean water distribution, especially in the extratropical Pacific basins, that may be responsible for this 52 change. New techniques based on satellite-to-satellite tracking will yield greatly improved observations for time-variable gravity, with much higher precision and spatial resolution @e., much higher harmonic degrees). The most important example is the GRACE mission launched in March 2002, following the success of the CHAMP mission. Such observations are becoming a new and powerful tool for remote sensing of geophysical fluid processes that involve larger-scale mass transports.

The Space-Wise Global Gravity Model from GOCE Nominal Mission Data

NASA Astrophysics Data System (ADS)

Gatti, A.; Migliaccio, F.; Reguzzoni, M.; Sampietro, D.; Sanso, F.

2011-12-01

In the framework of the GOCE data analysis, the space-wise approach implements a multi-step collocation solution for the estimation of a global geopotential model in terms of spherical harmonic coefficients and their error covariance matrix. The main idea is to use the collocation technique to exploit the spatial correlation of the gravity field in the GOCE data reduction. In particular the method consists of an along-track Wiener filter, a collocation gridding at satellite altitude and a spherical harmonic analysis by integration. All these steps are iterated, also to account for the rotation between local orbital and gradiometer reference frame. Error covariances are computed by Montecarlo simulations. The first release of the space-wise approach was presented at the ESA Living Planet Symposium in July 2010. This model was based on only two months of GOCE data and partially contained a priori information coming from other existing gravity models, especially at low degrees and low orders. A second release was distributed after the 4th International GOCE User Workshop in May 2011. In this solution, based on eight months of GOCE data, all the dependencies from external gravity information were removed thus giving rise to a GOCE-only space-wise model. However this model showed an over-regularization at the highest degrees of the spherical harmonic expansion due to the combination technique of intermediate solutions (based on about two months of data). In this work a new space-wise solution is presented. It is based on all nominal mission data from November 2009 to mid April 2011, and its main novelty is that the intermediate solutions are now computed in such a way to avoid over-regularization in the final solution. Beyond the spherical harmonic coefficients of the global model and their error covariance matrix, the space-wise approach is able to deliver as by-products a set of spherical grids of potential and of its second derivatives at mean satellite altitude. These grids have an information content that is very similar to the original along-orbit data, but they are much easier to handle. In addition they are estimated by local least-squares collocation and therefore, although computed by a unique global covariance function, they could yield more information at local level than the spherical harmonic coefficients of the global model. For this reason these grids seem to be useful for local geophysical investigations. The estimated grids with their estimated errors are presented in this work together with proposals on possible future improvements. A test to compare the different information contents of the along-orbit data, the gridded data and the spherical harmonic coefficients is also shown.

Propagation effects in the generation process of high-order vortex harmonics.

PubMed

Zhang, Chaojin; Wu, Erheng; Gu, Mingliang; Liu, Chengpu

2017-09-04

We numerically study the propagation of a Laguerre-Gaussian beam through polar molecular media via the exact solution of full-wave Maxwell-Bloch equations where the rotating-wave and slowly-varying-envelope approximations are not included. It is found that beyond the coexistence of odd-order and even-order vortex harmonics due to inversion asymmetry of the system, the light propagation effect results in the intensity enhancement of a high-order vortex harmonics. Moreover, the orbital momentum successfully transfers from the fundamental laser driver to the vortex harmonics which topological charger number is directly proportional to its order.

A critical analysis of the numerical and analytical methods used in the construction of the lunar gravity potential model.

NASA Astrophysics Data System (ADS)

Tuckness, D. G.; Jost, B.

1995-08-01

Current knowledge of the lunar gravity field is presented. The various methods used in determining these gravity fields are investigated and analyzed. It will be shown that weaknesses exist in the current models of the lunar gravity field. The dominant part of this weakness is caused by the lack of lunar tracking data information (farside, polar areas), which makes modeling the total lunar potential difficult. Comparisons of the various lunar models reveal an agreement in the low-order coefficients of the Legendre polynomials expansions. However, substantial differences in the models can exist in the higher-order harmonics. The main purpose of this study is to assess today's lunar gravity field models for use in tomorrow's lunar mission designs and operations.

Seismic tremor and gravity measurements at Inferno Crater Lake, Waimangu Geothermal Field, New Zealand

NASA Astrophysics Data System (ADS)

O'Brien, J. F.; Jolly, A. D.; Fournier, N.; Cole-Baker, J.; Hurst, T.; Roman, D. C.

2011-12-01

Volcanic crater lakes are often associated with active hydrothermal systems that induce cyclic behavior in the lake's level, temperature, and chemistry. Inferno Crater Lake, located in the Waimangu geothermal field within the Taupo Volcanic Zone (TVZ) on the North Island of New Zealand exhibits lake level fluctuations of >7m, and temperature fluctuations >40°C with a highly variable periodicity. Seismic and gravity monitoring of Inferno Lake was carried out from December, 2009 - March, 2010 and captured a full cycle of lake fluctuation. Results indicate that this cycle consisted of ~5 smaller fluctuations of ~3m in lake level followed by a larger fluctuation of ~7m. A broadband seismometer recorded strong seismic tremor in the hours leading up to each of the minor and major high stands in lake level. Spectral analysis of the tremor shows dominant frequencies in the range of ~10Hz and a fundamental harmonic frequency located in the 1Hz range. The 1Hz frequency band exhibits gliding spectral lines which increase in frequency at the end of each tremor period. Particle motion analysis of harmonic tremor waveforms indicate a ~100m upward migration of the source location from the onset of tremor until it ceases at the peak of each lake level high stand. Particle motions also indicate an azimuthal migration of the source by ~30° from the overflow outlet region of the lake toward the central vent location during the course of the tremor and lake level increase. Lake water temperature has a direct relationship with lake level and ranges between ~40°C - ~80°C. Gravity fluctuations were also continuously monitored using a Micro-g-LaCoste gPhone relative gravity meter with a 1Hz sampling rate and precision of 1 microgal. These data indicate a direct relationship between lake level and gravity showing a net increase of ~100 microgals between lake level low and high stands. A piezometer located beside the lake indicates an inflow of ground water into the subsoil during periods of lake level increase and outflow of groundwater during lake level decrease resulting in a ~0.5m overall change between high and low stands and suggests that groundwater flow underneath the gravity meter may be playing a significant role in observed gravity changes. Overall, the results are consistent with a hydrothermal system at Inferno Lake consisting of a one-phase liquid layer overlying a 2-phase liquid/gas layer. Heating from below initiates boiling at the boundary between the one- and two-phase regions, and may act as the source of harmonic tremor within the conduit system. The dynamic expansion and collapse of the two-phase layer may modify the resonator geometry and internal properties, producing the harmonic excitation and apparent source position migration. Further study of Inferno Lake's hydrothermal system will aid in understanding its complex nature and that of other volcanic lake-hydrothermal systems.

Mars - Crustal structure inferred from Bouguer gravity anomalies.

NASA Technical Reports Server (NTRS)

Phillips, R. J.; Saunders, R. S.; Conel, J. E.

1973-01-01

Bouguer gravity has been computed for the equatorial region of Mars by differencing free air gravity and the gravity predicted from topographic variations. The free air gravity was generated from an eighth-order set of spherical harmonic coefficients. The gravity from topographic variations was generated by integrating a two-dimensional Green's function over each contour level. The Bouguer gravity indicates crustal inhomogeneities on Mars that are postulated to be variations in crustal thickness. The Tharsis ridge is a region of thick continental type crust. The gravity data, structural patterns, topography, and surface geology of this region lead to the interpretation of the Tharsis topographic high as a broad crustal upwarp possibly associated with local formation of lower-density crustal material and subsequent rise of a thicker crust. The Amazonis region is one of several basins of relatively thin crust, analogous to terrestrial ocean basins. The Libya and Hellas basins, which are probable impact features, are also underlain by thin crust and are possible regions of mantle upwelling.

Time-Variable Gravity from Space: Quarter Century of Observations, Mysteries, and Prospects

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.

2003-01-01

Any large mass transport in the Earth system produces changes in the gravity field. Via the space geodetic technique of satellite-laser ranging in the last quarter century, the Earth's dynamic oblateness J2 (the lowest-degree harmonic component of the gravity field) has been observed to undergo a slight decrease -- until around 1998, when it switched quite suddenly to an increase trend which has continued to date. The secular decrease in J2 has long been attributed primarily to the post-glacial rebound in the mantle; the present increase signifies an even larger change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound, at least over interannual timescales. Intriguing evidences have been found in the ocean water distribution, especially in the extratropical Pacific basins, that may be responsible for this J2 change. New techniques based on satellite-to-satellite tracking will yield greatly improved observations for time-variable gravity, with much higher precision and spatial resolution (i.e., much higher harmonic degrees). The most important example is the GRACE mission launched in March 2002, following the success of the CHAMP mission. In addition, although less precise than GRACE, the GPS/Meteorology constellation mission COSMIC, with 6 mini-satellites to be launched in late 2005, is expected to provide continued and complementary time-variable gravity observations. Such observations are becoming a new and powerful tool for remote sensing of geophysical fluid processes that involve larger-scale mass transports.

On the recovery of gravity anomalies from high precision altimeter data

NASA Technical Reports Server (NTRS)

Lelgemann, D.

1976-01-01

A model for the recovery of gravity anomalies from high precision altimeter data is derived which consists of small correction terms to the inverse Stokes' formula. The influence of unknown sea surface topography in the case of meandering currents such as the Gulf Stream is discussed. A formula was derived in order to estimate the accuracy of the gravity anomalies from the known accuracy of the altimeter data. It is shown that for the case of known harmonic coefficients of lower order the range of integration in Stokes inverse formula can be reduced very much.

Influence of higher harmonics of the undulator in X-ray polarimetry and crystal monochromator design.

PubMed

Marx-Glowna, Berit; Schulze, Kai S; Uschmann, Ingo; Kämpfer, Tino; Weber, Günter; Hahn, Christoph; Wille, Hans Christian; Schlage, Kai; Röhlsberger, Ralf; Förster, Eckhart; Stöhlker, Thomas; Paulus, Gerhard G

2015-09-01

The spectrum of the undulator radiation of beamline P01 at Petra III has been measured after passing a multiple reflection channel-cut polarimeter. Odd and even harmonics up to the 15th order, as well as Compton peaks which were produced by the high harmonics in the spectrum, could been measured. These additional contributions can have a tremendous influence on the performance of the polarimeter and have to be taken into account for further polarimeter designs.

Spherical harmonic expansion of the Levitus Sea surface topography

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

Prior information for the stationary sea surface topography (SST) may be needed in altimetric solutions that intend to simultaneously improve the gravity field and determine the SST. For this purpose the oceanographically derived SST estimates are represented by a spherical harmonic expansion. The spherical harmonic coefficients are computed from a least squares adjustment of the data covering the majority of the oceanic regions of the world. Several tests are made to determine the optimum maximum degree of solution and the best configuration of the geometry of the data in order to obtain a solution that fits the data and also provides a good spectral representation of the SST.

A PRELIMINARY JUPITER MODEL

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hubbard, W. B.; Militzer, B.

In anticipation of new observational results for Jupiter's axial moment of inertia and gravitational zonal harmonic coefficients from the forthcoming Juno orbiter, we present a number of preliminary Jupiter interior models. We combine results from ab initio computer simulations of hydrogen–helium mixtures, including immiscibility calculations, with a new nonperturbative calculation of Jupiter's zonal harmonic coefficients, to derive a self-consistent model for the planet's external gravity and moment of inertia. We assume helium rain modified the interior temperature and composition profiles. Our calculation predicts zonal harmonic values to which measurements can be compared. Although some models fit the observed (pre-Juno) second-more » and fourth-order zonal harmonics to within their error bars, our preferred reference model predicts a fourth-order zonal harmonic whose absolute value lies above the pre-Juno error bars. This model has a dense core of about 12 Earth masses and a hydrogen–helium-rich envelope with approximately three times solar metallicity.« less

Generations of even-order harmonics from vibrating H2+ and T2+ in the rising and falling parts of the laser field

NASA Astrophysics Data System (ADS)

Feng, Liqiang; Kapteyn, Henry J.; Feng, April Y.

2018-04-01

The generations of the even-order harmonics from H2+ and one of its isotope T2+ have been theoretically investigated beyond the Born-Oppenheimer approximation. Normally, the high-order harmonic generation (HHG) only contains odd-order harmonics for the orbital symmetry along the direction of laser polarization. Here, we showed that due to asymmetric harmonic emission (asymmetric half-wave profile), the even-order harmonics can be generated in the rising and the falling part of the laser field. In detail, in the lower initial vibrational state, the even-order harmonics main come from the falling part of the laser field; while as the initial vibrational state increases, the identified even-order harmonics in the falling part of the laser field are decreased; while some other even-order harmonics coming from the rising part of the laser field can be produced. The interesting phenomena have been proved through studying the spatial distributions and the time profiles of the HHG.

Analysis of Even Harmonics Generation in an Isolated Electric Power System

NASA Astrophysics Data System (ADS)

Kanao, Norikazu; Hayashi, Yasuhiro; Matsuki, Junya

Harmonics bred from loads are mainly odd order because the current waveform has half-wave symmetry. Since the even harmonics are negligibly small, those are not generally measured in electric power systems. However, even harmonics were measured at a 500/275/154kV substation in Hokuriku Electric Power Company after removal of a transmission line fault. The even harmonics caused malfunctions of protective digital relays because the relays used 4th harmonics at the input filter as automatic supervisory signal. This paper describes the mechanism of generation of the even harmonics by comparing measured waveforms with ATP-EMTP simulation results. As a result of analysis, it is cleared that even harmonics are generated by three causes. The first cause is a magnetizing current of transformers due to flux deviation by DC component of a fault current. The second one is due to harmonic conversion of a synchronous machine which generates even harmonics when direct current component or even harmonic current flow into the machine. The third one is that increase of harmonic impedance due to an isolated power system produces harmonic voltages. The design of the input filter of protective digital relays should consider even harmonics generation in an isolated power system.

Precise and efficient evaluation of gravimetric quantities at arbitrarily scattered points in space

NASA Astrophysics Data System (ADS)

Ivanov, Kamen G.; Pavlis, Nikolaos K.; Petrushev, Pencho

2017-12-01

Gravimetric quantities are commonly represented in terms of high degree surface or solid spherical harmonics. After EGM2008, such expansions routinely extend to spherical harmonic degree 2190, which makes the computation of gravimetric quantities at a large number of arbitrarily scattered points in space using harmonic synthesis, a very computationally demanding process. We present here the development of an algorithm and its associated software for the efficient and precise evaluation of gravimetric quantities, represented in high degree solid spherical harmonics, at arbitrarily scattered points in the space exterior to the surface of the Earth. The new algorithm is based on representation of the quantities of interest in solid ellipsoidal harmonics and application of the tensor product trigonometric needlets. A FORTRAN implementation of this algorithm has been developed and extensively tested. The capabilities of the code are demonstrated using as examples the disturbing potential T, height anomaly ζ , gravity anomaly Δ g , gravity disturbance δ g , north-south deflection of the vertical ξ , east-west deflection of the vertical η , and the second radial derivative T_{rr} of the disturbing potential. After a pre-computational step that takes between 1 and 2 h per quantity, the current version of the software is capable of computing on a standard PC each of these quantities in the range from the surface of the Earth up to 544 km above that surface at speeds between 20,000 and 40,000 point evaluations per second, depending on the gravimetric quantity being evaluated, while the relative error does not exceed 10^{-6} and the memory (RAM) use is 9.3 GB.

A new Ellipsoidal Gravimetric-Satellite Altimetry Boundary Value Problem; Case study: High Resolution Geoid of Iran

NASA Astrophysics Data System (ADS)

Ardalan, A.; Safari, A.; Grafarend, E.

2003-04-01

A new ellipsoidal gravimetric-satellite altimetry boundary value problem has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential (ii) gravity intensity (iii) deflection of vertical and (iv) satellite altimetry data. The developed boundary value problem is enjoying the ellipsoidal nature and as such can take advantage of high precision GPS observations in the set-up of the problem. The highlights of the solution are as follows: begin{itemize} Application of ellipsoidal harmonic expansion up to degree/order and ellipsoidal centrifugal field for the reduction of global gravity and isostasy effects from the gravity observable at the surface of the Earth. Application of ellipsoidal Newton integral on the equal area map projection surface for the reduction of residual mass effects within a radius of 55 km around the computational point. Ellipsoidal harmonic downward continuation of the residual observables from the surface of the earth down to the surface of reference ellipsoid using the ellipsoidal height of the observation points derived from GPS. Restore of the removed effects at the application points on the surface of reference ellipsoid. Conversion of the satellite altimetry derived heights of the water bodies into potential. Combination of the downward continued gravity information with the potential equivalent of the satellite altimetry derived heights of the water bodies. Application of ellipsoidal Bruns formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights (i.e. ellipsoidal heights of the geoid) with respect to the reference ellipsoid. Computation of the high-resolution geoid of Iran has successfully tested this new methodology!

Mode Selection Rules for a Two-Delay System with Positive and Negative Feedback Loops

NASA Astrophysics Data System (ADS)

Takahashi, Kin'ya; Kobayashi, Taizo

2018-04-01

The mode selection rules for a two-delay system, which has negative feedback with a short delay time t1 and positive feedback with a long delay time t2, are studied numerically and theoretically. We find two types of mode selection rules depending on the strength of the negative feedback. When the strength of the negative feedback |α1| (α1 < 0) is sufficiently small compared with that of the positive feedback α2 (> 0), 2m + 1-th harmonic oscillation is well sustained in a neighborhood of t1/t2 = even/odd, i.e., relevant condition. In a neighborhood of the irrelevant condition given by t1/t2 = odd/even or t1/t2 = odd/odd, higher harmonic oscillations are observed. However, if |α1| is slightly less than α2, a different mode selection rule works, where the condition t1/t2 = odd/even is relevant and the conditions t1/t2 = odd/odd and t1/t2 = even/odd are irrelevant. These mode selection rules are different from the mode selection rule of the normal two-delay system with two positive feedback loops, where t1/t2 = odd/odd is relevant and the others are irrelevant. The two types of mode selection rules are induced by individually different mechanisms controlling the Hopf bifurcation, i.e., the Hopf bifurcation controlled by the "boosted bifurcation process" and by the "anomalous bifurcation process", which occur for |α1| below and above the threshold value αth, respectively.

Nonsingular expansions of the gravity potential and its derivatives at satellite altitudes in the ellipsoidal coordinate system

NASA Astrophysics Data System (ADS)

Vershkov, A. N.; Petrovskaya, M. S.

2016-11-01

The series in ellipsoidal harmonics for derivatives of the Earth's gravity potential are used only on the reference ellipsoid enveloping the Earth due to their very complex mathematical structure. In the current study, the series in ellipsoidal harmonics are constructed for first- and second-order derivatives of the potential at satellite altitudes; their structure is similar to the series on the reference ellipsoid. The point P is chosen at a random satellite altitude; then, the ellipsoid of revolution is described, which passes through this point and is confocal to the reference ellipsoid. An object-centered coordinate system with the origin at the point P is considered. Using a sequence of transformations, the nonsingular series in ellipsoidal harmonics is constructed for first and second derivatives of the potential in the object-centered coordinate system. These series can be applied to develop a model of the Earth's potential, based on combined use of surface gravitational force measurements, data on the satellite orbital position, its acceleration, or measurements of the gravitational force gradients of the first and second order. The technique is applicable to any other planet of the Solar System.

Time-Variable Gravity from Space: Quarter Century of Observations, Mysteries, and Prospects

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Boy, John-Paul

2003-01-01

Any large mass transport in the Earth system produces changes in the gravity field. Via the space geodetic technique of satellite-laser ranging in the last quarter century, the Earth's dynamic oblateness J2 (the lowest-degree harmonic component of the gravity field) has been observed to undergo a slight decrease -- until around 1998, when it switched quite suddenly to an increase trend which has continued to 2001 before sharply turning back to the value which it is "supposed to be"!. The secular decrease in J2 has long been attributed primarily to the post-glacial rebound in the mantle; the present increase signifies an even larger change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound, at least over interannual timescales. Intriguing evidences have been found in the ocean water distribution, especially in the extratropical Pacific basins, that may be responsible for this J2 change. New techniques based on satellite-to-satellite tracking will yield greatly improved observations for time-variable gravity, with much higher precision and spatial resolution (i.e., much higher harmonic degrees). The most important example is the GRACE mission launched in March 2002, following the success of the CHAMP mission. Such observations are becoming a new and powerful tool for remote sensing of geophysical fluid processes that involve larger-scale mass transports.

The non-hydrostatic figures of the terrestrial planets

NASA Technical Reports Server (NTRS)

Runcorn, S. K.

1985-01-01

Solid state creep being exponentially dependent on temperature must dominate the mechanical behavior of the mantles of terrestrial planets beneath their lithospheres. General arguments suggest that the lithospheres of the Moon and Mars are about 200 km thick; the Earth, Venus and Mercury much less. Short wavelength gravity anomalies are explained by the finite strength of the lithosphere: the lunar mascons being an example. The good correlation of the Venus and Mars gravity anomalies with topography up to spherical harmonics of degrees 10-15 is in striking contrast to the lack of correlation between the long wavelength components of the geoid and the continent-ocean distribution or even the plates. Attempts have been made to explain the former correlations by isostatic models but the depths of compensation seem implausible. Low degree harmonics of the gravity fields of the terrestrial planets as is certainly the case in the Earth must arise from the density variations driving solid state convection. In the case of Venus the less dense differentiated materials of the highlands seems to be positioned over the singular points of the convection pattern. Thus the correlated gravity field does not arise from the highlands but from the density difference in the convecting interior. In the Earth lack of correlation seems to arise from the fact that the plates have moved relative to the convection pattern the last 100 M yr.

Theoretical analysis of high-order harmonic generation from a coherent superposition of states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milosevic, Dejan B.; Max-Born-Institut, Max-Born-Strasse 2a, Berlin, 12489

2006-02-15

A quantum theory of high-order harmonic generation by a strong laser field in the presence of more bound states is formulated. The obtained numerical and analytical results for a two-state hydrogenlike atom model show that the harmonic spectrum consists of two parts: a usual single-state harmonic spectrum of odd harmonics having the energies (2k+1){omega} and a resonant part with the peaks around the excitation energy {delta}{omega}. The energy of the harmonics in the resonant part of the spectrum is equal to {delta}{omega}{+-}{omega}, {delta}{omega}{+-}3{omega}, .... For energies higher than the excitation energy, the resonant part forms a plateau, followed by amore » cutoff. The emission rate of the harmonics in this resonant plateau is many orders of magnitude higher than that of the harmonics generated in the presence of the ground state alone. The influence of the depletion of the initial states, as well as of the pulse shape and intensity, is analyzed.« less

Three-dimensional simulation of free-electron laser harmonics with FRED

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharp, W.M.; Scharlemann, E.T.; Fawley, W.M.

1989-11-20

FRED3D, a single-mode three-dimensional version of the FEL simulation code FRED, has been modified to follow the growth of signal components at the fundamental frequency and at even and odd harmonics. The Wiggle-averaged particle and field equations for this multi-mode formulation are derived here, and their implementation in FRED3D is discussed. 12 refs.

Azimuthal dependence in the gravity field induced by recent and past cryospheric forcings

NASA Technical Reports Server (NTRS)

Yuen, David A.; Gasperini, Paolo; Sabadini, Roberto; Boschi, Enzo

1987-01-01

Present-day glacial activities and the current variability of the Antarctic ice volume can cause variations in the long-wavelength gravity field as a consequence of transient viscoelastic responses in the mantle. The azimuthal dependence of the secular variations of the gravitational potential are studied and it is found that the nonaxisymmetric contributions are more important for recent glacial retreats than for Pleistocene deglaciation. Changes in land-based ice covering Antarctica can be detected by monitoring satellite orbits and their sensitivity to variations in gravitational harmonic for degree l greater than 3. Resonances in satellite orbits may be useful for detecting these azimuthally-dependent gravity signals.

The GRACE Mission: Meeting the Technical Challenges

NASA Technical Reports Server (NTRS)

Davis, E. S.; Dunn, C. E.; Stanton, R. H.; Thomas, J. B.

2000-01-01

The Gravity Recovery and Climate Experiment (GRACE) Mission is scheduled for launch in June 2001. Within the first year of the GRACE Mission, the project has a minimum science requirement to deliver a new model of the Earth's static geoid with an error of less than 1 cm to spherical harmonic degree seventy (70). However, the performance of the GRACE Mission is designed to exceed this minimum requirement by a factor of 25 or more. For spherical harmonic degrees of up to 40, we expect to improve the current knowledge of the gravity field by one thousand (1000x). The GRACE Mission uses the satellite-to-satellite tracking (SST) technique. The twin GRACE satellites are the instruments that measure the nonuniformities in the Earth's gravity field. Nonuniformities in the gravity field cause the relative distance between the centers-of-mass of the two satellites to vary as they fly over the Earth. Atmospheric drag is the largest non-gravitational disturbing force. Drag is measured and will be used to correct changes in the satellite-to-satellite range measured by an SST microwave link. The microwave link will measure changes in the range between the two GRACE satellites with an error approaching 1 micron. We will discuss how these instrumentation requirements affect the configuration, the mass balance, the thermal control and the aerodynamic design of the satellites, and the design of the microwave SST link and the accelerometer. Finally, the question of how noise in these components limits the overall accuracy of the gravity models will be addressed.

Effect of difference of cupula and endolymph densities on the dynamics of semicircular canal.

PubMed

Kondrachuk, A V; Sirenko, S P; Boyle, R

2008-01-01

The effect of different densities of a cupula and endolymph on the dynamics of the semicircular canals is considered within the framework of a simplified one-dimensional mathematical model where the canal is approximated by a torus. If the densities are equal, the model is represented by Steinhausen's phenomenological equation. The difference of densities results in the complex dynamics of the cupulo-endolymphatic system, and leads to a dependence on the orientation of both the gravity vector relative to the canal plane and the axis of rotation, as well as on the distance between the axis of rotation and the center of the semicircular canal. Our analysis focused on two cases of canal stimulation: rotation with a constant velocity and a time-dependent (harmonically oscillating) angular velocity. Two types of spatial orientation of the axis of rotation, the axis of canal symmetry, and the vector of gravity were considered: i) the gravity vector and axis of rotation lie in the canal plane, and ii) the axis of rotation and gravity vector are normal to the canal plane. The difference of the cupula and endolymph densities reveals new features of cupula dynamics, for instance--a shift of the cupula to a new position of equilibrium that depends on the gravity vector and the parameters of head rotation, and the onset of cupula oscillations with multiple frequencies that results in the distortion of cupula dynamics relative to harmonic stimulation. Factors that might influence the density difference effects and the conditions under which these effects occur are discussed.

Canonical Gravity, Non-Inertial Frames, Relativistic Metrology and Dark Matter

NASA Astrophysics Data System (ADS)

Lusanna, Luca

Clock synchronization leads to the definition of instantaneous 3-spaces (to be used as Cauchy surfaces) in non-inertial frames, the only ones allowed by the equivalence principle. ADM canonical tetrad gravity in asymptotically Minkowskian space-times can be described in this framework. This allows to find the York canonical basis in which the inertial (gauge) and tidal (physical) degrees of freedom of the gravitational field can be identified. A Post-Minkowskian linearization with respect to the asymptotic Minkowski metric (asymptotic background) allows to solve the Dirac constraints in non-harmonic 3-orthogonal gauges and to find non-harmonic TT gravitational waves. The inertial gauge variable York time (the trace of the extrinsic curvature of the 3-space) describes the general relativistic freedom in clock synchronization. After a digression on the gauge problem in general relativity and its connection with relativistic metrology, it is shown that dark matter, whose experimental signatures are the rotation curves and the mass of galaxies, may be described (at least partially) as an inertial relativistic effect (absent in Newtonian gravity) connected with the York time, namely with the non-Euclidean nature of 3-spaces as 3-sub-manifolds of space-time.

Status of the geopotential. [earth gravity measurement

NASA Technical Reports Server (NTRS)

Lerch, F. J.

1983-01-01

Satellite laser ranging, satellite altimetry, and improved measurements of surface gravitational anomalies have broadened the data base on intermediate and short wavelength regions of the earth gravity field. The global data set served to develop new geopotential models with a resolution in spherical harmonics out to degree 180. The resolution was made possible using Seasat altimetry data containing 56,761 values of 1 x 1 deg gravity anomalies. Satellite-to-satellite tracking techniques involving the Geos-3 and Apollo spacecraft data for the sea surface temperature have yielded accurate intermediate wavelength gravity variations which correlate well with residual depth anomalies. Oceanic gravity anomalies have been computed directly from satellite altimetry or through statistical estimation using oceanic geoid heights. The data sets for gravimetric geoids have been compared with altimetric surfaces to identify areas which were of interest for geophysical investigation. Future data sets could become available from a proposed satellite-to-satellite Doppler tracking system (Gravsat) launched by NASA.

Gravity model improvement using GEOS-3 (GEM 9 and 10)

NASA Technical Reports Server (NTRS)

Lerch, F. J.; Klosko, S. M.; Laubscher, R. E.; Wagner, C. A.

1977-01-01

The use of collocation permitted GEM 9 to be a larger field than previous derived satellite models, GEM 9 having harmonics complete to 20 x 20 with selected higher degree terms. The satellite data set has approximately 840,000 observations, of which 200,000 are laser ranges taken on 9 satellites equipped with retroreflectors. GEM 10 is complete to 22 x 22 with selected higher degree terms out to degree and order 30 amounting to a total of 592 coefficients. Comparisons with surface gravity and altimeter data indicate a substantial improvement in GEM 9 over previous satellite solutions; GEM 9 is in even closer agreement with surface data than the previously published GEM 6 solution which contained surface gravity. In particular the free air gravity anomalies calculated from GEM 9 and a surface gravity solution are in excellent agreement for the high degree terms.

Role of antenna modes and field enhancement in second harmonic generation from dipole nanoantennas.

PubMed

de Ceglia, Domenico; Vincenti, Maria Antonietta; De Angelis, Costantino; Locatelli, Andrea; Haus, Joseph W; Scalora, Michael

2015-01-26

We study optical second harmonic generation from metallic dipole antennas with narrow gaps. Enhancement of the fundamental-frequency field in the gap region plays a marginal role on conversion efficiency. In the symmetric configuration, i.e., with the gap located at the center of the antenna axis, reducing gap size induces a significant red-shift of the maximum conversion efficiency peak. Either enhancement or inhibition of second-harmonic emission may be observed as gap size is decreased, depending on the antenna mode excited at the harmonic frequency. The second-harmonic signal is extremely sensitive to the asymmetry introduced by gap's displacements with respect to the antenna center. In this situation, second-harmonic light can couple to all the available antenna modes. We perform a multipolar analysis that allows engineering the far-field SH emission and find that the interaction with quasi-odd-symmetry modes generates radiation patterns with a strong dipolar component.

Thermally and electrically controllable multiple high harmonics generation by harmonically driven quasi-two-dimensional electron gas

NASA Astrophysics Data System (ADS)

Maglevanny, I. I.; Smolar, V. A.; Karyakina, T. I.

2018-06-01

In this paper, we consider the activation processes in nonlinear meta-stable system based on a lateral (quasi-two-dimensional) superlattice and study the dynamics of such a system externally driven by a harmonic force. The internal control parameters are the longitudinal applied electric field and the sample temperature. The spontaneous transverse electric field is considered as an order parameter. The forced violations of order parameter are considered as a response of a system to periodic driving. We investigate the cooperative effects of self-organization and high harmonic forcing from the viewpoint of catastrophe theory and show the possibility of generation of third and higher odd harmonics in output signal that lead to distortion of its wave front. A higher harmonics detection strategy is further proposed and explained in detail by exploring the influences of system parameters on the response output of the system that are discussed through numerical simulations.

The shift of harmonics with different initial vibrational states in the H{}_{2}^{+} molecular ion

NASA Astrophysics Data System (ADS)

Zhang, Jun; Pan, Xue-Fei; Xu, Tong-Tong; Liu, Xue-Shen

2017-05-01

Molecular high-order harmonic generation of H{}2+ and its isotopes is investigated by numerical simulations of the non-Born-Oppenheimer time-dependent Schrödinger equations. The general characteristic of the typical high-order harmonic generation (HHG) spectra for the H{}2+ molecule indicates that only the odd harmonics can be generated. Here we show that how the initial vibrational states and nuclear dynamics break down this standard characteristic, i.e. a redshift or blueshift of the harmonics appears. We investigate the effect of the initial vibrational states on the redshift or blueshift of the HHG spectrum under trapezoidal laser pulses. The ionization probability and time-frequency analysis are used to illustrate the physical mechanism of the shift of the harmonics. We also show the HHG spectra from the different isotopes of H2+ molecule with different initial vibrational states.

Multiple harmonic frequencies resonant cavity design and half-scale prototype measurements for a fast kicker

DOE PAGES

Huang, Yulu; Wang, Haipeng; Wang, Shaoheng; ...

2016-12-09

Quarter wavelength resonator (QWR) based deflecting cavities with the capability of supporting multiple odd-harmonic modes have been developed for an ultrafast periodic kicker system in the proposed Jefferson Lab Electron Ion Collider (JLEIC, formerly MEIC). Previous work on the kicking pulse synthesis and the transverse beam dynamics tracking simulations show that a flat-top kicking pulse can be generated with minimal emittance growth during injection and circulation of the cooling electron bunches. This flat-top kicking pulse can be obtained when a DC component and 10 harmonic modes with appropriate amplitude and phase are combined together. To support 10 such harmonic modes,more » four QWR cavities are used with 5, 3, 1, and 1 modes, respectively. In the multiple-mode cavities, several slightly tapered segments of the inner conductor are introduced to tune the higher order deflecting modes to be harmonic, and stub tuners are used to fine tune each frequency to compensate for potential errors. In this paper, we summarize the electromagnetic design of the five-mode cavity, including the geometry optimization to get high transverse shunt impedance, the frequency tuning and sensitivity analysis, and the single loop coupler design for coupling to all of the harmonic modes. In particular we report on the design and fabrication of a half-scale copper prototype of this proof-of-principle five-odd-mode cavity, as well as the rf bench measurements. Lastly, we demonstrate mode superposition in this cavity experimentally, which illustrates the kicking pulse generation concept.« less

First independent lunar gravity field solution in the framework of project GRAZIL

NASA Astrophysics Data System (ADS)

Wirnsberger, Harald; Krauss, Sandro; Klinger, Beate; Mayer-Gürr, Torsten

2017-04-01

The twin satellite mission Gravity Recovery and Interior Laboratory (GRAIL) aims to recovering the lunar gravity field by means of intersatellite Ka-band ranging (KBR) observations. In order to exploit the potential of KBR data, absolute position information of the two probes is required. Hitherto, the Graz lunar gravity field models (GrazLGM) relies on the official orbit products provided by NASA. In this contribution, we present for the first time a completely independent Graz lunar gravity field model to spherical harmonic degree and order 420. The reduced dynamic orbits of the two probes are determined using variational equations following a batch least squares differential adjustment process. These orbits are based on S-band radiometric tracking data collected by the Deep Space Network and are used for the independent GRAIL gravity field recovery. To reveal a highly accurate lunar gravity field, an integral equation approach using short orbital arcs is adopted to process the KBR data. A comparison to state-of-the-art lunar gravity models computed at NASA-GSFC, NASA-JPL and AIUB demonstrate the progress of Graz lunar gravity field models derived within the project GRAZIL.

Low- and high-order harmonic generation in the extended plasmas produced by laser ablation of zinc and manganese targets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganeev, R. A., E-mail: rashid-ganeev@mail.ru; Physical Department, Voronezh State University, Voronezh 394006; Baba, M.

The systematic studies of the harmonic generation of ultrashort laser pulses in the 5-mm-long Zn and Mn plasmas (i.e., application of nanosecond, picosecond, and femtosecond pulses for ablation, comparison of harmonic generation from atomic, ionic, and cluster-contained species of plasma, variation of plasma length, two-color pump of plasmas, etc.) are presented. The conversion efficiency of the 11th–19th harmonics generated in the Zn plasma was ∼5 × 10{sup −5}. The role of the ionic resonances of Zn near the 9th and 10th harmonics on the enhancement of harmonics is discussed. The enhancement of harmonics was also analyzed using the two-color pump of extendedmore » plasmas, which showed similar intensities of the odd and even harmonics along the whole range of generation. The harmonics up to the 107th order were demonstrated in the case of manganese plasma. The comparison of harmonic generation in the 5-mm-long and commonly used short (≤0.5 mm) plasma plumes showed the advanced properties of extended media.« less

A new ultrasonic transducer for improved contrast nonlinear imaging

NASA Astrophysics Data System (ADS)

Bouakaz, Ayache; ten Cate, Folkert; de Jong, Nico

2004-08-01

Second harmonic imaging has provided significant improvement in contrast detection over fundamental imaging. This improvement is a result of a higher contrast-to-tissue ratio (CTR) achievable at the second harmonic frequency. Nevertheless, the differentiation between contrast and tissue at the second harmonic frequency is still in many situations cumbersome and contrast detection remains nowadays as one of the main challenges, especially in the capillaries. The reduced CTR is mainly caused by the generation of second harmonic energy from nonlinear propagation effects in tissue, which hence obscures the echoes from contrast bubbles. In a previous study, we demonstrated theoretically that the CTR increases with the harmonic number. Therefore the purpose of our study was to increase the CTR by selectively looking to the higher harmonic frequencies. In order to be able to receive these high frequency components (third up to the fifth harmonic), a new ultrasonic phased array transducer has been constructed. The main advantage of the new design is its wide frequency bandwidth. The new array transducer contains two different types of elements arranged in an interleaved pattern (odd and even elements). This design enables separate transmission and reception modes. The odd elements operate at 2.8 MHz and 80% bandwidth, whereas the even elements have a centre frequency of 900 kHz with a bandwidth of 50%. The probe is connected to a Vivid 5 system (GE-Vingmed) and proper software is developed for driving. The total bandwidth of such a transducer is estimated to be more than 150% which enables higher harmonic imaging at an adequate sensitivity and signal to noise ratio compared to standard medical array transducers. We describe in this paper the design and fabrication of the array transducer. Moreover its acoustic properties are measured and its performances for nonlinear contrast imaging are evaluated in vitro and in vivo. The preliminary results demonstrate the advantages of such a transducer design for improved contrast detection.

Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission.

PubMed

Zuber, Maria T; Smith, David E; Watkins, Michael M; Asmar, Sami W; Konopliv, Alexander S; Lemoine, Frank G; Melosh, H Jay; Neumann, Gregory A; Phillips, Roger J; Solomon, Sean C; Wieczorek, Mark A; Williams, James G; Goossens, Sander J; Kruizinga, Gerhard; Mazarico, Erwan; Park, Ryan S; Yuan, Dah-Ning

2013-02-08

Spacecraft-to-spacecraft tracking observations from the Gravity Recovery and Interior Laboratory (GRAIL) have been used to construct a gravitational field of the Moon to spherical harmonic degree and order 420. The GRAIL field reveals features not previously resolved, including tectonic structures, volcanic landforms, basin rings, crater central peaks, and numerous simple craters. From degrees 80 through 300, over 98% of the gravitational signature is associated with topography, a result that reflects the preservation of crater relief in highly fractured crust. The remaining 2% represents fine details of subsurface structure not previously resolved. GRAIL elucidates the role of impact bombardment in homogenizing the distribution of shallow density anomalies on terrestrial planetary bodies.

Use of satellite gravimetry for estimating recent solid Earth changes

NASA Astrophysics Data System (ADS)

Ramillien, Guillaume

2014-05-01

Since its launch in March 2002, the Gravity Recovery & Climate Experiment (GRACE) satellite mission provides a global mapping of the time variations of the Earth's gravity field for the recent period. Official centers such as Center of Space Research (CSR) in Austin, TX, Jet Propulsion Laboratory (JPL) in Pasadena, CA and GeoForschungZentrum (GFZ) in Potsdam, Germany, provide 10-day and monthly solutions of Stokes coefficients (i.e., spherical harmonic coefficients of the geopotential) up to harmonic degree 50-60 (or, equivalently, a spatial resolution of 300-400 km) for the timespan 2002-2012. Tiny variations of the gravity measured by GRACE are mainly due to the total water storage change on continents. Therefore, these solutions of water mass can be used to correct other datasets, and then isolate the gravity signatures of large and sudden earthquakes, as well as of the continuous Post Glacial Rebound (PGR) rate. As these measured seasonal variations of continental hydrology represent the variations of water mass load, it is also possible to derive the deformation of the terrestrial surface associated to this varying load using Love numbers. These latter numbers are obtained by assuming an elastic Earth model. In the center of the Amazon basin, the seasonal displacements of the surface due to hydrology reach amplitudes of a few centimeters typically. Time-series of GRACE-based radial displacement of the surface can be analysed and compared with independent local GPS records for validation.

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

NASA Technical Reports Server (NTRS)

Lemoine, Frank; Smith, David; Rowlands, David; Zuber, Maria; Neumann, G.; Chinn, Douglas; Pavlis, D.

2000-01-01

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

NASA Technical Reports Server (NTRS)

Rapp, Richard H.; Wang, Yan Ming; Pavlis, Nikolaos K.

1991-01-01

The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

Constraints on Ceres' Internal Structure and Evolution From Its Shape and Gravity Measured by the Dawn Spacecraft

NASA Astrophysics Data System (ADS)

Ermakov, A. I.; Fu, R. R.; Castillo-Rogez, J. C.; Raymond, C. A.; Park, R. S.; Preusker, F.; Russell, C. T.; Smith, D. E.; Zuber, M. T.

2017-11-01

Ceres is the largest body in the asteroid belt with a radius of approximately 470 km. In part due to its large mass, Ceres more closely approaches hydrostatic equilibrium than major asteroids. Pre-Dawn mission shape observations of Ceres revealed a shape consistent with a hydrostatic ellipsoid of revolution. The Dawn spacecraft Framing Camera has been imaging Ceres since March 2015, which has led to high-resolution shape models of the dwarf planet, while the gravity field has been globally determined to a spherical harmonic degree 14 (equivalent to a spatial wavelength of 211 km) and locally to 18 (a wavelength of 164 km). We use these shape and gravity models to constrain Ceres' internal structure. We find a negative correlation and admittance between topography and gravity at degree 2 and order 2. Low admittances between spherical harmonic degrees 3 and 16 are well explained by Airy isostatic compensation mechanism. Different models of isostasy give crustal densities between 1,200 and 1,400 kg/m3 with our preferred model giving a crustal density of 1,287+70-87 kg/m3. The mantle density is constrained to be 2,434+5-8 kg/m3. We compute isostatic gravity anomaly and find evidence for mascon-like structures in the two biggest basins. The topographic power spectrum of Ceres and its latitude dependence suggest that viscous relaxation occurred at the long wavelengths (>246 km). Our density constraints combined with finite element modeling of viscous relaxation suggests that the rheology and density of the shallow surface are most consistent with a rock, ice, salt and clathrate mixture.

Airborne geoid mapping of land and sea areas of East Malaysia

NASA Astrophysics Data System (ADS)

Jamil, H.; Kadir, M.; Forsberg, R.; Olesen, A.; Isa, M. N.; Rasidi, S.; Mohamed, A.; Chihat, Z.; Nielsen, E.; Majid, F.; Talib, K.; Aman, S.

2017-02-01

This paper describes the development of a new geoid-based vertical datum from airborne gravity data, by the Department of Survey and Mapping Malaysia, on land and in the South China Sea out of the coast of East Malaysia region, covering an area of about 610,000 square kilometres. More than 107,000 km flight line of airborne gravity data over land and marine areas of East Malaysia has been combined to provide a seamless land-to-sea gravity field coverage; with an estimated accuracy of better than 2.0 mGal. The iMAR-IMU processed gravity anomaly data has been used during a 2014-2016 airborne survey to extend a composite gravity solution across a number of minor gaps on selected lines, using a draping technique. The geoid computations were all done with the GRAVSOFT suite of programs from DTU-Space. EGM2008 augmented with GOCE spherical harmonic model has been used to spherical harmonic degree N = 720. The gravimetric geoid first was tied at one tide-gauge (in Kota Kinabalu, KK2019) to produce a fitted geoid, my_geoid2017_fit_kk. The fitted geoid was offset from the gravimetric geoid by +0.852 m, based on the comparison at the tide-gauge benchmark KK2019. Consequently, orthometric height at the six other tide gauge stations was computed from HGPS Lev = hGPS - Nmy_geoid2017_.t_kk. Comparison of the conventional (HLev) and GPS-levelling heights (HGPS Lev) at the six tide gauge locations indicate RMS height difference of 2.6 cm. The final gravimetric geoidwas fitted to the seven tide gauge stations and is known as my_geoid2017_fit_east. The accuracy of the gravimetric geoid is estimated to be better than 5 cm across most of East Malaysia land and marine areas

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

NASA Astrophysics Data System (ADS)

Zamaro, M.; Biggs, J. D.

2015-07-01

The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

Multi-loop control of UPS inverter with a plug-in odd-harmonic repetitive controller.

PubMed

Razi, Reza; Karbasforooshan, Mohammad-Sadegh; Monfared, Mohammad

2017-03-01

This paper proposes an improved multi-loop control scheme for the single-phase uninterruptible power supply (UPS) inverter by using a plug-in odd-harmonic repetitive controller to regulate the output voltage. In the suggested control method, the output voltage and the filter capacitor current are used as the outer and inner loop feedback signals, respectively and the instantaneous value of the reference voltage feedforwarded to the output of the controller. Instead of conventional linear (proportional-integral/-resonant) and conventional repetitive controllers, a plug-in odd-harmonic repetitive controller is employed in the outer loop to regulate the output voltage, which occupies less memory space and offers faster tracking performance compared to the conventional one. Also, a simple proportional controller is used in the inner loop for active damping of possible resonances and improving the transient performance. The feedforward of the converter reference voltage enhances the robust performance of the system and simplifies the system modelling and the controller design. A step-by-step design procedure is presented for the proposed controller, which guarantees stability of the system under worst-case scenarios. Simulation and experimental results validate the excellent steady-state and transient performance of the proposed control scheme and provide the exact comparison of the proposed method with the conventional multi-loop control method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Vacuum energy in Einstein-Gauss-Bonnet anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kofinas, Georgios; Olea, Rodrigo

2006-10-15

A finite action principle for Einstein-Gauss-Bonnet anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, andmore » to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti-de Sitter spacetime in all odd dimensions.« less

Use of Massive Parallel Computing Libraries in the Context of Global Gravity Field Determination from Satellite Data

NASA Astrophysics Data System (ADS)

Brockmann, J. M.; Schuh, W.-D.

2011-07-01

The estimation of the global Earth's gravity field parametrized as a finite spherical harmonic series is computationally demanding. The computational effort depends on the one hand on the maximal resolution of the spherical harmonic expansion (i.e. the number of parameters to be estimated) and on the other hand on the number of observations (which are several millions for e.g. observations from the GOCE satellite missions). To circumvent these restrictions, a massive parallel software based on high-performance computing (HPC) libraries as ScaLAPACK, PBLAS and BLACS was designed in the context of GOCE HPF WP6000 and the GOCO consortium. A prerequisite for the use of these libraries is that all matrices are block-cyclic distributed on a processor grid comprised by a large number of (distributed memory) computers. Using this set of standard HPC libraries has the benefit that once the matrices are distributed across the computer cluster, a huge set of efficient and highly scalable linear algebra operations can be used.

Downward continuation of gravity information from satellite to satellite tracking or satellite gradiometry in local areas

NASA Technical Reports Server (NTRS)

Rummel, R.

1975-01-01

Integral formulas in the parameter domain are used instead of a representation by spherical harmonics. The neglected regions will cause a truncation error. The application of the discrete form of the integral equations connecting the satellite observations with surface gravity anomalies is discussed in comparison with the least squares prediction method. One critical point of downward continuation is the proper choice of the boundary surface. Practical feasibilities are in conflict with theoretical considerations. The properties of different approaches for this question are analyzed.

Selection rules for harmonic generation in solids

NASA Astrophysics Data System (ADS)

Moiseyev, Nimrod

2015-05-01

High-order harmonic generation (HHG) in a bulk crystal was first observed in 2011 [S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, Nat. Phys. 7, 138 (2011), 10.1038/nphys1847]. Only odd-order harmonics were observed as expected on the basis of the selection rules in solids, which were derived when only the interband currents were taken into consideration. Here we study HHG in solids when the intraband currents are taken into consideration as well. We show that the dynamical selection rules are broken in solids and the possibility of generation of even-order harmonics cannot be excluded on the basis of the dynamical symmetry analysis. However, a simple analysis of the expression we obtained for the amplitude of the emitted high-order harmonics shows, without the need to carry out numerical calculations, that the even-order harmonics are suppressed due to the localization of the field-free one-electron density probability on the atoms in the solids.

Mixed higher-order flow harmonics and nonlinear response coefficients in PbPb collisions at 2.76 and 5.02 TeV with CMS

NASA Astrophysics Data System (ADS)

Tuo, Shengquan; CMS Collaboration

2017-11-01

The mixed higher-order flow harmonics and nonlinear response coefficients of charged particles are presented as a function of pT and centrality in PbPb collisions at √{sNN} = 2.76 TeV and 5.02 TeV with the CMS detector. The results are obtained using the scalar product method, and cover a pT range from 0.3 GeV/c to 8.0 GeV/c, pseudorapidity | η | < 2.4, and a centrality range of 0-60%. The mixed harmonic results at 5.02 TeV are compared to the matching higher-order flow harmonics from two-particle correlations, which measure vn values with respect to the n-th order event plane. It is observed that the nonlinear response coefficients of the odd harmonics are larger than the even harmonics ones. The results are compared with hydrodynamic predictions using different shear viscosity to entropy density ratios and different initial conditions.

Detection of cyclic-fold bifurcation in electrostatic MEMS transducers by motion-induced current

NASA Astrophysics Data System (ADS)

Park, Sangtak; Khater, Mahmoud; Effa, David; Abdel-Rahman, Eihab; Yavuz, Mustafa

2017-08-01

This paper presents a new detection method of cyclic-fold bifurcations in electrostatic MEMS transducers based on a variant of the harmonic detection of resonance method. The electrostatic transducer is driven by an unbiased harmonic signal at half its natural frequency, ω a   =  1/2 ω o . The response of the transducer consists of static displacement and a series of harmonics at 2 ω a , 4 ω a , and so on. Its motion-induced current is shifted by the excitation frequency, ω a , to appear at 3 ω a , 5 ω a , and higher odd harmonics, providing higher sensitivity to the measurement of harmonic motions. With this method, we successfully detected the variation in the location of the cyclic-fold bifurcation of an encapsulated electrostatic MEMS transducer. We also detected a regime of tapping mode motions subsequent to the bifurcation.

Geometrical Theory of Spherical Harmonics for Geosciences

NASA Astrophysics Data System (ADS)

Svehla, Drazen

2010-05-01

Spherical harmonics play a central role in the modelling of spatial and temporal processes in the system Earth. The gravity field of the Earth and its temporal variations, sea surface topography, geomagnetic field, ionosphere etc., are just a few examples where spherical harmonics are used to represent processes in the system Earth. We introduce a novel method for the computation and rotation of spherical harmonics, Legendre polynomials and associated Legendre functions without making use of recursive relations. This novel geometrical approach allows calculation of spherical harmonics without any numerical instability up to an arbitrary degree and order, e.g. up to degree and order 106 and beyond. The algorithm is based on the trigonometric reduction of Legendre polynomials and the geometric rotation in hyperspace. It is shown that Legendre polynomials can be computed using trigonometric series by pre-computing amplitudes and translation terms for all angular arguments. It is shown that they can be treated as vectors in the Hilbert hyperspace leading to unitary hermitian rotation matrices with geometric properties. Thus, rotation of spherical harmonics about e.g. a polar or an equatorial axis can be represented in the similar way. This novel method allows stable calculation of spherical harmonics up to an arbitrary degree and order, i.e. up to degree and order 106 and beyond.

An Online Gravity Modeling Method Applied for High Precision Free-INS

PubMed Central

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-01-01

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS. PMID:27669261

An Online Gravity Modeling Method Applied for High Precision Free-INS.

PubMed

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-09-23

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS.

Theory of an experiment in an orbiting space laboratory to determine the gravitational constant.

NASA Technical Reports Server (NTRS)

Vinti, J. P.

1972-01-01

An experiment is discussed for determining the gravitational constant with the aid of an isolated system consisting of an artificial satellite moving around an artificial planet. The experiment is to be conducted in a spherical laboratory traveling in an orbit around the earth. Difficulties due to the gravity-gradient term are considered, and the three-tunnel method proposed by Wilk (1969) is examined. The rotation of the sphere is discussed together with aspects of the reference systems used, the equations of motion of the spacecraft and of the test objects, the field from the earth's gravity gradient at the test object, higher harmonic terms in the gravity gradient force, gravitational effects of the spacecraft itself, and a computer simulation.

Quantum correction to classical gravitational interaction between two polarizable objects

NASA Astrophysics Data System (ADS)

Wu, Puxun; Hu, Jiawei; Yu, Hongwei

2016-12-01

When gravity is quantized, there inevitably exist quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable objects and produce a quantum correction to the classical Newtonian interaction between them. Here, based upon linearized quantum gravity and the leading-order perturbation theory, we study, from a quantum field-theoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as two-level harmonic oscillators. We find that the interaction potential behaves like r-11 in the retarded regime and r-10 in the near regime. Our result agrees with what were recently obtained in different approaches. Our study seems to indicate that linearized quantum gravity is robust in dealing with quantum gravitational effects at low energies.

High-resolution combined global gravity field modelling: Solving large kite systems using distributed computational algorithms

NASA Astrophysics Data System (ADS)

Zingerle, Philipp; Fecher, Thomas; Pail, Roland; Gruber, Thomas

2016-04-01

One of the major obstacles in modern global gravity field modelling is the seamless combination of lower degree inhomogeneous gravity field observations (e.g. data from satellite missions) with (very) high degree homogeneous information (e.g. gridded and reduced gravity anomalies, beyond d/o 1000). Actual approaches mostly combine such data only on the basis of the coefficients, meaning that previously for both observation classes (resp. models) a spherical harmonic analysis is done independently, solving dense normal equations (NEQ) for the inhomogeneous model and block-diagonal NEQs for the homogeneous. Obviously those methods are unable to identify or eliminate effects as spectral leakage due to band limitations of the models and non-orthogonality of the spherical harmonic base functions. To antagonize such problems a combination of both models on NEQ-basis is desirable. Theoretically this can be achieved using NEQ-stacking. Because of the higher maximum degree of the homogeneous model a reordering of the coefficient is needed which leads inevitably to the destruction of the block diagonal structure of the appropriate NEQ-matrix and therefore also to the destruction of simple sparsity. Hence, a special coefficient ordering is needed to create some new favorable sparsity pattern leading to a later efficient computational solving method. Such pattern can be found in the so called kite-structure (Bosch, 1993), achieving when applying the kite-ordering to the stacked NEQ-matrix. In a first step it is shown what is needed to attain the kite-(NEQ)system, how to solve it efficiently and also how to calculate the appropriate variance information from it. Further, because of the massive computational workload when operating on large kite-systems (theoretically possible up to about max. d/o 100.000), the main emphasis is put on to the presentation of special distributed algorithms which may solve those systems parallel on an indeterminate number of processes and are therefore suitable for the application on supercomputers (such as SuperMUC). Finally, (if time or space) some in-detail problems are shown that occur when dealing with high degree spherical harmonic base functions (mostly due to instabilities of Legendre polynomials), introducing also an appropriate solution for each.

Innovative Technique for Noise Reduction in Spacecraft Doppler Tracking for Planetary Interior Studies

NASA Astrophysics Data System (ADS)

Notaro, V.; Armstrong, J. W.; Asmar, S.; Di Ruscio, A.; Iess, L.; Mariani, M., Jr.

2017-12-01

Precise measurements of spacecraft range rate, enabled by two-way microwave links, are used in radio science experiments for planetary geodesy including the determination of planetary gravitational fields for the purpose of modeling the interior structure. The final accuracies in the estimated gravity harmonic coefficients depend almost linearly on the Doppler noise in the link. We ran simulations to evaluate the accuracy improvement attainable in the estimation of the gravity harmonic coefficients of Venus (with a representative orbiter) and Mercury (with the BepiColombo spacecraft), using our proposed innovative noise-cancellation technique. We showed how the use of an additional, smaller and stiffer, receiving-only antenna could reduce the leading noise sources in a Ka-band two-way link such as tropospheric and antenna mechanical noises. This is achieved through a suitable linear combination (LC) of Doppler observables collected at the two antennas at different times. In our simulations, we considered a two-way link either from NASA's DSS 25 antenna in California or from ESA's DSA-3 antenna in Malargüe (Argentina). Moreover, we selected the 12-m Atacama Pathfinder EXperiment (APEX) in Chile as the three-way antenna and developed its tropospheric noise model using available atmospheric data and mechanical stability specifications. For an 8-hour Venus orbiter tracking pass in Chajnantor's winter/night conditions, the accuracy of the simulated LC Doppler observable at 10-s integration time is 6 mm/s, to be compared to 23 mm/s for the two-way link. For BepiColombo, we obtained 16.5 mm/s and 35 mm/s, respectively for the LC and two-way links. The benefits are even larger at longer time scales. Numerical simulations indicate that such noise reduction would provide significant improvements in the determination of Venus's and Mercury's gravity field coefficients. If implemented, this noise-reducing technique will be valuable for planetary geodesy missions, where the accuracy in the estimation of high-order gravity harmonic coefficients is limited by tropospheric and antenna mechanical noises that are difficult to reduce at short integration times. Benefits are however expected in all precision radio science experiments with deep space probes.

A new degree-2190 (10 km resolution) gravity field model for Antarctica developed from GRACE, GOCE and Bedmap2 data

NASA Astrophysics Data System (ADS)

Hirt, Christian; Rexer, Moritz; Scheinert, Mirko; Pail, Roland; Claessens, Sten; Holmes, Simon

2016-02-01

The current high-degree global geopotential models EGM2008 and EIGEN-6C4 resolve gravity field structures to ˜ 10 km spatial scales over most parts of the of Earth's surface. However, a notable exception is continental Antarctica, where the gravity information in these and other recent models is based on satellite gravimetry observations only, and thus limited to about ˜ 80-120 km spatial scales. Here, we present a new degree-2190 global gravity model (GGM) that for the first time improves the spatial resolution of the gravity field over the whole of continental Antarctica to ˜ 10 km spatial scales. The new model called SatGravRET2014 is a combination of recent Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite gravimetry with gravitational signals derived from the 2013 Bedmap2 topography/ice thickness/bedrock model with gravity forward modelling in ellipsoidal approximation. Bedmap2 is a significantly improved description of the topographic mass distribution over the Antarctic region based on a multitude of topographic surveys, and a well-suited source for modelling short-scale gravity signals as we show in our study. We describe the development of SatGravRET2014 which entirely relies on spherical harmonic modelling techniques. Details are provided on the least-squares combination procedures and on the conversion of topography to implied gravitational potential. The main outcome of our work is the SatGravRET2014 spherical harmonic series expansion to degree 2190, and derived high-resolution grids of 3D-synthesized gravity and quasigeoid effects over the whole of Antarctica. For validation, six data sets from the IAG Subcommission 2.4f "Gravity and Geoid in Antarctica" (AntGG) database were used comprising a total of 1,092,981 airborne gravimetric observations. All subsets consistently show that the Bedmap2-based short-scale gravity modelling improves the agreement over satellite-only data considerably (improvement rates ranging between 9 and 75 % with standard deviations from residuals between SatGravRET2014 and AntGG gravity ranging between 8 and 25 mGal). For comparison purposes, a degree-2190 GGM was generated based on the year-2001 Bedmap1 (using the ETOPO1 topography) instead of 2013 Bedmap2 topography product. Comparison of both GGMs against AntGG consistently reveals a closer fit over all test areas when Bedmap2 is used. This experiment provides evidence for clear improvements in Bedmap2 topographic information over Bedmap1 at spatial scales of ˜ 80-10 km, obtained from independent gravity data used as validation tool. As a general conclusion, our modelling effort fills—in approximation—some gaps in short-scale gravity knowledge over Antarctica and demonstrates the value of the Bedmap2 topography data for short-scale gravity refinement in GGMs. SatGravRET2014 can be used, e.g. as a reference model for future gravity modelling efforts over Antarctica, e.g. as foundation for a combination with the AntGG data set to obtain further improved gravity information.

Gravity field and shape of Ceres from Dawn

NASA Astrophysics Data System (ADS)

Park, Ryan; Konopliv, Alexander; Vaughan, Andrew; Bills, Bruce; Castillo-Rogez, Julie; Ermakov, Anton; Fu, Roger; Raymond, Carol; Russell, Chris; Zuber, Maria

2017-04-01

The Dawn gravity science investigation utilizes the DSN radio tracking of the spacecraft and on-board framing camera images to determine the gravity field and global shape of Ceres. The gravity science data collected during Approach, Survey, High-Altitude Mapping Orbit, and Low-Altitude Mapping Orbit phases were processed. The final gravity science solution yielded a degree and order 18 gravity field, called CERES18C, which is globally accurate to degree and order 14. Also, the final Ceres shape using the stereo-photoclinometry method is available with the height uncertainty better than 30 meters. The degree-2 gravity harmonics show that the rotation of Ceres is very nearly about a principal axis. Combining the gravity field and topography gives the bulk density of 2162.6±2.0 kg/m3. The estimated spin pole vector yields RA=(291.42744±0.00022)° and Dec=(66.76065±0.00022)° with the prime meridian and rotation rate of (170.374±0.012)° and (952.1532638±0.0000019)°/day, respectively. The low Bouguer gravity at high topographic areas, and vice versa, indicates that the topography of Ceres is compensated, which can be explained by a low-viscosity layer at depth. Further studies on Ceres interior show that low gravity-topography admittances are consistent with Airy isostasy and finite-element modeling require a decrease of viscosity with depth.

Mercury's lithospheric thickness and crustal density, as inferred from MESSENGER observations

NASA Astrophysics Data System (ADS)

James, P. B.; Mazarico, E.; Genova, A.; Smith, D. E.; Neumann, G. A.; Solomon, S. C.

2015-12-01

The gravity field and topography of Mercury measured by the MESSENGER spacecraft have provided insights into the thickness of the planet's elastic lithosphere, Te. We localized the HgM006 free-air gravity anomaly and gtmes_125v03 shape datasets to search for theoretical elastic thickness solutions that best fit a variety of localized coherence spectra between Bouguer gravity anomaly and topography. We adopted a crustal density of ρcrust =2700 kg m-3 for the Bouguer gravity correction, but density uncertainty did not markedly affect the elastic thickness estimates. A best-fit solution in the northern smooth plains (NSP) gives an elastic thickness of Te =30-60 km at the time of formation of topography for a range of ratios of top to bottom loading from 1 to 5. For a mechanical lithosphere with a thickness of ~2Te and a temperature of 1600 °C at the base, this solution is consistent with a geothermal gradient of 9-18 K km-1. A similar coherence analysis exterior to the NSP produces an elastic thickness estimate of Te =20-50 km, albeit with a poorer fit. Coherence in the northern hemisphere as a whole does not approach zero at any wavelength, because of the presence of variations in crustal thickness that are unassociated with elastic loading. The ratios and correlations of gravity and topography at intermediate wavelengths (harmonic degree l between 30 and 50) also constrain regional crustal densities. We localized gravity and topography with a moving Slepian taper and calculated regionally averaged crustal densities with the approximation ρcrust=Zl/(2πG), where Zl is the localized admittance and G is the gravitational constant. The only regional density estimates greater than 2000 kg m-3 for l=30 correspond to the NSP. Density estimates outside of the NSP were unreasonably low, even for highly porous crust. We attribute these low densities to the confounding effects of crustal thickness variations and Kaula filtering of the gravity dataset at the highest harmonic degrees, both of which tend to introduce a downward bias to crustal density estimation. An alternative analysis—which corrected for crustal thickness variability and was restricted to regions with gravity/topography coherence greater than 0.6—yielded an aggregate crustal density of ρcrust=2602 ± 470 kg m-3 for Mercury's high northern latitudes.

Torus Approach in Gravity Field Determination from Simulated GOCE Gravity Gradients

NASA Astrophysics Data System (ADS)

Liu, Huanling; Wen, Hanjiang; Xu, Xinyu; Zhu, Guangbin

2016-08-01

In Torus approach, observations are projected to the nominal orbits with constant radius and inclination, lumped coefficients provides a linear relationship between observations and spherical harmonic coefficients. Based on the relationship, two-dimensional FFT and block-diagonal least-squares adjustment are used to recover Earth's gravity field model. The Earth's gravity field model complete to degree and order 200 is recovered using simulated satellite gravity gradients on a torus grid, and the degree median error is smaller than 10-18, which shows the effectiveness of Torus approach. EGM2008 is employed as a reference model and the gravity field model is resolved using the simulated observations without noise given on GOCE orbits of 61 days. The error from reduction and interpolation can be mitigated by iterations. Due to polar gap, the precision of low-order coefficients is lower. Without considering these coefficients the maximum geoid degree error and cumulative error are 0.022mm and 0.099mm, respectively. The Earth's gravity field model is also recovered from simulated observations with white noise 5mE/Hz1/2, which is compared to that from direct method. In conclusion, it is demonstrated that Torus approach is a valid method for processing massive amount of GOCE gravity gradients.

An atlas of Rapp's 180-th order geopotential.

NASA Astrophysics Data System (ADS)

Melvin, P. J.

1986-08-01

Deprit's 1979 approach to the summation of the spherical harmonic expansion of the geopotential has been modified to spherical components and normalized Legendre polynomials. An algorithm has been developed which produces ten fields at the users option: the undulations of the geoid, three anomalous components of the gravity vector, or six components of the Hessian of the geopotential (gravity gradient). The algorithm is stable to high orders in single precision and does not treat the polar regions as a special case. Eleven contour maps of components of the anomalous geopotential on the surface of the ellipsoid are presented to validate the algorithm.

Are higher degree even zonals really harmful for the LARES/LAGEOS frame-dragging experiment?

NASA Astrophysics Data System (ADS)

Renzetti, G.

2012-08-01

The low-altitude effects of LARES are examined to determined how they can impact the outcome of the hoped 1% frame-dragging measurement in the LARES-LAGEOS experiment. This analysis, based on a different approach than other studies recently appearing in the literature, shows that the spherical harmonics of the Earth gravity field with degree ℓ > 60 may represent a threat because their errors map significantly into LARES orbital disturbances compared to frame-dragging. The GIF48 model was used. It is questionable whether future Earth gravity models by GRACE and GOCE will be of sufficient accuracy.

Stopped-pipe wind instruments: Acoustics of the panpipes

NASA Astrophysics Data System (ADS)

Fletcher, N. H.

2005-01-01

Stopped-pipe jet-excited musical instruments are known in many cultures, those best-known today being the panpipes or syrinx of Eastern Europe and of the Peruvian Andes. Although the playing style differs, in each case the instrument consists of a set of graduated bamboo pipes excited by blowing across the open tops. Details of the excitation aerodynamics warrant examination, particularly as the higher notes contain amplitudes of the even harmonics approaching those of the odd harmonics expected from a stopped pipe. Analysis shows that the jet offset is controlled by the fluid dynamics of the jet, and is such that appreciable even-harmonic excitation is generated. The theory is largely confirmed by measurements on a player. .

Stopped-pipe wind instruments: acoustics of the panpipes.

PubMed

Fletcher, N H

2005-01-01

Stopped-pipe jet-excited musical instruments are known in many cultures, those best-known today being the panpipes or syrinx of Eastern Europe and of the Peruvian Andes. Although the playing style differs, in each case the instrument consists of a set of graduated bamboo pipes excited by blowing across the open tops. Details of the excitation aerodynamics warrant examination, particularly as the higher notes contain amplitudes of the even harmonics approaching those of the odd harmonics expected from a stopped pipe. Analysis shows that the jet offset is controlled by the fluid dynamics of the jet, and is such that appreciable even-harmonic excitation is generated. The theory is largely confirmed by measurements on a player.

Generation of higher odd harmonics in a defective photonic crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramanujam, N. R., E-mail: wilsonpra@yahoo.co.in; Wilson, K. S. Joseph

2015-06-24

A photonic crystal (AB){sup 2}(DB)(AB){sup 2} with high refractive index medium as silicon and low refractive medium as air is considered. Using the transfer matrix method, the transmission properties as a function of wavelength with photonic band gaps has been obtained. We are able to demonstrate the generation of third, fifth, seventh and ninth harmonics in the present work. We show that if the air medium is removed in the defect, the defect modes are generated but not harmonics. It can be designed to have a frequency conversion, and have a potential for becoming the basis for the next generationmore » of optical devices.« less

Multi-Frequency Harmonics Technique for HIFU Tissue Treatment

NASA Astrophysics Data System (ADS)

Rybyanets, Andrey N.; Lugovaya, Maria A.; Rybyanets, Anastasia A.

2010-03-01

New technique for enhancing of tissue lysis and enlarging treatment volume during one HIFU sonification is proposed. The technique consists in simultaneous or alternative (at optimal repetition frequency) excitation of single element HIFU transducer on a frequencies corresponding to odd natural harmonics of piezoceramic element at ultrasound energy levels sufficient for producing cavitational, thermal or mechanical damage of fat cells at each of aforementioned frequencies. Calculation and FEM modeling of transducer vibrations and acoustic field patterns for different frequencies sets were performed. Acoustic pressure in focal plane was measured in water using calibrated hydrophone and 3D acoustic scanning system. In vitro experiments on different tissues and phantoms confirming the advantages of multifrequency harmonic method were performed.

Worldwide complete spherical Bouguer and isostatic anomaly maps

NASA Astrophysics Data System (ADS)

Bonvalot, S.; Balmino, G.; Briais, A.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2011-12-01

We present here a set of digital maps of the Earth's gravity anomalies (surface "free air", Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW). The free air and Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, submitted). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial Intelligence Agency (NGA) (Pavlis et al., 2008), which represents the best up-to-date global gravity model (including surface gravity measurements from land, marine and airborne surveys as well as gravity and altimetry satellite measurements). The surface gravity anomaly (free air) is computed at the Earth's surface in the context of Molodensky theory and includes corrections from the mass of the atmosphere. The way gravity anomalies are computed on a worldwide basis slightly differs from the classical usage, but meets modern concerns which tend to take the real Earth into account. The resulting anomaly maps and grids will be distributed for scientific and education purposes by the Commission for the Geological Map of the World (CGMW) with support of UNESCO and other institutions. Upgraded versions might be done as soon as new global gravity model is available (including satellite GOCE and new surface measurements: ground, airborne). Visit / contact BGI (http://bgi.omp.obs-mip.fr) and CCMW (http://ccgm.free.fr) for more information.

Phase-matched second- and third-harmonic generation in plasmas with density ripple

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dahiya, Deepak; Sajal, Vivek; Sharma, A. K.

The generation of second and third harmonics by the interaction of an ultrashort laser pulse with underdense plasma having a density ripple is studied at intensities I{lambda}{sup 2}=10{sup 16}-10{sup 19} W cm{sup -2} {mu}m{sup 2} using fully relativistic two-dimensional particle-in-cell simulations with high spectral resolution. A theoretical model is developed for second- and third-harmonic conversion efficiencies. When the laser is plane polarized in the simulation plane even and odd harmonics are excited in the same polarization as the laser polarization. The highest efficiency of generation of a specific harmonic occurs when the ripple wave vector value k{sub q} satisfies phase-matchingmore » conditions. The efficiency of phase-matched harmonic generation is an order of magnitude higher than the one without phase matching. The efficiency increases rapidly in weak and moderate relativistic regime and tends to saturate in strong relativistic regime. At moderately relativistic intensities and low plasma densities, the simulation and recent experimental results are fairly reproduced by an analytical theory.« less

Comparing T-odd and T-even spin sum rules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Teryaev, O.V.

2015-04-10

Sum rules for T-even and T-odd structure functions and parton distributions are considered. The case of spin-dependent distributions related to energy-momentum tensor (EMT) is specifically addressed. The Burkardt sum rule for T-odd Sivers functions may be related to EMT provided the imaginary prescription for gluonic pole correlator is incorporated. The momentum sum rule for deuteron tensor spin structure function allows one to probe indirectly the gravity couplings to quarks and gluons.

Pure Lovelock gravity and Chern-Simons theory

NASA Astrophysics Data System (ADS)

Concha, P. K.; Durka, R.; Inostroza, C.; Merino, N.; Rodríguez, E. K.

2016-07-01

We explore the possibility of finding pure Lovelock gravity as a particular limit of a Chern-Simons action for a specific expansion of the AdS algebra in odd dimensions. We derive in detail this relation at the level of the action in five and seven dimensions. We provide a general result for higher dimensions and discuss some issues arising from the obtained dynamics.

An Experiment on a Physical Pendulum and Steiner's Theorem

ERIC Educational Resources Information Center

Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.

2010-01-01

Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…

Europe's Preparation For GOCE Gravity Field Recovery

NASA Astrophysics Data System (ADS)

Suenkel, H.; Suenkel, H.

2001-12-01

The European Space Agency ESA is preparing for its first dedicated gravity field mission GOCE (Gravity Field and Steady-state Ocean Circulation Explorer) with a proposed launch in fall 2005. The mission's goal is the mapping of the Earth's static gravity field with very high resolution and utmost accuracy on a global scale. GOCE is a drag-free mission, flown in a circular and sun-synchronous orbit at an altitude between 240 and 250 km. Each of the two operational phases will last for 6 months. GOCE is based on a sensor fusion concept combining high-low satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG). The transformation of the GOCE sensor data into a scientific product of utmost quality and reliability requires a well-coordinated effort of experts in satellite geodesy, applied mathematics and computer science. Several research groups in Europe do have this expertise and decided to form the "European GOCE Gravity Consortium (EGG-C)". The EGG-C activities are subdivided into tasks such as standard and product definition, data base and data dissemination, precise orbit determination, global gravity field model solutions and regional solutions, solution validation, communication and documentation, and the interfacing to level 3 product scientific users. The central issue of GOCE data processing is, of course, the determination of the global gravity field model using three independent mathematical-numerical techniques which had been designed and pre-developed in the course of several scientific preparatory studies of ESA: 1. The direct solution which is a least squares adjustment technique based on a pre-conditioned conjugated gradient method (PCGM). The method is capable of efficiently transforming the calibrated and validated SST and SGG observations directly or via lumped coefficients into harmonic coefficients of the gravitational potential. 2. The time-wise approach considers both SST and SGG data as a time series. For an idealized repeat mission such a time series can be very efficiently transformed into lumped coefficients using fast Fourier techniques. For a realistic mission scenario this transformation has to be extended by an iteration process. 3. The space-wise approach which, after having transformed the original observations onto a spatial geographical grid, transforms the pseudo-observations into harmonic coefficients using a fast collocation technique. A successful mission presupposed, GOCE will finally deliver the Earth's gravity field with a resolution of about 70 km half wavelength and a global geoid with an accuracy of about 1 cm.

Three-Gorge Reservoir: A 'Controlled Experiment' for Calibration/Validation of Time-Variable Gravity Signals Detected from Space

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Boy, J. P.

2003-01-01

With the advances of measurements, modern space geodesy has become a new type of remote sensing for the Earth dynamics, especially for mass transports in the geophysical fluids on large spatial scales. A case in point is the space gravity mission GRACE (Gravity Recovery And Climate Experiment) which has been in orbit collecting gravity data since early 2002. The data promise to be able to detect changes of water mass equivalent to sub-cm thickness on spatial scale of several hundred km every month or so. China s Three-Gorge Reservoir has already started the process of water impoundment in phases. By 2009,40 km3 of water will be stored behind one of the world s highest dams and spanning a section of middle Yangtze River about 600 km in length. For the GRACE observations, the Three-Gorge Reservoir would represent a geophysical controlled experiment , one that offers a unique opportunity to do detailed geophysical studies. -- Assuming a complete documentation of the water level and history of the water impoundment process and aided with a continual monitoring of the lithospheric loading response (such as in area gravity and deformation), one has at hand basically a classical forwardinverse modeling problem of surface loading, where the input and certain output are known. The invisible portion of the impounded water, i.e. underground storage, poses either added values as an observable or a complication as an unknown to be modeled. Wang (2000) has studied the possible loading effects on a local scale; we here aim for larger spatial scales upwards from several hundred km, with emphasis on the time-variable gravity signals that can be detected by GRACE and follow-on missions. Results using the Green s function approach on the PREM elastic Earth model indicate the geoid height variations reaching several millimeters on wavelengths of about a thousand kilometers. The corresponding vertical deformations have amplitude of a few centimeters. In terms of long-wavelength spherical harmonics, the induced geoid height variations are very close to the accuracy of GRACE- recoverable gravity field, while the low-degree (2 to 5) harmonics should be detectable. With a large regional time-variable gravity signal, the Three-Gorge experiment can serve as a useful calibration/verification for GRACE (including the elastic loading effects), and future gravity missions (especially for visco-elastic yielding as well as underground water variations).

From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

NASA Astrophysics Data System (ADS)

Lusanna, Luca

Clock synchronization leads to the definition of instantaneous 3-spaces (to be used as Cauchy surfaces) in non-inertial frames, the only ones allowed by the equivalence principle. ADM canonical tetrad gravity in asymptotically Minkowskian space-times can be described in this framework. This allows to find the York canonical basis in which the inertial (gauge) and tidal (physical) degrees of freedom of the gravitational field can be identified. A Post-Minkowskian linearization with respect to the asymptotic Minkowski metric (asymptotic background) allows to solve the Dirac constraints in non-harmonic 3-orthogonal gauges and to find non-harmonic TT gravitational waves. The inertial gauge variable York time (the trace of the extrinsic curvature of the 3-space) describes the general relativistic freedom in clock synchronization. After a digression on the gauge problem in general relativity, it is shown that dark matter, whose experimental signatures are the rotation curves and the mass of galaxies, may be described (at least partially) as an inertial relativistic effect (absent in Newton gravity) connected with the York time.

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

2017-12-01

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

High-resolution gravity and geoid models in Tahiti obtained from new airborne and land gravity observations: data fusion by spectral combination

NASA Astrophysics Data System (ADS)

Shih, Hsuan-Chang; Hwang, Cheinway; Barriot, Jean-Pierre; Mouyen, Maxime; Corréia, Pascal; Lequeux, Didier; Sichoix, Lydie

2015-08-01

For the first time, we carry out an airborne gravity survey and we collect new land gravity data over the islands of Tahiti and Moorea in French Polynesia located in the South Pacific Ocean. The new land gravity data are registered with GPS-derived coordinates, network-adjusted and outlier-edited, resulting in a mean standard error of 17 μGal. A crossover analysis of the airborne gravity data indicates a mean gravity accuracy of 1.7 mGal. New marine gravity around the two islands is derived from Geosat/GM, ERS-1/GM, Jason-1/GM, and Cryosat-2 altimeter data. A new 1-s digital topography model is constructed and is used to compute the topographic gravitational effects. To use EGM08 over Tahiti and Moorea, the optimal degree of spherical harmonic expansion is 1500. The fusion of the gravity datasets is made by the band-limited least-squares collocation, which best integrates datasets of different accuracies and spatial resolutions. The new high-resolution gravity and geoid grids are constructed on a 9-s grid. Assessments of the grids by measurements of ground gravity and geometric geoidal height result in RMS differences of 0.9 mGal and 0.4 cm, respectively. The geoid model allows 1-cm orthometric height determination by GPS and Lidar and yields a consistent height datum for Tahiti and Moorea. The new Bouguer anomalies show gravity highs and lows in the centers and land-sea zones of the two islands, allowing further studies of the density structure and volcanism in the region.

The Early Shape of the Moon

NASA Astrophysics Data System (ADS)

Garrick-Bethell, I.; Perera, V.; Nimmo, F.; Zuber, M. T.

2013-12-01

The origin and nature of the long-wavelength shape of the Moon has been a puzzle for at least 100 years [1-5]. Understanding its origin would provide insight into the patterns of mare volcanism, early thermal evolution, the history of the Moon's orientation, and the Moon's orbital evolution. Previously, we explained the shape and structure of the lunar farside highlands with a model of early tidal heating in the crust [6]. However, we left open the problem of the rest of the Moon's low-order shape, and we did not consider the lunar gravity field together with topography. To address these problems, and further assess the tidal-rotation (spherical harmonic degree-2) origins of the lunar shape, we consider three effects: the Moon's degree-1 spherical harmonics, the Moon's largest basins and mascons, and the choice of reference frame in which we analyze topography. We find that removing the degree-1 terms from a topography map helps illustrate the Moon's degree-2 shape, since the degree-1 harmonics have relatively high power. More importantly, however, when we fit spherical harmonics to topography outside of the largest lunar basins (including South-Pole Aitken, Imbrium, Serenitatis, Nectaris, and Orientale), the degree-2 coefficient values change significantly. When these best-fit harmonics are rotated into a reference frame that only contains the C2,0 and C2,2 harmonics (equivalent to the frame that would have once faced the Earth if the early Moon's shape controlled the moments of inertia), we find that gravity and topography data together imply a mixture of compensated and uncompensated degree-2 topography components. The compensated topography component can be explained by global-scale tidal heating in the early crust, while the uncompensated component can be explained by a frozen 'fossil bulge' that formed at a semi-major axis of about 32 Earth radii. To check these explanations, we can examine the ratios of the C2,0 and C2,2 harmonics for each component. We find that the values of C2,0/C2,2 are approximately equal to the values expected for each unique process: -1.3 and -1.0, for compensated (tidal-heating) and uncompensated (fossil bulge) topography components, respectively. However, if we had not removed the effects of large basins, the ratios would not be in agreement. In conclusion, a combination of early tidal heating in the crust and a frozen fossil bulge can help explain the global, pre-basin shape of the Moon. References [1] W.F. Sedgwick, On the figure of the Moon, Messenger Math. 27 (1898) 171. [2] H. Jeffreys, On the figures of the Earth and Moon, Geophys. J. Int. 4 (1937) 1-13. [3] H.C. Urey, et al., Note on the internal structure of the Moon, Ap. J. 129 (1959) 842. [4] K. Lambeck, S. Pullan, The lunar fossil bulge hypothesis revisited, Phys. Earth Planet. Inter. 22 (1980) 29-35. [5] D.J. Stevenson, Origin and implications of the degree two lunar gravity field, Proc. Lunar Sci. Conf. 32nd (2001) 1175. [6] I. Garrick-Bethell, et al., Structure and formation of the lunar farside highlands, Science 330 (2010) 949-951.

Studying the Representation Accuracy of the Earth's Gravity Field in the Polar Regions Based on the Global Geopotential Models

NASA Astrophysics Data System (ADS)

Koneshov, V. N.; Nepoklonov, V. B.

2018-05-01

The development of studies on estimating the accuracy of the Earth's modern global gravity models in terms of the spherical harmonics of the geopotential in the problematic regions of the world is discussed. The comparative analysis of the results of reconstructing quasi-geoid heights and gravity anomalies from the different models is carried out for two polar regions selected within a radius of 1000 km from the North and South poles. The analysis covers nine recently developed models, including six high-resolution models and three lower order models, including the Russian GAOP2012 model. It is shown that the modern models determine the quasi-geoid heights and gravity anomalies in the polar regions with errors of 5 to 10 to a few dozen cm and from 3 to 5 to a few dozen mGal, respectively, depending on the resolution. The accuracy of the models in the Arctic is several times higher than in the Antarctic. This is associated with the peculiarities of gravity anomalies in every particular region and with the fact that the polar part of the Antarctic has been comparatively less explored by the gravity methods than the polar Arctic.

Very accurate upward continuation to low heights in a test of non-Newtonian theory

NASA Technical Reports Server (NTRS)

Romaides, Anestis J.; Jekeli, Christopher

1989-01-01

Recently, gravity measurements were made on a tall, very stable television transmitting tower in order to detect a non-Newtonian gravitational force. This experiment required the upward continuation of gravity from the Earth's surface to points as high as only 600 m above ground. The upward continuation was based on a set of gravity anomalies in the vicinity of the tower whose data distribution exhibits essential circular symmetry and appropriate radial attenuation. Two methods were applied to perform the upward continuation - least-squares solution of a local harmonic expansion and least-squares collocation. Both methods yield comparable results, and have estimated accuracies on the order of 50 microGal or better (1 microGal = 10(exp -8) m/sq s). This order of accuracy is commensurate with the tower gravity measurments (which have an estimated accuracy of 20 microGal), and enabled a definitive detection of non-Newtonian gravity. As expected, such precise upward continuations require very dense data near the tower. Less expected was the requirement of data (though sparse) up to 220 km away from the tower (in the case that only an ellipsoidal reference gravity is applied).

GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data

PubMed Central

Lemoine, Frank G; Goossens, Sander; Sabaka, Terence J; Nicholas, Joseph B; Mazarico, Erwan; Rowlands, David D; Loomis, Bryant D; Chinn, Douglas S; Neumann, Gregory A; Smith, David E; Zuber, Maria T

2014-01-01

We have derived a gravity field solution in spherical harmonics to degree and order 900, GRGM900C, from the tracking data of the Gravity Recovery and Interior Laboratory (GRAIL) Primary (1 March to 29 May 2012) and Extended Missions (30 August to 14 December 2012). A power law constraint of 3.6 ×10−4/ℓ2 was applied only for degree ℓ greater than 600. The model produces global correlations of gravity, and gravity predicted from lunar topography of ≥ 0.98 through degree 638. The model's degree strength varies from a minimum of 575–675 over the central nearside and farside to 900 over the polar regions. The model fits the Extended Mission Ka-Band Range Rate data through 17 November 2012 at 0.13 μm/s RMS, whereas the last month of Ka-Band Range-Rate data obtained from altitudes of 2–10 km fit at 0.98 μm/s RMS, indicating that there is still signal inherent in the tracking data beyond degree 900. PMID:26074638

GRGM900C: A degree 900 lunar gravity model from GRAIL primary and extended mission data.

PubMed

Lemoine, Frank G; Goossens, Sander; Sabaka, Terence J; Nicholas, Joseph B; Mazarico, Erwan; Rowlands, David D; Loomis, Bryant D; Chinn, Douglas S; Neumann, Gregory A; Smith, David E; Zuber, Maria T

2014-05-28

We have derived a gravity field solution in spherical harmonics to degree and order 900, GRGM900C, from the tracking data of the Gravity Recovery and Interior Laboratory (GRAIL) Primary (1 March to 29 May 2012) and Extended Missions (30 August to 14 December 2012). A power law constraint of 3.6 ×10 -4 / ℓ 2 was applied only for degree ℓ greater than 600. The model produces global correlations of gravity, and gravity predicted from lunar topography of ≥ 0.98 through degree 638. The model's degree strength varies from a minimum of 575-675 over the central nearside and farside to 900 over the polar regions. The model fits the Extended Mission Ka-Band Range Rate data through 17 November 2012 at 0.13 μm/s RMS, whereas the last month of Ka-Band Range-Rate data obtained from altitudes of 2-10 km fit at 0.98 μm/s RMS, indicating that there is still signal inherent in the tracking data beyond degree 900.

GRGM900C: A Degree 900 Lunar Gravity Model from GRAIL Primary and Extended Mission Data

NASA Technical Reports Server (NTRS)

Lemoine, Frank G.; Goossens, Sander; Sabaka, Terence J.; Nicholas, Joseph B.; Mazarico, Erwan; Rowlands, David D.; Bryant, D. Loomis; Chinn, Douglas S.; Neumann, Gregory A.; Smith, David E.;

Evidence for active hotspots on Venus from analysis of Magellan gravity data

NASA Technical Reports Server (NTRS)

Smrekar, Suzanne E.

1994-01-01

The 500-Myr average crater retention age for Venus has raised questions about the present-day level of tectonic activity. In this study we examine the relationship between the gravity and topography of four large volcanic swells, Beta, Atla, Bell, and Western Eistla Regiones, for clues about their stage evolution. The Magellan line-of-sight gravity data are inverted using a point mass model of the anomalous mass to solve for the local vertical gravity field. Spectral admittance calculated from both the local gravity inversions and a spherical harmonic model is compared to three models of compensation: local compensation, a 'flexural' model with local and regional compensation of surface and subsurface loads, and a 'hotspot' model of compensation that includes top loading by volcanoes and subsurface loading due to a deep, low density mass anomaly. The coherence is also calculated in each region, but yields an elastic thickness estimate only at Bell Regio. In all models, the long wavelengths are compensated locally. Our results may indicate a relatively old, possibly inactive plume.

Exploring correlations in the CGC wave function: Odd azimuthal anisotropy

DOE PAGES

Kovner, Alex; Lublinsky, Michael; Skokov, Vladimir

2017-07-17

In this paper, we extend the color glass condensate (CGC) approach to a calculation of the double inclusive gluon production by including the high density effect in the CGC wave function of the projectile (proton). Our main result is that these effects lead to the appearance of odd harmonics in the two particle correlation C(k,p). We find that in the high momentum limit, |k|, |p| >> Q s, this results in a positive c 1{2}. Additionally when the magnitudes of the two momenta are approximately equal, |k|/|p| ≈ 1, the density effects also generate a positive third harmonic c 3{2},more » which translates into a nonvanishing v 3 when the momenta of the trigger and an associated particle are in the same momentum bin. Finally, the sign of c 3{2} becomes negative when |k|/|p| > 1.1 suggesting an interesting experimental signature.« less

Terrestrial Water Mass Load Changes from Gravity Recovery and Climate Experiment (GRACE)

NASA Technical Reports Server (NTRS)

Seo, K.-W.; Wilson, C. R.; Famiglietti, J. S.; Chen, J. L.; Rodell M.

2006-01-01

Recent studies show that data from the Gravity Recovery and Climate Experiment (GRACE) is promising for basin- to global-scale water cycle research. This study provides varied assessments of errors associated with GRACE water storage estimates. Thirteen monthly GRACE gravity solutions from August 2002 to December 2004 are examined, along with synthesized GRACE gravity fields for the same period that incorporate simulated errors. The synthetic GRACE fields are calculated using numerical climate models and GRACE internal error estimates. We consider the influence of measurement noise, spatial leakage error, and atmospheric and ocean dealiasing (AOD) model error as the major contributors to the error budget. Leakage error arises from the limited range of GRACE spherical harmonics not corrupted by noise. AOD model error is due to imperfect correction for atmosphere and ocean mass redistribution applied during GRACE processing. Four methods of forming water storage estimates from GRACE spherical harmonics (four different basin filters) are applied to both GRACE and synthetic data. Two basin filters use Gaussian smoothing, and the other two are dynamic basin filters which use knowledge of geographical locations where water storage variations are expected. Global maps of measurement noise, leakage error, and AOD model errors are estimated for each basin filter. Dynamic basin filters yield the smallest errors and highest signal-to-noise ratio. Within 12 selected basins, GRACE and synthetic data show similar amplitudes of water storage change. Using 53 river basins, covering most of Earth's land surface excluding Antarctica and Greenland, we document how error changes with basin size, latitude, and shape. Leakage error is most affected by basin size and latitude, and AOD model error is most dependent on basin latitude.

GLGM-3: A Degree-ISO Lunar Gravity Model from the Historical Tracking Data of NASA Moon Orbiters

NASA Technical Reports Server (NTRS)

Mazarico, E.; Lemoine, F. G.; Han, Shin-Chan; Smith, D. E.

2010-01-01

In preparation for the radio science experiment of the Lunar Reconnaissance Orbiter (LRO) mission, we analyzed the available radio tracking data of previous NASA lunar orbiters. Our goal was to use these historical observations in combination with the new low-altitude data to be obtained by LRO. We performed Precision Orbit Determination on trajectory arcs from Lunar Orbiter 1 in 1966 to Lunar Prospector in 1998, using the GEODYN II program developed at NASA Goddard Space Flight Center. We then created a set of normal equations and solved for the coefficients of a spherical harmonics expansion of the lunar gravity potential up to degree and order 150. The GLGM-3 solution obtained with a global Kaula constraint (2.5 x 10(exp -4)/sq l) shows good agreement with model LP150Q from the Jet Propulsion Laboratory, especially over the nearside. The levels of data fit with both gravity models are very similar (Doppler RMS of approx.0.2 and approx. 1-2 mm/s in the nominal and extended phases, respectiVely). Orbit overlaps and uncertainties estimated from the covariance matrix also agree well. GLGM-3 shows better correlation with lunar topography and admittance over the nearside at high degrees of expansion (l > 100), particularly near the poles. We also present three companion solutions, obtained with the same data set but using alternate inversion strategies that modify the power law constraint and expectation of the individual spherical harmonics coefficients. We give a detailed discussion of the performance of this family of gravity field solutions in terms of observation fit, orbit quality, and geophysical consistency.

High Degree and Order Gravity Fields of the Moon Derived from GRAIL Data

NASA Technical Reports Server (NTRS)

Lemoine, F. G.; Goossens, S. J.; Sabaka, T. J.; Nicholas, J. B.; Mazarico, E.; Rowlands, D. D.; Loomis, B. D.; Chinn, D. S.; Caprette, D. S.; McCarthy, J. J.;

Helioseismic Constraints on the Depth Dependence of Large-Scale Solar Convection

NASA Astrophysics Data System (ADS)

Woodard, Martin F.

2017-08-01

A recent helioseismic statistical waveform analysis of subsurface flow based on a 720-day time series of SOHO/MDI Medium-l spherical-harmonic coefficients has been extended to cover a greater range of subphotospheric depths. The latest analysis provides estimates of flow-dependent oscillation-mode coupling-strength coefficients b(s,t;n,l) over the range l = 30 to 150 of mode degree (angular wavenumber) for solar p-modes in the approximate frequency range 2 to 4 mHz. The range of penetration depths of this mode set covers most of the solar convection zone. The most recent analysis measures spherical harmonic (s,t) components of the flow velocity for odd s in the angular wavenumber range 1 to 19 for t not much smaller than s at a given s. The odd-s b(s,t;n,l) coefficients are interpreted as averages over depth of the depth-dependent amplitude of one spherical-harmonic (s,t) component of the toroidal part of the flow velocity field. The depth-dependent weighting function defining the average velocity is the fractional kinetic energy density in radius of modes of the (n,l) multiplet. The b coefficients have been converted to estimates of root velocity power as a function of l0 = nu0*l/nu(n,l), which is a measure of mode penetration depth. (nu(n,l) is mode frequency and nu0 is a reference frequency equal to 3 mHz.) A comparison of the observational results with simple convection models will be presented.

Contribution of the pre-ionized H2 and the ionized H2+ subsystems to the HHG Spectra of H2 in intense laser fields

NASA Astrophysics Data System (ADS)

Iravani, Hossein; Sabzyan, Hassan; Vafaee, Mohsen; Buzari, Behnaz

2018-04-01

Contributions of the pre-ionized H2 (PI-H2) and ionized {{{H}}}2+ subsystems of the two-electron H2 system to its high-order harmonic generation in eight-cycle sin2-like ultrafast intense laser pulses are calculated and analyzed based on the solution of the time-dependent Schrödinger equation for the one-dimensional two-electronic H2 system with fixed nuclei. The laser pulses have λ = 390 and 532 nm wavelengths and I = 1 × 1014, 5 × 1014, 1 × 1015 and 5 × 1015 W cm‑2 intensities. It is found that at the two lower intensities, the PI-H2 subsystem dominantly produces the HHG spectra. However, at the two higher intensities, both PI-H2 and ionized {{{H}}}2+ subsystems contribute comparably to the HHG spectra. In the {{{H}}}2+ subsystem, the symmetry of the populations of {{{H}}}2+(I) and {{{H}}}2+(II) regions (left and right regions of {{{H}}}2+ subsystem) is broken by increasing the laser intensity. Complex patterns and even harmonics also appear at these two higher intensities. For instance, at 1 × 1015 W cm‑2 intensity and λ = 532 nm wavelength, the even harmonics are appeared near cutoff region. Interestingly, at 5 × 1015 W cm‑2 intensity and λ = 390 nm wavelength, the even harmonics replaced by the odd harmonics with red shift. At λ = 390 and 532 nm wavelengths and I = 1 × 1015 intensity, the two-electron cutoffs corresponding to nonsequential double-recombination with maximum return kinetic energy of 4.70Up are detected. The HHG spectra of the whole H2 system obtained with and without nuclear dynamics treated classically are approximately similar. However, at 1 × 1015 W cm‑2 intensity and λ = 532 nm wavelength, if we take into account nuclear dynamics, the even harmonics which are appeared near cutoff region, replaced by the odd harmonics with blue shift.

Gravity Field Recovery from the Cartwheel Formation by the Semi-analytical Approach

NASA Astrophysics Data System (ADS)

Li, Huishu; Reubelt, Tilo; Antoni, Markus; Sneeuw, Nico; Zhong, Min; Zhou, Zebing

2016-04-01

Past and current gravimetric satellite missions have contributed drastically to our knowledge of the Earth's gravity field. Nevertheless, several geoscience disciplines push for even higher requirements on accuracy, homogeneity and time- and space-resolution of the Earth's gravity field. Apart from better instruments or new observables, alternative satellite formations could improve the signal and error structure. With respect to other methods, one significant advantage of the semi-analytical approach is its effective pre-mission error assessment for gravity field missions. The semi-analytical approach builds a linear analytical relationship between the Fourier spectrum of the observables and the spherical harmonic spectrum of the gravity field. The spectral link between observables and gravity field parameters is given by the transfer coefficients, which constitutes the observation model. In connection with a stochastic model, it can be used for pre-mission error assessment of gravity field mission. The cartwheel formation is formed by two satellites on elliptic orbits in the same plane. The time dependent ranging will be considered in the transfer coefficients via convolution including the series expansion of the eccentricity functions. The transfer coefficients are applied to assess the error patterns, which are caused by different orientation of the cartwheel for range-rate and range acceleration. This work will present the isotropy and magnitude of the formal errors of the gravity field coefficients, for different orientations of the cartwheel.

Major Fault Patterns in Zanjan State of Iran Based of GECO Global Geoid Model

NASA Astrophysics Data System (ADS)

Beheshty, Sayyed Amir Hossein; Abrari Vajari, Mohammad; Raoufikelachayeh, SeyedehSusan

2016-04-01

A new Earth Gravitational Model (GECO) to degree 2190 has been developed incorporates EGM2008 and the latest GOCE based satellite solutions. Satellite gradiometry data are more sensitive information of the long- and medium- wavelengths of the gravity field than the conventional satellite tracking data. Hence, by utilizing this new technique, more accurate, reliable and higher degrees/orders of the spherical harmonic expansion of the gravity field can be achieved. Gravity gradients can also be useful in geophysical interpretation and prospecting. We have presented the concept of gravity gradients with some simple interpretations. A MATLAB based computer programs were developed and utilized for determining the gravity and gradient components of the gravity field using the GGMs, followed by a case study in Zanjan State of Iran. Our numerical studies show strong (more than 72%) correlations between gravity anomalies and the diagonal elements of the gradient tensor. Also, strong correlations were revealed between the components of the deflection of vertical and the off-diagonal elements as well as between the horizontal gradient and magnitude of the deflection of vertical. We clearly distinguished two big faults in North and South of Zanjan city based on the current information. Also, several minor faults were detected in the study area. Therefore, the same geophysical interpretation can be stated for gravity gradient components too. Our mathematical derivations support some of these correlations.

Free-air and Bouguer gravity anomalies and the Martian crustal dichotomy

NASA Technical Reports Server (NTRS)

Frey, Herbert; Bills, Bruce G.; Kiefer, Walter S.; Nerem, R. Steven; Roark, James H.; Zuber, Maria T.

1993-01-01

Free-air and Bouguer gravity anomalies from a 50x50 field, derived from re-analysis of Viking Orbiter and Mariner 9 tracking data and using a 50x50 expansion of the current Mars topography and the GSFC degree 50 geoid as the equipotential reference surface, with the Martian crustal dichotomy are compared. The spherical harmonic topography used has zero mean elevation, and differs from the USGS maps by about 2 km. In this field the dichotomy boundary in eastern Mars lies mostly at -1 to -2 km elevation. Bouguer gravity anomalies are shown on a map of Noachian, Hesperian, and Amazonian age terrains, simplified from current geologic maps. The map is centered at 300 deg W to show the continuity of the dichotomy boundary. Contour interval is 100 mgals. Gravity and topography were compared along approximately 40 profiles oriented parallel to the dichotomy boundary topographic gradient, to determine how the geophysical character of the boundary changes along its length and what this implies for its origin and development.

Novel symmetries in Weyl-invariant gravity with massive gauge field

NASA Astrophysics Data System (ADS)

Abhinav, K.; Shukla, A.; Panigrahi, P. K.

2016-11-01

The background field method is used to linearize the Weyl-invariant scalar-tensor gravity, coupled with a Stückelberg field. For a generic background metric, this action is found not to be invariant, under both a diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both transformations independently. The Becchi-Rouet-Stora-Tyutin symmetry of scalar-tensor gravity coupled with a Stückelberg-like massive gauge particle, possessing a diffeomorphism and generalized Weyl symmetry, reveals that in both cases negative-norm states with unphysical degrees of freedom do exist. We then show that, by combining diffeomorphism and generalized Weyl symmetries, all the ghost states decouple, thereby removing the unphysical redundancies of the theory. During this process, the scalar field does not represent any dynamic mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.

Weekly Solutions of Time-Variable Gravity from 1993 to 2010

NASA Technical Reports Server (NTRS)

Lemoine, F.; Chinn, D.; Le Bail, K.; Zelensky, N.; Melachroinos, S.; Beall, J.

2011-01-01

The GRACE mission has been highly successful in determining the time-variable gravity field of the Earth, producing monthly or even more frequent solutions (cf. 10-day) solutions using both spherical harmonics and mascons. However the GRACE time series only commences in 2002 - 2003 and a gap of several years may occur in the series before a GRACE follow-on satellite is launched. Satellites tracked by SLR and DORIS have also been used to study time variations in the Earth's gravitational field. These include (most recently) the solutions of Cox and Chao (2002), Cheng et al. (2004, 2007) and Lemoine et al. (2007). In this paper we discuss the development of a new time series of low degree spherical harmonic fields based on the available SLR, DORIS and GPS data. We develop simultaneous solutions for both the geocenter and the low degree harmonics up to 5x5. The solutions integrate data from SLR geodetic satellites (e.g., Lageos1, Lageos2, Starlette, Stella, Ajisai, Larets, Westpac), altimetry satellites (TOPEX/Poseidon, Envisat, Jason-1, Jason-2), and satellites tracked solely by DORIS (e.g. SPOT2-5). We discuss some pertinent aspects of the satellite-specific modeling. We include altimeter crossovers in the weekly solutions where feasible and time permits. The resulting geocenter time series is compared with geophysical model predictions and other independently-derived solutions. Over the GRACE time period the fidelity and consistency with the GRACE solutions are presented.

An oblate ellipsoidal approach to update a high-resolution geopotential model over the oceans: Study case of EGM2008 and DTU10

NASA Astrophysics Data System (ADS)

Sebera, Josef; Bezděk, Aleš; Kostelecký, Jan; Pešek, Ivan; Shum, C. K.

2016-01-01

The most important high-resolution geopotential models such as EGM96 and EGM2008 have been released approximately once per decade. In light of the ability of modern satellite, airborne or terrestrial techniques to provide new data sets every year (e.g., in polar and ocean areas), these data can be readily included in existing models without waiting for a new release. In this article, we present a novel ellipsoidal approach for updating high-resolution models over the oceans with new gridded data. The problem is demonstrated using the EGM2008 model updated with DTU10 geoid and gravity grids that provide additional signal over the Arctic oceans. The result of the procedure are the ellipsoidal and the spherical harmonic coefficients up to degree 4320 and 4400, respectively. These coefficients represent the input data set to within 0.08 mGal globally, with the largest differences located at the land-ocean boundaries, which is two orders of magnitude less than real accuracy of gravity data from satellite altimetry. Along with the harmonic coefficients a detailed map of the second vertical derivative of the anomalous potential (or vertical gravitational gradient) on 1 arc-min grid is anticipated to improve or complement the original DTU10 geoid model. Finally, an optimized set of Jekeli's functions is provided as they allow for computing oblate ellipsoidal harmonics up to a very high degree and order (>10,000) in terms of the hypergeometric formulation.

Thermodynamics of "exotic" Bañados-Teitelboim-Zanelli black holes.

PubMed

Townsend, Paul K; Zhang, Baocheng

2013-06-14

A number of three-dimensional (3D) gravity models, such as 3D conformal gravity, admit "exotic" black hole solutions: the metric is the same as the Bañados-Teitelboim-Zanelli metric of 3D Einstein gravity but with reversed roles for mass and angular momentum, and an entropy proportional to the length of the inner horizon instead of the event horizon. Here we show that the Bañados-Teitelboim-Zanelli solutions of the exotic 3D Einstein gravity (with parity-odd action but Einstein field equations) are exotic black holes, and we investigate their thermodynamics. The first and second laws of black hole thermodynamics still apply, and the entropy still has a statistical interpretation.

Generalized uncertainty principle and quantum gravity phenomenology

NASA Astrophysics Data System (ADS)

Bosso, Pasquale

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canonical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.

Comparative Analysis of Models of the Earth's Gravity: 3. Accuracy of Predicting EAS Motion

NASA Astrophysics Data System (ADS)

Kuznetsov, E. D.; Berland, V. E.; Wiebe, Yu. S.; Glamazda, D. V.; Kajzer, G. T.; Kolesnikov, V. I.; Khremli, G. P.

2002-05-01

This paper continues a comparative analysis of modern satellite models of the Earth's gravity which we started in [6, 7]. In the cited works, the uniform norms of spherical functions were compared with their gradients for individual harmonics of the geopotential expansion [6] and the potential differences were compared with the gravitational accelerations obtained in various models of the Earth's gravity [7]. In practice, it is important to know how consistently the EAS motion is represented by various geopotential models. Unless otherwise stated, a model version in which the equations of motion are written using the classical Encke scheme and integrated together with the variation equations by the implicit one-step Everhart's algorithm [1] was used. When calculating coordinates and velocities on the integration step (at given instants of time), the approximate Everhart formula was employed.

Lower Side Switching Modification of SHEPWM for Single H-Bridge Unipolar Inverter

NASA Astrophysics Data System (ADS)

Aihsan, M. Z.

2018-03-01

Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) is a famous fundamental frequency method for both single stage H-bridge inverter and cascaded multilevel inverters. The main function of SHEPWM is to eliminate the selective lower order of odd harmonic such 3rd, 5th 7th and 9th of the output voltage of the inverter but maintain the fundamental component. In this paper, the 5kHz of the unipolar SHEPWM switching scheme of the inverter is developed and later will be compared to the modified SHEPWM switching scheme. The performance of this inverter is measured through the final total harmonic distortion (THD), the efficiency of the whole system and the natural shape of the output after LC filter.

Venus gravity: Summary and coming events

NASA Technical Reports Server (NTRS)

Sjogren, W. L.

1992-01-01

The first significant dataset to provide local measures of venusian gravity field variations was that acquired from the Pioneer Venus Orbiter (PVO) during the 1979-1981 period. These observations were S-band Doppler radio signals from the orbiting spacecraft received at Earth-based tracking stations. Early reductions of these data were performed using two quite different techniques. Estimates of the classical spherical harmonics were made to various degrees and orders up to 10. At that time, solutions of much higher degree and order were very difficult due to computer limitations. These reductions, because of low degree and order, revealed only the most prominent features with poor spatial resolution and very reduced peak amplitudes.

Estimation of the Earth's gravity field by combining normal equation matrices from GRACE and SLR

NASA Astrophysics Data System (ADS)

Haberkorn, Christoph; Bloßfeld, Mathis; Bouman, Johannes

2014-05-01

Since 2002, GRACE observes the Earth's gravity field with a spatial resolution up to 150 km. The main goal of this mission is the determination of temporal variations in the Earth's gravity field to detect mass displacements. The GRACE mission consists of two identical satellites, which observe the range along the line of sight of both satellites. GRACE observations can be linked with the Earth's gravitational potential, which is expressed in terms of spherical harmonics for global solutions. However, the estimation of low degree coefficients is difficult with GRACE. In contrast to gravity field missions, which observe the gravity field with high spectral resolution, SLR data allow to estimate the lower degree coefficients. Therefore, the coefficient C20 is often replaced by a value derived from Satellite Laser Ranging (SLR). Instead of replacing C20, it can be determined consistently by a combined estimation using GRACE and SLR data. We compute monthly normal equation (NEQ) matrices for GRACE and SLR. Coefficients from monthly GRACE gravity field models of different institutions (Center for Space Research (CSR), USA, Geoforschungszentrum Potsdam (GFZ), Germany and Jet Propulsion Laboratory (JPL), USA) and coefficients from monthly gravity field models of our SLR processing are then combined using the NEQ matrices from both techniques. We will evaluate several test scenarios with gravity field models from different institutions and with different set ups for the SLR NEQ matrices. The effect of the combination on the estimated gravity field will be analysed and presented.

Localized Gravity/Topography Correlation and Admittance Spectra one the Moon

NASA Astrophysics Data System (ADS)

Ishihara, Y.; Namiki, N.; Sugita, S.; Matsumoto, K.; Goossens, S.; Araki, H.; Noda, H.; Sasaki, S.; Iwata, T.; Hanada, H.

2009-04-01

Lunar surface and structure can be separate into two parts. The lunar near side crust and far side crust differ remarkably in thickness. This difference probably caused by difference of thermal evolution and state (elastic thickness) and catering history on both side. The correlations and admittance between the topography and gravity anomalies provide important information on the level of isostatic compensation of the lithosphere at the geological timescale, and reflect its thermo-mechanical state. Therefore, localized correlation and admittance analysis is one of the most important studies of selenodesy. A global correlation between topography and gravity of the Moon obtained by Clementine and Lunar Prospector missions, respectively, reveals high value at long wavelength and low value at short wavelength. Such characteristics are distinguished from those of the Earth and other terrestrial planets, whose global correlation between topography and gravity is low at long wavelength. The distinct correlation between topography and gravity of the Moon may indicate that the lunar topography is supported by multiple compensation mechanism. Further, an incomplete coverage of Doppler tracking data prior to Kaguya (SELENE) gravity experiment probably contributed to the correlation. Because the Moon is synchronously rotating with its revolution around the Earth, a spacecraft orbiting over the far side is not visible from ground stations. In either case, it is significant to decompose local correlation from global ones in order to investigate internal structure of the Moon from spherical harmonic model of gravity (LP75G [1]) and topography (GLTM-2 [2]). Japanese lunar exploration Kaguya (SELENE) has two kinds of selenodesical experiments. One is RSAT/VRAD (gravity mapping with direct tracking over far-side) experiment and another is Laser ALTimeter (LALT; topography mapping) experiment. These two experiments enable us to conduct localized analysis for the Moon. Therefore we attempt localized spectral analysis of the Moon first and then apply possible compensation mechanisms to explain the observed admittance. Kaguya mission has been yielding representation of lunar gravity and topography (shape) substantially superior in resolution and accuracy to earlier solutions. For global lunar gravity field, an accurate spherical harmonic model of gravitational potential up to degree and order 100 (SGM100g) was derived from one year tracking (including 4-way Doppler) data [3]. For topography, LALT has obtained more than 6 million altitude measurements with 5 m precision, from which a spherical harmonic expansion of topography to degree and order 359 (STM359_grid-02) has been determined [4]. In this study, we use those new models. We employ the spatio-spectral localization technique [5] to obtain gravity/shape correlation and admittance spectra as function of position on the Moon. In this analysis, we localize harmonic field with axisymmetric windows of constant diameter, described by Lwin zonal harmonic coefficients. This restricts the permissible range of l in the windowed fields at both the low- (l > Lwin) and high-wave number ends (l < Lobs-Lwin, ; Lobs is the maximum degree of observation) . We chose four fixed windows with Lwin = 5, 10, 17, 26 (equivalent to spatial scales 2200, 1100, 640 and 420 km, respectively). These window sizes correspond to huge-, large-, middle-, and small-size of impact basins. For up to degree 50 with Lwin = 5 scale, it is clearly shown that the near-side contains distinct anti-correlation regions whereas the far-side is mostly occupied by high correlation regions. This difference is mainly due to large mascon basins in near-side, such as mare Imbrium. For Lwin = 10 and 17 scales, we can see anti-correlation regions at not only near-side but also far-side. Locations of anti-correlation regions in the far-side correspond to impact basins (Type II basin [6]). However, lots of far side basins (Type I basin [6]) are not indicated by anti-correlations for these window sizes. For Lwin = 26 scale, we can see weak and spatially small anti-correlation at center of Type I basins. This difference mainly due to spatial size of anti-correlation. In contrast, almost all near-side basins show anti-correlations for all window sizes. This difference is probably due to the difference of elastic thickness between near-side and far-side during the age of impact basin formation. It provides important information on the origin of lunar dichotomy and lunar thermal history. The admittance spectra of the South Pole-Aitken basin (SPA) and far-side highland terrain (FHT) show no significant difference. This means that elastic thickness of two regions are not so different. On the other hand, crustal thickness of two regions are drastically different. It suggests that elatic part of upper mantle of SPA region is probably thicker than FHT. Acknowledgements: SHTOOLS2.4 [7] was used for calculating localized correlation and admittance spectra. References: [1] A. S. Konopliv et al. (1998) Science, 281, 1476-1480. [2] D. E. Smith et al. (1997) JGR, 102, 1591-1611. [3] K. Matsumoto et al. this meeting. [4] H. Araki et al. Submitted to Science. [5] M. Simons et al., (1997) Geophys. J. Int., 131, 24-44. [6] N. Namiki et al. Science in press. [7] M. Wieczorek, (2007) http://www.ipgp.jussieu.fr/~wieczor/SHTOOLS/SHTOOLS.html.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

Effects of electron relaxation on multiple harmonic generation from metal surfaces with femtosecond laser pulses

NASA Astrophysics Data System (ADS)

Karatzas, N. E.; Georges, A. T.

2006-11-01

Calculations are presented for the first four (odd and even) harmonics of an 800 nm laser from a gold surface, with pulse widths ranging from 100 down to 14 fs. For peak laser intensities above 1 GW/cm 2 the harmonics are enhanced because of a partial depletion of the initial electron states. At 10 11 W/cm 2 of peak laser intensity the calculated conversion efficiency for 2nd-harmonic generation is 3 × 10 -9, while for the 5th-harmonic it is 10 -10. The generated harmonic pulses are broadened and delayed relative to the laser pulse because of the finite relaxation times of the excited electronic states. The finite electron relaxation times cause also the broadening of the autocorrelations of the laser pulses obtained from surface harmonic generation by two time-delayed identical pulses. Comparison with recent experimental results shows that the response time of an autocorrelator using nonlinear optical processes in a gold surface is shorter than the electron relaxation times. This seems to indicate that for laser pulses shorter than ˜30 fs, the fast nonresonant channel for multiphoton excitation via continuum-continuum transitions in metals becomes important as the resonant channel becomes slow (relative to the laser pulse) and less efficient.

World Gravity Map: a set of global complete spherical Bouguer and isostatic anomaly maps and grids

NASA Astrophysics Data System (ADS)

Bonvalot, S.; Balmino, G.; Briais, A.; Kuhn, M.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2012-04-01

We present here a set of digital maps of the Earth's gravity anomalies (surface free air, Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW) with support of UNESCO and other institutions. The Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, 2011). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy-Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial Intelligence Agency (NGA) (Pavlis et al., 2008) and the DTU10 (Andersen, 2010) who represents the best up-to-date global gravity models (including surface gravity measurements from land, marine and airborne surveys as well as gravity and altimetry satellite measurements). The surface free-air anomaly is computed at the Earth's surface in the context of Molodensky theory and includes corrections from the mass of the atmosphere. The way gravity anomalies are computed on a worldwide basis slightly differs from the classical usage, but meets modern concerns which tend to take into account of the real Earth. The resulting anomaly maps and grids will be distributed for scientific and education purposes by the Commission for the Geological Map of the World (CGMW) (http://ccgm.free.fr) and by the Bureau Gravimetrique International (BGI) (http://bgi.omp.obs-mip.fr). Upgraded versions might be done as soon as new global gravity model will be available (including satellite GOCE data for instance). Institutions who are interested to contribute with new datasets of surface gravity measurements (i.e. ground, marine or airborne gravity data) are also invited to contact BGI bgi@cnes.fr.

Couplings of gravitational currents with Chern-Simons gravities

NASA Astrophysics Data System (ADS)

Ertem, Ümit; Açık, Özgür

2013-02-01

The coupling of conserved p-brane currents with non-Abelian gauge theories is done consistently by using Chern-Simons forms. Conserved currents localized on p-branes that have a gravitational origin can be constructed from Killing-Yano forms of the underlying spacetime. We propose a generalization of the coupling procedure with Chern-Simons gravities to the case of gravitational conserved currents. In odd dimensions, the field equations of coupled Chern-Simons gravities that describe the local curvature on p-branes are obtained. In special cases of three and five dimensions, the field equations are investigated in detail.

Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wünsche, Martin; Fuchs, Silvio; Aull, Stefan

A quasi-supercontinuum source in the extreme ultraviolet (XUV) is demonstrated using a table-top femtosecond laser and a tunable optical parametric amplifier (OPA) as a driver for high-harmonic generation (HHG). The harmonic radiation, which is usually a comb of odd multiples of the fundamental frequency, is generated by near-infrared (NIR) laser pulses from the OPA. A quasi-continuous XUV spectrum in the range of 30 to 100 eV is realized by averaging over multiple harmonic comb spectra with slightly different fundamental frequencies and thus different spectral spacing between the individual harmonics. The driving laser wavelength is swept automatically during an averaging timemore » period. With a total photon flux of 4×10 9 photons/s in the range of 30 eV to 100 eV and 1×10 7 photons/s in the range of 100 eV to 200 eV, the resulting quasi-supercontinuum XUV source is suited for applications such as XUV coherence tomography (XCT) or near-edge absorption fine structure spectroscopy (NEXAFS).« less

Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation

DOE PAGES

Wünsche, Martin; Fuchs, Silvio; Aull, Stefan; ...

2017-03-16

A quasi-supercontinuum source in the extreme ultraviolet (XUV) is demonstrated using a table-top femtosecond laser and a tunable optical parametric amplifier (OPA) as a driver for high-harmonic generation (HHG). The harmonic radiation, which is usually a comb of odd multiples of the fundamental frequency, is generated by near-infrared (NIR) laser pulses from the OPA. A quasi-continuous XUV spectrum in the range of 30 to 100 eV is realized by averaging over multiple harmonic comb spectra with slightly different fundamental frequencies and thus different spectral spacing between the individual harmonics. The driving laser wavelength is swept automatically during an averaging timemore » period. With a total photon flux of 4×10 9 photons/s in the range of 30 eV to 100 eV and 1×10 7 photons/s in the range of 100 eV to 200 eV, the resulting quasi-supercontinuum XUV source is suited for applications such as XUV coherence tomography (XCT) or near-edge absorption fine structure spectroscopy (NEXAFS).« less

On the local well-posedness of Lovelock and Horndeski theories

NASA Astrophysics Data System (ADS)

Papallo, Giuseppe; Reall, Harvey S.

2017-08-01

We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes "k-essence" like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields.

On the role of covariance information for GRACE K-band observations in the Celestial Mechanics Approach

NASA Astrophysics Data System (ADS)

Bentel, Katrin; Meyer, Ulrich; Arnold, Daniel; Jean, Yoomin; Jäggi, Adrian

2017-04-01

The Astronomical Institute at the University of Bern (AIUB) derives static and time-variable gravity fields by means of the Celestial Mechanics Approach (CMA) from GRACE (level 1B) data. This approach makes use of the close link between orbit and gravity field determination. GPS-derived kinematic GRACE orbit positions, inter-satellite K-band observations, which are the core observations of GRACE, and accelerometer data are combined to rigorously estimate orbit and spherical harmonic gravity field coefficients in one adjustment step. Pseudo-stochastic orbit parameters are set up to absorb unmodeled noise. The K-band range measurements in along-track direction lead to a much higher correlation of the observations in this direction compared to the other directions and thus, to north-south stripes in the unconstrained gravity field solutions, so-called correlated errors. By using a full covariance matrix for the K-band observations the correlation can be taken into account. One possibility is to derive correlation information from post-processing K-band residuals. This is then used in a second iteration step to derive an improved gravity field solution. We study the effects of pre-defined covariance matrices and residual-derived covariance matrices on the final gravity field product with the CMA.

The visual representations of motion and of gravity are functionally independent: Evidence of a differential effect of smooth pursuit eye movements.

PubMed

De Sá Teixeira, Nuno Alexandre

2016-09-01

The memory for the final position of a moving object which suddenly disappears has been found to be displaced forward, in the direction of motion, and downwards, in the direction of gravity. These phenomena were coined, respectively, Representational Momentum and Representational Gravity. Although both these and similar effects have been systematically linked with the functioning of internal representations of physical variables (e.g. momentum and gravity), serious doubts have been raised for a cognitively based interpretation, favouring instead a major role of oculomotor and perceptual factors which, more often than not, were left uncontrolled and even ignored. The present work aims to determine the degree to which Representational Momentum and Representational Gravity are epiphenomenal to smooth pursuit eye movements. Observers were required to indicate the offset locations of targets moving along systematically varied directions after a variable imposed retention interval. Each participant completed the task twice, varying the eye movements' instructions: gaze was either constrained or left free to track the targets. A Fourier decomposition analysis of the localization responses was used to disentangle both phenomena. The results show unambiguously that constraining eye movements significantly eliminates the harmonic components which index Representational Momentum, but have no effect on Representational Gravity or its time course. The found outcomes offer promising prospects for the study of the visual representation of gravity and its neurological substrates.

The effects of patch-potentials on the gravity probe B gyroscopes.

PubMed

Buchman, S; Turneaure, J P

2011-07-01

Gravity probe B (GP-B) was designed to measure the geodetic and frame dragging precessions of gyroscopes in the near field of the Earth using a drag-free satellite in a 642 km polar orbit. Four electrostatically suspended cryogenic gyroscopes were designed to measure the precession of the local inertial frame of reference with a disturbance drift of about 0.1 marc sec/yr-0.2 marc sec/yr. A number of unexpected gyro disturbance effects were observed during the mission: spin-speed and polhode damping, misalignment and roll-polhode resonance torques, forces acting on the gyroscopes, and anomalies in the measurement of the gyro potentials. We show that all these effects except possibly polhode damping can be accounted for by electrostatic patch potentials on both the gyro rotors and the gyro housing suspension and ground-plane electrodes. We express the rotor and housing patch potentials as expansions in spherical harmonics Y(l,m)(θ,φ). Our analysis demonstrates that these disturbance effects are approximated by a power spectrum for the coefficients of the spherical harmonics of the form V(0)(2)/l(r) with V(0) ≈ 100 mV and r ≈ 1.7.

High-resolution gravity field modeling using GRAIL mission data

NASA Astrophysics Data System (ADS)

Lemoine, F. G.; Goossens, S. J.; Sabaka, T. J.; Nicholas, J. B.; Mazarico, E.; Rowlands, D. D.; Neumann, G. A.; Loomis, B.; Chinn, D. S.; Smith, D. E.; Zuber, M. T.

2015-12-01

The Gravity Recovery and Interior Laboratory (GRAIL) spacecraft were designed to map the structure of the Moon through high-precision global gravity mapping. The mission consisted of two spacecraft with Ka-band inter-satellite tracking complemented by tracking from Earth. The mission had two phases: a primary mapping mission from March 1 until May 29, 2012 at an average altitude of 50 km, and an extended mission from August 30 until December 14, 2012, with an average altitude of 23 km before November 18, and 20 and 11 km after. High-resolution gravity field models using both these data sets have been estimated, with the current resolution being degree and order 1080 in spherical harmonics. Here, we focus on aspects of the analysis of the GRAIL data: we investigate eclipse modeling, the influence of empirical accelerations on the results, and we discuss the inversion of large-scale systems. In addition to global models we also estimated local gravity adjustments in areas of particular interest such as Mare Orientale, the south pole area, and the farside. We investigate the use of Ka-band Range Rate (KBRR) data versus numerical derivatives of KBRR data, and show that the latter have the capability to locally improve correlations with topography.

Millimeter-wave active probe

DOEpatents

Majidi-Ahy, Gholamreza; Bloom, David M.

1991-01-01

A millimeter-wave active probe for use in injecting signals with frequencies above 50GHz to millimeter-wave and ultrafast devices and integrated circuits including a substrate upon which a frequency multiplier consisting of filter sections and impedance matching sections are fabricated in uniplanar transmission line format. A coaxial input and uniplanar 50 ohm transmission line couple an approximately 20 GHz input signal to a low pass filter which rolls off at approximately 25 GHz. An input impedance matching section couples the energy from the low pass filter to a pair of matched, antiparallel beam lead diodes. These diodes generate odd-numberd harmonics which are coupled out of the diodes by an output impedance matching network and bandpass filter which suppresses the fundamental and third harmonics and selects the fifth harmonic for presentation at an output.

An Empirical Method for Determining the Lunar Gravity Field. Ph.D. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Ferrari, A. J.

1971-01-01

A method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Observation of gravity waves during the extreme tornado outbreak of 3 April 1974

NASA Technical Reports Server (NTRS)

Hung, R. J.; Phan, T.; Smith, R. E.

1978-01-01

A continuous wave-spectrum high-frequency radiowave Doppler sounder array was used to observe upper-atmospheric disturbances during an extreme tornado outbreak. The observations indicated that gravity waves with two harmonic wave periods were detected at the F-region ionospheric height. Using a group ray path computational technique, the observed gravity waves were traced in order to locate potential sources. The signals were apparently excited 1-3 hours before tornado touchdown. Reverse ray tracing indicated that the wave source was located at the aurora zone with a Kp index of 6 at the time of wave excitation. The summation of the 24-hour Kp index for the day was 36. The results agree with existing theories (Testud, 1970; Titheridge, 1971; Kato, 1976) for the excitation of large-scale traveling ionospheric disturbances associated with geomagnetic activity in the aurora zone.

Comparison of Polar Motion Excitation Series Derived from GRACE and from Analyses of Geophysical Fluids

NASA Technical Reports Server (NTRS)

Nastula, J.; Ponte, R. M.; Salstein, D. A.

2007-01-01

Three sets of degree-2, order-1 harmonics of the gravity field, derived from the Gravity Recovery and Climate Experiment (GRACE) data processed at the Center for Space Research (CSR), Jet Propulsion Laboratory (JPL) and GeoforschungsZentrum (GFZ), are used to compute polar motion excitation functions X1 and X2. The GFZ and JPL excitations and the CSR X2, excitation compare generally well with geodetically observed excitation after removal of effects of oceanic currents and atmospheric winds. The agreement considerably exceeds that from previous GRACE data releases. For the JPL series, levels of correlation with the geodetic observations and the variance explained are comparable to, but still lower than, those obtained independently from available models and analyses of the atmosphere, ocean, and land hydrology. Improvements in data quality of gravity missions are still needed to deliver even tighter constraints on mass-related excitation of polar motion.

Comparison of polar motion excitation series derived from GRACE and from analyses of geophysical fluids

NASA Astrophysics Data System (ADS)

Nastula, J.; Ponte, R. M.; Salstein, D. A.

2007-06-01

Three sets of degree-2, order-1 harmonics of the gravity field, derived from the Gravity Recovery and Climate Experiment (GRACE) data processed at the Center for Space Research (CSR), Jet Propulsion Laboratory (JPL) and GeoforschungsZentrum (GFZ), are used to compute polar motion excitation functions χ 1 and χ 2. The GFZ and JPL excitations and the CSR χ 2 excitation compare generally well with geodetically observed excitation after removal of effects of oceanic currents and atmospheric winds. The agreement considerably exceeds that from previous GRACE data releases. For the JPL series, levels of correlation with the geodetic observations and the variance explained are comparable to, but still lower than, those obtained independently from available models and analyses of the atmosphere, ocean, and land hydrology. Improvements in data quality of gravity missions are still needed to deliver even tighter constraints on mass-related excitation of polar motion.

Bounce-harmonic Landau Damping of Plasma Waves

NASA Astrophysics Data System (ADS)

Anderegg, Francois

2015-11-01

We present measurement of plasma wave damping, spanning the temperature regimes of direct Landau damping, bounce-harmonic Landau damping, inter-species drag damping, and viscous damping. Direct Landau damping is dominant at high temperatures, but becomes negligible as v

Application of the Convolution Formalism to the Ocean Tide Potential: Results from the Gravity and Recovery and Climate Experiment (GRACE)

NASA Technical Reports Server (NTRS)

Desai, S. D.; Yuan, D. -N.

2006-01-01

A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment (GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright (1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4-5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

Assessment of the suitability of GOCE-based geoid models for the unification of the North American vertical datums

NASA Astrophysics Data System (ADS)

Amjadiparvar, Babak; Sideris, Michael

2015-04-01

Precise gravimetric geoid heights are required when the unification of vertical datums is performed using the Geodetic Boundary Value Problem (GBVP) approach. Five generations of Global Geopotential Models (GGMs) derived from Gravity field and steady-state Ocean Circulation Explorer (GOCE) observations have been computed and released so far (available via IAG's International Centre for Global Earth Models, ICGEM, http://icgem.gfz-potsdam.de/ICGEM/). The performance of many of these models with respect to geoid determination has been studied in order to select the best performing model to be used in height datum unification in North America. More specifically, Release-3, 4 and 5 of the GOCE-based global geopotential models have been evaluated using GNSS-levelling data as independent control values. Comparisons against EGM2008 show that each successive release improves upon the previous one, with Release-5 models showing an improvement over EGM2008 in Canada and CONUS between spherical harmonic degrees 100 and 210. In Alaska and Mexico, a considerable improvement over EGM2008 was brought by the Release-5 models when used up to spherical harmonic degrees of 250 and 280, respectively. The positive impact of the Release-5 models was also felt when a gravimetric geoid was computed using the GOCE-based GGMs together with gravity and topography data in Canada. This geoid model, with appropriately modified Stokes kernel between spherical harmonic degrees 190 and 260, performed better than the official Canadian gravimetric geoid model CGG2013, thus illustrating the advantages of using the latest release GOCE-based models for vertical datum unification in North America.

Properties of thermospheric gravity waves on earth, Venus and Mars

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Pesnell, W. D.

1992-01-01

A spectral model with spherical harmonics and Fourier components that can simulate atmospheric perturbations in the global geometry of a multiconstituent atmosphere is presented. The boundaries are the planetary surface where the transport velocities vanish and the exobase where molecular heat conduction and viscosity dominate. The time consuming integration of the conservation equations is reduced to computing the transfer function (TF) which describes the dynamic properties of the medium divorced from the complexities in the temporal and horizontal variations of the excitation source. Given the TF, the atmospheric response to a chosen source distribution is then obtained in short order. Theoretical studies are presented to illuminate some properties of gravity waves on earth, Venus and Mars.

Estimation of regional mass anomalies from Gravity Recovery and Climate Experiment (GRACE) over Himalayan region

NASA Astrophysics Data System (ADS)

Agrawal, R.; Singh, S. K.; Rajawat, A. S.; Ajai

2014-11-01

Time-variable gravity changes are caused by a combination of postglacial rebound, redistribution of water and snow/ice on land and as well as in the ocean. The Gravity Recovery and Climate Experiment (GRACE) satellite mission, launched in 2002, provides monthly average of the spherical harmonic co-efficient. These spherical harmonic co-efficient describe earth's gravity field with a resolution of few hundred kilometers. Time-variability of gravity field represents the change in mass over regional level with accuracies in cm in terms of Water Equivalent Height (WEH). The WEH reflects the changes in the integrated vertically store water including snow cover, surface water, ground water and soil moisture at regional scale. GRACE data are also sensitive towards interior strain variation, surface uplift and surface subsidence cover over a large area. GRACE data was extracted over the three major Indian River basins, Indus, Ganga and Brahmaputra, in the Himalayas which are perennial source of fresh water throughout the year in Northern Indian Plain. Time series analysis of the GRACE data was carried out from 2003-2012 over the study area. Trends and amplitudes of the regional mass anomalies in the region were estimated using level 3 GRACE data product with a spatial resolution at 10 by 10 grid provided by Center for Space Research (CSR), University of Texas at Austin. Indus basin has shown a subtle decreasing trend from 2003-2012 however it was observed to be statistically insignificant at 95 % confidence level. Ganga and Brahmaputra basins have shown a clear decreasing trend in WEH which was also observed to be statistically significant. The trend analysis over Ganga and Brahamputra basins have shown an average annual change of -1.28 cm and -1.06 cm in terms of WEH whereas Indus basin has shown a slight annual change of -0.07 cm. This analysis will be helpful to understand the loss of mass in terms of WEH over Indian Himalayas and will be crucial for hydrological and climate applications at regional scale.

Gravity Compensation Using EGM2008 for High-Precision Long-Term Inertial Navigation Systems

PubMed Central

Wu, Ruonan; Wu, Qiuping; Han, Fengtian; Liu, Tianyi; Hu, Peida; Li, Haixia

2016-01-01

The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs. PMID:27999351

Gravity Compensation Using EGM2008 for High-Precision Long-Term Inertial Navigation Systems.

PubMed

Wu, Ruonan; Wu, Qiuping; Han, Fengtian; Liu, Tianyi; Hu, Peida; Li, Haixia

2016-12-18

The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs.

Quantum collapse of dust shells in 2 + 1 gravity

NASA Astrophysics Data System (ADS)

Ortíz, L.; Ryan, M. P.

2007-08-01

This paper considers the quantum collapse of infinitesimally thin dust shells in 2 + 1 gravity. In 2 + 1 gravity a shell is no longer a sphere, but a ring of matter. The classical equation of motion of such shells in terms of variables defined on the shell has been considered by Peleg and Steif (Phys Rev D 51:3992, 1995), using the 2 + 1 version of the original formulation of Israel (Nuovo Cimento B 44:1, 1966), and Crisóstomo and Olea (Phys Rev D 69:104023, 2004), using canonical methods. The minisuperspace quantum problem can be reduced to that of a harmonic oscillator in terms of the curvature radius of the shell, which allows us to use well-known methods to find the motion of coherent wave packets that give the quantum collapse of the shell. Classically, as the radius of the shell falls below a certain point, a horizon forms. In the quantum problem one can define various quantities that give “indications” of horizon formation. Without a proper definition of a “horizon” in quantum gravity, these can be nothing but indications.

Changes in gravitational parameters inferred from time variable GRACE data-A case study for October 2005 Kashmir earthquake

NASA Astrophysics Data System (ADS)

Hussain, Matloob; Eshagh, Mehdi; Ahmad, Zulfiqar; Sadiq, M.; Fatolazadeh, Farzam

2016-09-01

The earth's gravity changes are attributed to the redistribution of masses within and/or on the surface of the earth, which are due to the frictional sliding, tensile cracking and/or cataclastic flow of rocks along the faults and detectable by earthquake events. Inversely, the gravity changes are useful to describe the earthquake seismicity over the active orogenic belts. The time variable gravimetric data are hardly available to the public domain. However, Gravity Recovery and Climatic Experiment (GRACE) is the only satellite mission dedicated to model the variation of the gravity field and an available source to the science community. Here, we have tried to envisage gravity changes in terms of gravity anomaly (Δg), geoid (N) and the gravity gradients over the Indo-Pak plate with emphasis upon Kashmir earthquake of October 2005. For this purpose, we engaged the spherical harmonic coefficients of monthly gravity solutions from the GRACE satellite mission, which have good coverage over the entire globe with unprecedented accuracy. We have analysed numerically the solutions after removing the hydrological signals, during August to November 2005, in terms of corresponding monthly differentials of gravity anomaly, geoid and the gradients. The regional structures like Main Mantle Thrust (MMT), Main Karakoram Thrust (MKT), Herat and Chaman faults are in closed association with topography and with gravity parameters from the GRACE gravimetry and EGM2008 model. The monthly differentials of these quantities indicate the stress accumulation in the northeast direction in the study area. Our numerical results show that the horizontal gravity gradients seem to be in good agreement with tectonic boundaries and differentials of the gravitational elements are subtle to the redistribution of rock masses and topography caused by 2005 Kashmir earthquake. Moreover, the gradients are rather more helpful for extracting the coseismic gravity signatures caused by seismicity over the area. Higher positive values of gravity components having higher terrain elevations are more vulnerable to the seismicity and lower risk of diastrophism otherwise.

Off-Resonance Acoustic Levitation Without Rotation

NASA Technical Reports Server (NTRS)

Barmatz, M. B.; Allen, J. L.

1984-01-01

Orthogonal acoustic-levitation modes excited at slightly different frequencies to control rotation. Rotation of object in square cross-section acoustic-levitation chamber stopped by detuning two orthogonal (x and y) excitation drivers in plane of square cross section. Detuning done using fundamental degenerate modes or odd harmonic modes.

Ellipsoidal Harmonic Vertical Deflections. Global and Regional Modeling of The Horizontal Derivative of The Terrestrial Garvity Field

NASA Astrophysics Data System (ADS)

Grafarend, E. W.; Ardalan, A.; Finn, G.

In terms of elliptic coordinates of Jacobi type (longitude, latitude, semi-minor axis) the horizontal derivative is computed as a linear operator acting on an ellipsoidal har- monic disturbing/incremental gravitational potential. Such disturbing potential is de- fined with respect to the Somigliana-Pizzetti Reference Potential, the potential field of a level ellipsoid, and the International Reference Ellipsoid/WGS84 or World Geode- tic Datum 2000/WGD2000. Case studies of those vertical deflections on a global as well as regional scale are presented which take advantage of SEGEN (Special Ellipsoidal Gravity Earth Normal: ellipsoidal harmonics expansion 130321 coeffi- cients: http://www.uni-stuttgart.de/gi/research/paper/coefficients/coefficients.zip) and of CENT (precise centrifugal potential)

Recent Mascon Solutions from GRACE

NASA Technical Reports Server (NTRS)

Yuan, Dah-Ning; Watkins, M. M.

2006-01-01

Mascon (mass concentration) solutions computed for entire land area of Earth with several variants from Jul. 2003 through Dec. 2005 Automated scripts developed, "pipeline" now in place. Solutions generally consistent with harmonics for large features but appear able to resolve and localize smaller features more cleanly. Greenland solutions generally consistent with areas of max ice mass loss in South, but mascons seem to clearly identify sub-regions of ice mass growth. May be amplified by mascon sensitivity and ground tracks. Irregular coverage, errors due to tides in Arctic or other leakage from nearby sources? Although mascons are technically 30+ years old, gravity/geodesy community has vastly more experience with harmonics and thus we are still learning the full advantages, limitations, and idiosyncrasies of mascons.

Global Ray Tracing Simulations of the SABER Gravity Wave Climatology

DTIC Science & Technology

2009-01-01

atmosphere , the residual temperature profiles are analyzed by a combi- nation of maximum entropy method (MEM) and harmonic analysis, thus providing the...accepted 24 February 2009; published 30 April 2009. [1] Since February 2002, the SABER (sounding of the atmosphere using broadband emission radiometry...satellite instrument has measured temperatures throughout the entire middle atmosphere . Employing the same techniques as previously used for CRISTA

Testing the gravitational inverse-square law at centimeter scales

NASA Astrophysics Data System (ADS)

Bonicalzi, Ricco

Many attempts to unify gravity with the Standard Model entail a gravitational inverse-square-law violation (ISLV) at some low level. This dissertation reports on the initial phase of a torsion-pendulum null experiment searching for such a violation in the interaction between two macroscopic bodies with a characteristic separation of 12 cm. Central to the experimental design is the special configuration of the mass distributions of both the pendulum and source mass to provide high-sensitivity to the horizontal gradient of the Laplacian of the interaction potential (a signature of ISLV), while strongly suppressing coupling through Newtonian gravity. Specifically, this design ensures that gravitational systematic effects arise only at second order in the fabrication errors of the pendulum and source mass. A key aspect of this work is the choice of the second-harmonic amplitude of pendulum oscillation as the torque observable, instead of the traditional oscillation frequency. This relatively recent torsion-pendulum method is markedly less sensitive to changes in torsion-fiber temperature and enables the ambient-temperature instrumentation of the initial phase to achieve necessary noise performance without heroic efforts to stabilize temperature. As details of the second-harmonic method have not yet been published, the presentation here dwells on a number of subtleties involved in analyzing the data. Experimental results are reported assuming a Yukawa-type interaction anomaly, where a is the strength of the Yukawa term relative to Newtonian gravity. A preliminary set of 34 data runs, each around a day in duration, produced a value of alpha = (-6.3 +/- 7.5) x 10-5. In the absence of significant systematic effects, even this interim result would have placed tighter bounds on ISLV than previously appearing in the literature. Unfortunately, an accelerated Department of Energy deadline for demolition of our Hanford laboratory facility compelled a shift of focus to the principal phase of this experiment before resolving two apparently marginal, but significant sources of systematic error. These and resolved systematic effects are discussed in the context of the second-harmonic method.

Rigorous covariance propagation of geoid errors to geodetic MDT estimates

NASA Astrophysics Data System (ADS)

Pail, R.; Albertella, A.; Fecher, T.; Savcenko, R.

2012-04-01

The mean dynamic topography (MDT) is defined as the difference between the mean sea surface (MSS) derived from satellite altimetry, averaged over several years, and the static geoid. Assuming geostrophic conditions, from the MDT the ocean surface velocities as important component of global ocean circulation can be derived from it. Due to the availability of GOCE gravity field models, for the very first time MDT can now be derived solely from satellite observations (altimetry and gravity) down to spatial length-scales of 100 km and even below. Global gravity field models, parameterized in terms of spherical harmonic coefficients, are complemented by the full variance-covariance matrix (VCM). Therefore, for the geoid component a realistic statistical error estimate is available, while the error description of the altimetric component is still an open issue and is, if at all, attacked empirically. In this study we make the attempt to perform, based on the full gravity VCM, rigorous error propagation to derived geostrophic surface velocities, thus also considering all correlations. For the definition of the static geoid we use the third release of the time-wise GOCE model, as well as the satellite-only combination model GOCO03S. In detail, we will investigate the velocity errors resulting from the geoid component in dependence of the harmonic degree, and the impact of using/no using covariances on the MDT errors and its correlations. When deriving an MDT, it is spectrally filtered to a certain maximum degree, which is usually driven by the signal content of the geoid model, by applying isotropic or non-isotropic filters. Since this filtering is acting also on the geoid component, the consistent integration of this filter process into the covariance propagation shall be performed, and its impact shall be quantified. The study will be performed for MDT estimates in specific test areas of particular oceanographic interest.

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

NASA Astrophysics Data System (ADS)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

Interaction of finite-amplitude sound with air-filled porous materials

NASA Technical Reports Server (NTRS)

Nelson, D. A.

1985-01-01

The propagation of high intensity sound waves through an air-filled porus material was studied. The material is assumed: (1) to be rigid, incompressible, and homogeneous, and (2) to be adequately described by two properties: resistivity r and porosity. The resulting wave equation is still nonlinear, however, because of the u sgn(u) term in the resistivity. The equation is solved in the frequency domain as an infinite set of coupled inhomogeneous Helmholtz equations, one for each harmonic. An approximate but analytical solution leads to predictions of excess attenuation, saturation, and phase speed reduction for the fundamental component. A more general numerical solution is used to calculate the propagation curves for the higher harmonics. The u sgn(u) nonlinearity produces a cubic distortion pattern; when the input signal is a pure tone, only odd harmonic distortion products are generated.

Flexural isostasy: Constraints from gravity and topography power spectra

NASA Astrophysics Data System (ADS)

Watts, Tony; Moore, James

2017-04-01

We have used the spherical harmonic coefficients that describe the EGM2008 gravity and topography model (Pavlis et al. 2010) to quantify the role of flexural isostasy in contributing to Earth's gravity and topography. Power spectra show that the gravity effect of the topography and its flexural compensation contributes significantly to the observed free-air gravity anomaly field for degree 33-180, which corresponds approximately to wavelengths of 220-1200 km. The best fit is for an elastic thickness of the lithosphere, Te, of 34.0±4.0 km. Smaller values of Te, under-predict while high values of Te, over-predict the observed gravity spectra. The best fit value is a global average and so it is reasonable to speculate that regions exist where Te is both lower and higher. This is confirmed in studies of selected regions such as the Hawaiian-Emperor seamount chain and the Ganges-Himalaya foreland fold and thrust belt where we show that flexural isostatic anomalies are near zero in regions where Te approaches 34 km (e.g. Hawaiian ridge) and of large amplitude in regions of lower (e.g. Emperor) and higher Te (e.g. Ganges-Himalaya). Plate flexure may be significant at higher (180-441) and lower (12-33) degrees, but topography appears either uncompensated or fully compensated at these degrees, irrespective of the actual Te. Nevertheless, all isostatic models under-predict the observed gravity spectra at degree <12 and so we interpret the low order Earth's gravity field as caused by non-isostatic processes due to dynamic motions such as those associated with mantle convection.

Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields.

PubMed

Gandikota, G; Chatain, D; Amiroudine, S; Lyubimova, T; Beysens, D

2014-01-01

The frozen-wave instability which appears at a liquid-vapor interface when a harmonic vibration is applied in a direction tangential to it has been less studied until now. The present paper reports experiments on hydrogen (H2) in order to study this instability when the temperature is varied near its critical point for various gravity levels. Close to the critical point, a liquid-vapor density difference and surface tension can be continuously varied with temperature in a scaled, universal way. The effect of gravity on the height of the frozen waves at the interface is studied by performing the experiments in a magnetic facility where effective gravity that results from the coupling of the Earth's gravity and magnetic forces can be varied. The stability diagram of the instability is obtained. The experiments show a good agreement with an inviscid model [Fluid Dyn. 21 849 (1987)], irrespective of the gravity level. It is observed in the experiments that the height of the frozen waves varies weakly with temperature and increases with a decrease in the gravity level, according to a power law with an exponent of 0.7. It is concluded that the wave height becomes of the order of the cell size as the gravity level is asymptotically decreased to zero. The interface pattern thus appears as a bandlike pattern of alternate liquid and vapor phases, a puzzling phenomenon that was observed with CO2 and H2 near their critical point in weightlessness [Acta Astron. 61 1002 (2007); Europhys. Lett. 86 16003 (2009)].

Gravity model for the North Atlantic ocean mantle: results, uncertainties and links to regional geodynamics

NASA Astrophysics Data System (ADS)

Barantsrva, O.; Artemieva, I. M.; Thybo, H.

2015-12-01

We present the results of gravity modeling for the North Atlantic region based on interpretation of GOCE gravity satellite data. First, to separate the gravity signal caused by density anomalies within the crust and the upper mantle, we subtract the lower harmonics in the gravity field, which are presumably caused by deep density structure of the Earth (the core and the lower mantle). Next, the gravity effect of the upper mantle is calculated by subtracting the gravity effect of the crustal model. Our "basic model" is constrained by a recent regional seismic model EUNAseis for the crustal structure (Artemieva and Thybo, 2013); for bathymetry and topography we use a global ETOPO1 model by NOAA. We test sensitivity of the results to different input parameters, such as bathymetry, crustal structure, and gravity field. For bathymetry, we additionally use GEBCO data; for crustal correction - a global model CRUST 1.0 (Laske, 2013); for gravity - EGM2008 (Pavlis, 2012). Sensitivity analysis shows that uncertainty in the crustal structure produces the largest deviation from "the basic model". Use of different bathymetry data has little effect on the final results, comparable to the interpolation error. The difference in mantle residual gravity models based on GOCE and EMG2008 gravity data is 5-10 mGal. The results based on two crustal models have a similar pattern, but differ significantly in amplitude (ca. 250 mGal) for the Greenland-Faroe Ridge. The results demonstrate the presence of a strong gravity and density heterogeneity in the upper mantle in the North Atlantic region. A number of mantle residual gravity anomalies are robust features, independent of the choice of model parameters. This include (i) a sharp contrast at the continent-ocean transition, (ii) positive mantle gravity anomalies associated with continental fragments (microcontinents) in the North Atlantic ocean; (iii) negative mantle gravity anomalies which mark regions with anomalous oceanic mantle and the Mid-Atlantic Ridge. To understand better a complex geodynamics mosaic in the region, we compare our results with regional geochemical data (Korenaga and Klemen, 2000), and find that residual mantle gravity anomalies are well correlated with anomalies in epsilon-Nd and iron-depletion.

Preliminary Correlations of Gravity and Topography from Mars Global Surveyor

NASA Technical Reports Server (NTRS)

Zuber, M. T.; Tyler, G. L.; Smith, D. E.; Balmino, G. S.; Johnson, G. L.; Lemoine, F. G.; Neumann, G. A.; Phillips, R. J.; Sjogren, W. L.; Solomon, S. C.

1999-01-01

The Mars Global Surveyor (MGS) spacecraft is currently in a 400-km altitude polar mapping orbit and scheduled to begin global mapping of Mars in March of 1999. Doppler tracking data collected in this Gravity Calibration Orbit prior to the nominal mapping mission combined with observations from the MGS Science Phasing Orbit in Spring - Summer 1999 and the Viking and mariner 9 orbiters has led to preliminary high resolution gravity fields. Spherical harmonic expansions have been performed to degree and order 70 and are characterized by the first high spatial resolution coverage of high latitudes. Topographic mapping by the Mars Orbiter Laser Altimeter on MGS is providing measurements of the height of the martian surface with sub-meter vertical resolution and 5-30 m absolute accuracy. Data obtained during the circular mapping phase are expected to provide the first high resolution measurements of surface heights in the southern hemisphere. The combination of gravity and topography measurements provides information on the structure of the planetary interior, i.e. the rigidity and distribution of internal density. The observations can also be used to address the mechanisms of support of surface topography. Preliminary results of correlations of gravity and topography at long planetary wavelengths will be presented and the implications for internal structure will be addressed.

Modeling and estimation of a low degree geopotential model from terrestrial gravity data

NASA Technical Reports Server (NTRS)

Pavlis, Nikolaos K.

1988-01-01

The development of appropriate modeling and adjustment procedures for the estimation of harmonic coefficients of the geopotential, from surface gravity data was studied, in order to provide an optimum way of utilizing the terrestrial gravity information in combination solutions currently developed at NASA/Goddard Space Flight Center, for use in the TOPEX/POSEIDON mission. The mathematical modeling was based on the fundamental boundary condition of the linearized Molodensky boundary value problem. Atmospheric and ellipsoidal corrections were applied to the surface anomalies. Terrestrial gravity solutions were found to be in good agreement with the satellite ones over areas which are well surveyed (gravimetrically), such as North America or Australia. However, systematic differences between the terrestrial only models and GEMT1, over extended regions in Africa, the Soviet Union, and China were found. In Africa, gravity anomaly differences on the order of 20 mgals and undulation differences on the order of 15 meters, over regions extending 2000 km in diameter, occur. Comparisons of the GEMT1 implied undulations with 32 well distributed Doppler derived undulations gave an RMS difference of 2.6 m, while corresponding comparison with undulations implied by the terrestrial solution gave RMS difference on the order of 15 m, which implies that the terrestrial data in that region are substantially in error.

Earth's isostatic gravity anomaly field: Contributions to National Geodetic Satellite Program

NASA Technical Reports Server (NTRS)

Khan, M. A.

1973-01-01

On the assumption that the compensation for the topographic load is achieved in the manner of Airy-Heiskenenan hypothesis at a compensation depth of 30 kilometers, the spherical harmonic coefficients of the isostatic reduction potential U are computed. The degree power spectra of these coefficients are compared with the power spectra of the isostatic reduction coefficients given by Uotila. Results are presented in tabular form.

Venus: mass, gravity field, atmosphere, and ionosphere as measured by the mariner 10 dual-frequency radio system.

PubMed

Howard, H T; Tyler, G L; Fjeldbo, G; Kliore, A J; Levy, G S; Brunn, D L; Dickinson, R; Edelson, R E; Martin, W L; Postal, R B; Seidel, B; Sesplaukis, T T; Shirley, D L; Stelzried, C T; Sweetnam, D N; Zygielbaum, A I; Esposito, P B; Anderson, J D; Shapiro, I I; Reasenberg, R D

1974-03-29

Analysis of the Doppler tracking data near encounter yields a value for the ratio of the mass of the sun to that of Venus of 408,523.9 +/- 1.2, which is in good agreement with prior determinations based on data from Mariner 2 and Mariner 5. Preliminary analysis indicates that the magnitudes of the fractional differences in the principal moments of inertia of Venus are no larger than 10(-4), given that the effects of gravity-field harmonics higher than the second are negligible. Additional analysis is needed to determine the influence of the higher order harmonics on this bound. Four distinct temperature inversions exist at altitudes of 56, 58, 61, and 63 kilometers. The X-band signal was much more rapidly attenuated than the S-band signal and disappeared completely at 52-kilometer altitude. The nightside ionosphere consists of two layers having a peak density of 10(4) electrons per cubic centimeter at altitudes of 140 and 120 kilometers. The dayside ionosphere has a peak density of 3 X 10(5) electrons per cubic centimeter at an altitude of 145 kilometers. The electron number density observed at higher altitudes was ten times less than that observed by Mariner 5, and no strong evidence for a well-defined plasmapause was found.

Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lan Pengfei; Lu Peixiang; Cao Wei

2007-08-15

High-order harmonic generation from asymmetric molecules is investigated, and the concept of phase-stabilized infrared ultrashort laser pulses is extended to the extreme ultraviolet regime. It is shown that the ionization symmetry in consecutive half optical cycles is broken for asymmetric molecules, and both even and odd harmonics with comparable intensity are produced. In the time domain, only one attosecond pulse is generated in each cycle of the driving field, and the carrier-envelope phases of the attosecond pulses are equal. Consequently, a clean attosecond pulse train with the same carrier-envelope phase from pulse to pulse is obtained in the extreme ultravioletmore » regime.« less

High order harmonic generation in rare gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budil, Kimberly Susan

1994-05-01

The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~10 13-10 14 W/cm 2) is focused into a dense (~10 17 particles/cm 3) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as wellmore » as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.« less

Pearson's random walk in the space of the CMB phases: Evidence for parity asymmetry

NASA Astrophysics Data System (ADS)

Hansen, M.; Frejsel, A. M.; Kim, J.; Naselsky, P.; Nesti, F.

2011-05-01

The temperature fluctuations of the cosmic microwave background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.

Two- and Three-Dimensional Probes of Parity in Primordial Gravity Waves.

PubMed

Masui, Kiyoshi Wesley; Pen, Ue-Li; Turok, Neil

2017-06-02

We show that three-dimensional information is critical to discerning the effects of parity violation in the primordial gravity-wave background. If present, helical gravity waves induce parity-violating correlations in the cosmic microwave background (CMB) between parity-odd polarization B modes and parity-even temperature anisotropies (T) or polarization E modes. Unfortunately, EB correlations are much weaker than would be naively expected, which we show is due to an approximate symmetry resulting from the two-dimensional nature of the CMB. The detectability of parity-violating correlations is exacerbated by the fact that the handedness of individual modes cannot be discerned in the two-dimensional CMB, leading to a noise contribution from scalar matter perturbations. In contrast, the tidal imprints of primordial gravity waves fossilized into the large-scale structure of the Universe are a three-dimensional probe of parity violation. Using such fossils the handedness of gravity waves may be determined on a mode-by-mode basis, permitting future surveys to probe helicity at the percent level if the amplitude of primordial gravity waves is near current observational upper limits.

Odd harmonics-enhanced supercontinuum in bulk solid-state dielectric medium.

PubMed

Garejev, N; Jukna, V; Tamošauskas, G; Veličkė, M; Šuminas, R; Couairon, A; Dubietis, A

2016-07-25

We report on generation of ultrabroadband, more than 4 octave spanning supercontinuum in thin CaF₂ crystal, as pumped by intense mid-infrared laser pulses with central wavelength of 2.4 μm. The supercontinuum spectrum covers wavelength range from the ultraviolet to the mid-infrared and its short wavelength side is strongly enhanced by cascaded generation of third, fifth and seventh harmonics. Our results capture the transition from Kerr-dominated to plasma-dominated filamentation regime and uncover that in the latter the spectral superbroadening originates from dramatic plasma-induced compression of the driving pulse, which in turn induces broadening of the harmonics spectra due to cross-phase modulation effects. The experimental measurements are backed up by the numerical simulations based on a nonparaxial unidirectional propagation equation for the electric field of the pulse, which accounts for the cubic nonlinearity-induced effects, and which reproduce the experimental data in great detail.

Odd Harmonics in Exoplanet Photometry: Weather or Artifact?

NASA Astrophysics Data System (ADS)

Chayes, Victoria; Cowan, Nicholas; Bouffard, Élie; Haggard, Hal

2017-01-01

In the Fourier decomposition of light curves of exoplanets observed by the Kepler mission, one expects to see power in the first mode, from the planet orbiting the star, and the second mode, from ellipsoidal variations. Observations of power in the third mode of planets such as HAT-P-7b and Kepler-13Ab are as of yet unexplained. Using a spherical harmonic basis we analyze planet maps to find their corresponding light curves and show that no planet observed edge-on can produce these third harmonics with either reflected light or thermal emissions. Further numerical and analytic calculations put upper bounds on the power in the third mode that can be produced by planets not transiting perfectly edge-on, or with time-variable maps. We find the expected order of magnitude of these contributions to be at most two orders of magnitude below the first harmonic. The North-South asymmetric features or time-variable maps that could produce such harmonics would suggest exoplanetary weather if observed. However, more careful analysis of tidal effects on the stars of HAT-P-7b and Kepler-13Ab suggest that these particular harmonics are stellar in origin. Élie Bouffard was supported by an iREx summer internship. We thank the International Space Science Institute in Bern, Switzerland, for hosting the Exo-Cartography workshop series.

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Lateral density anomalies and the earth's gravitational field

NASA Technical Reports Server (NTRS)

Lowrey, B. E.

1978-01-01

The interpretation of gravity is valuable for understanding lithospheric plate motion and mantle convection. Postulated models of anomalous mass distributions in the earth and the observed geopotential as expressed in the spherical harmonic expansion are compared. In particular, models of the anomalous density as a function of radius are found which can closely match the average magnitude of the spherical harmonic coefficients of a degree. These models include: (1) a two-component model consisting of an anomalous layer at 200 km depth (below the earth's surface) and at 1500 km depth (2) a two-component model where the upper component is distributed in the region between 1000 and 2800 km depth, and(3) a model with density anomalies which continuously increase with depth more than an order of magnitude.

High-harmonic generation by field enhanced femtosecond pulses in metal-sapphire nanostructure

PubMed Central

Han, Seunghwoi; Kim, Hyunwoong; Kim, Yong Woo; Kim, Young-Jin; Kim, Seungchul; Park, In-Yong; Kim, Seung-Woo

2016-01-01

Plasmonic high-harmonic generation (HHG) drew attention as a means of producing coherent extreme ultraviolet (EUV) radiation by taking advantage of field enhancement occurring in metallic nanostructures. Here a metal-sapphire nanostructure is devised to provide a solid tip as the HHG emitter, replacing commonly used gaseous atoms. The fabricated solid tip is made of monocrystalline sapphire surrounded by a gold thin-film layer, and intended to produce EUV harmonics by the inter- and intra-band oscillations of electrons driven by the incident laser. The metal-sapphire nanostructure enhances the incident laser field by means of surface plasmon polaritons, triggering HHG directly from moderate femtosecond pulses of ∼0.1 TW cm−2 intensities. The measured EUV spectra exhibit odd-order harmonics up to ∼60 nm wavelengths without the plasma atomic lines typically seen when using gaseous atoms as the HHG emitter. This experimental outcome confirms that the plasmonic HHG approach is a promising way to realize coherent EUV sources for nano-scale near-field applications in spectroscopy, microscopy, lithography and atto-second physics. PMID:27721374

Time-Variable Gravity Signal due to Extratropic Pacific Water Mass Redistribution

NASA Technical Reports Server (NTRS)

Chao, B. F.; Boy, J. -P.; Cox, C. M.; Au, A. Y.

2003-01-01

Using the satellite-laser-ranging (SLR) data, Cox and Chao [2002] reported the detection of a large post-1998 anomaly (in the form of a positive jump) in the time series of Earth s lowest-degree gravity harmonic 52, or the dynamic oblateness. Among several groups now examining the mass redistribution in the global geophysical fluids in search of the cause(s), we report here a temporally coinciding anomalies found in the extratropic north + south Pacific basins. Clearly seen in the leading EOFPC mode for extratropic Pacific, these anomalies occurred in sea-surface height, sea-surface temperature, and temperature- and salinity-depth profiles. We based our analysis on two different data sources: TOPEX/Poseidon altimetry, and the ECCO ocean general circulation model output assimilating T/P data. The magnitude of these changes, when converted to equivalent J2 change, appears to be a few times too small to explain the observed J2 directly. These findings, and the fact that the anomalies occurred following the strong 1997-98 El Nino, suggest strong geophysical connection of the interannual-to-decadal variation of 52 with the Pacific Decadal Oscillation (PDO) and the ultimate global-change processes that cause PDO. More work is underway, and additional independent data sources are examined, paying close attention to the fact that the J2 anomaly has been reversing back to normal since 2001. These include: (1) cryospheric contributions (melting of glaciers and ice sheets); (2) land hydrological contributions; (3) polar sea influences ( e g , via deep flow); (4) fluid flow in Earth's core; (5) time-variable gravity signals from SLR in higher harmonic degree/order, including J3,J4, (2,1), and (2,2) coefficients, considering their lower signal-to-noise ratios; (6) Earth rotation data in terms of length-of-day and polar motion.

Derivation of gravity wave intrinsic parameters and vertical wavelength using a single scanning OH(3-1) airglow spectrometer

NASA Astrophysics Data System (ADS)

Wüst, Sabine; Offenwanger, Thomas; Schmidt, Carsten; Bittner, Michael; Jacobi, Christoph; Stober, Gunter; Yee, Jeng-Hwa; Mlynczak, Martin G.; Russell, James M., III

2018-05-01

For the first time, we present an approach to derive zonal, meridional, and vertical wavelengths as well as periods of gravity waves based on only one OH* spectrometer, addressing one vibrational-rotational transition. Knowledge of these parameters is a precondition for the calculation of further information, such as the wave group velocity vector.OH(3-1) spectrometer measurements allow the analysis of gravity wave ground-based periods but spatial information cannot necessarily be deduced. We use a scanning spectrometer and harmonic analysis to derive horizontal wavelengths at the mesopause altitude above Oberpfaffenhofen (48.09° N, 11.28° E), Germany for 22 nights in 2015. Based on the approximation of the dispersion relation for gravity waves of low and medium frequencies and additional horizontal wind information, we calculate vertical wavelengths. The mesopause wind measurements nearest to Oberpfaffenhofen are conducted at Collm (51.30° N, 13.02° E), Germany, ca. 380 km northeast of Oberpfaffenhofen, by a meteor radar.In order to compare our results, vertical temperature profiles of TIMED-SABER (thermosphere ionosphere mesosphere energetics dynamics, sounding of the atmosphere using broadband emission radiometry) overpasses are analysed with respect to the dominating vertical wavelength.

Local Lunar Gravity Field Analysis over the South Pole-aitken Basin from SELENE Farside Tracking Data

NASA Technical Reports Server (NTRS)

Goossens, Sander Johannes; Ishihara, Yoshiaki; Matsumoto, Koji; Sasaki, Sho

2012-01-01

We present a method with which we determined the local lunar gravity field model over the South Pole-Aitken (SPA) basin on the farside of the Moon by estimating adjustments to a global lunar gravity field model using SELENE tracking data. Our adjustments are expressed in localized functions concentrated over the SPA region in a spherical cap with a radius of 45deg centered at (191.1 deg E, 53.2 deg S), and the resolution is equivalent to a 150th degree and order spherical harmonics expansion. The new solution over SPA was used in several applications of geophysical analysis. It shows an increased correlation with high-resolution lunar topography in the frequency band l = 40-70, and admittance values are slightly different and more leveled when compared to other, global gravity field models using the same data. The adjustments expressed in free-air anomalies and differences in Bouguer anomalies between the local solution and the a priori global solution correlate with topographic surface features. The Moho structure beneath the SPA basin is slightly modified in our solution, most notably at the southern rim of the Apollo basin and around the Zeeman crater

Time Changes of the European Gravity Field from GRACE: A Comparison with Ground Measurements from Superconducting Gravimeters and with Hydrology Model Predictions

NASA Technical Reports Server (NTRS)

Hinderer, J.; Lemoine, Frank G.; Crossley, D.; Boy, J.-P.

2004-01-01

We investigate the time-variable gravity changes in Europe retrieved from the initial GRACE monthly solutions spanning a 18 month duration from April 2002 to October 2003. Gravity anomaly maps are retrieved in Central Europe from the monthly satellite solutions we compare the fields according to various truncation levels (typically between degree 10 and 20) of the initial fields (expressed in spherical harmonics to degree 120). For these different degrees, an empirical orthogonal function (EOF) decomposition of the time-variable gravity field leads us to its main spatial and temporal characteristics. We show that the dominant signal is found to be annual with an amplitude and a phase both in agreement with predictions in Europe modeled using snow and soil-moisture variations from recent hydrology models. We compare these GRACE gravity field changes to surface gravity observations from 6 superconducting gravimeters of the GGP (Global Geodynamics Project) European sub-network, with a special attention to loading corrections. Initial results suggest that all 3 data sets (GRACE, hydrology and GGP) are responding to annual changes in near-surface water in Europe of a few microGal (at length scales of approx.1000 km) that show a high value in winter and a summer minimum. We also point out that the GRACE gravity field evolution seems to indicate that there is a trend in gravity between summer 2002 and summer 2003 which can be related to the 2003 heatwave in Europe and its hydrological consequences (drought). Despite the limited time span of our analysis and the uncertainties in retrieving a regional solution from the network of gravimeters, the calibration and validation aspects of the GRACE data processing based on the annual hydrology cycle in Europe are in progress.

Design of Superconducting Gravity Gradiometer Cryogenic System for Mars Mission

NASA Technical Reports Server (NTRS)

Li, X.; Lemoine, F. G.; Paik, H. J.; Zagarola, M.; Shirron, P. J.; Griggs, C. E.; Moody, M. V.; Han, S.-C.

2016-01-01

Measurement of a planet's gravity field provides fundamental information about the planet's mass properties. The static gravity field reveals information about the internal structure of the planet, including crustal density variations that provide information on the planet's geological history and evolution. The time variations of gravity result from the movement of mass inside the planet, on the surface, and in the atmosphere. NASA is interested in a Superconducting Gravity Gradiometer (SGG) with which to measure the gravity field of a planet from orbit. An SGG instrument is under development with the NASA PICASSO program, which will be able to resolve the Mars static gravity field to degree 200 in spherical harmonics, and the time-varying field on a monthly basis to degree 20 from a 255 x 320 km orbit. The SGG has a precision two orders of magnitude better than the electrostatic gravity gradiometer that was used on the ESA's GOCE mission. The SGG operates at the superconducting temperature lower than 6 K. This study developed a cryogenic thermal system to maintain the SGG at the design temperature in Mars orbit. The system includes fixed radiation shields, a low thermal conductivity support structure and a two-stage cryocooler. The fixed radiation shields use double aluminized polyimide to emit heat from the warm spacecraft into the deep space. The support structure uses carbon fiber reinforced plastic, which has low thermal conductivity at cryogenic temperature and very high stress. The low vibration cryocooler has two stages, of which the high temperature stage operates at 65 K and the low temperature stage works at 6 K, and the heat rejection radiator works at 300 K. The study also designed a second option with a 4-K adiabatic demagnetization refrigerator (ADR) and two-stage 10-K turbo-Brayton cooler.

Design of Superconducting Gravity Gradiometer Cryogenic System for Mars Mission

NASA Technical Reports Server (NTRS)

Li, X.; Lemoine, F. G.; Shirron, P. J.; Paik, H. J.; Griggs, C. E.; Moody, M. V.; Han, S. C.; Zagarola, M.

2016-01-01

Measurement of a planets gravity field provides fundamental information about the planets mass properties. The static gravity field reveals information about the internal structure of the planet, including crustal density variations that provide information on the planets geological history and evolution. The time variations of gravity result from the movement of mass inside the planet, on the surface, and in the atmosphere. NASA is interested in a Superconducting Gravity Gradiometer (SGG) with which to measure the gravity field of a planet from orbit. An SGG instrument is under development with the NASA PICASSO program, which will be able to resolve the Mars static gravity field to degree 200 in spherical harmonics, and the time-varying field on a monthly basis to degree 20 from a 255 x 320 km orbit. The SGG has a precision two orders of magnitude better than the electrostatic gravity gradiometer that was used on the ESAs GOCE mission. The SGG operates at the superconducting temperature lower than 6 K. This study developed a cryogenic thermal system to maintain the SGG at the design temperature in Mars orbit. The system includes fixed radiation shields, a low thermal conductivity support structure and a two-stage cryocooler. The fixed radiation shields use double aluminized polyimide to emit heat from the warm spacecraft into the deep space. The support structure uses carbon fiber reinforced plastic, which has low thermal conductivity at cryogenic temperature and very high stress. The low vibration cryocooler has two stages, of which the high temperature stage operates at 65 K and the low temperature stage works at 6 K, and the heat rejection radiator works at 300 K. The study also designed a second option with a 4-K adiabatic demagnetization refrigerator (ADR) and two-stage 10-K turbo-Brayton cooler.

Surface Gravity Data Contribution to the Puerto Rico and U.S. Virgin Islands Geoid Model

NASA Astrophysics Data System (ADS)

Li, X.; Gerhards, C.; Holmes, S. A.; Saleh, J.; Shaw, B.

2015-12-01

The Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project provides updated local gravity field information for the XGEOID15 models. In particular, its airborne gravity data in the area of Puerto Rico and U.S. Virgin Islands (PRVI) made substantial improvements (~60%) on the precision of the geoid models at the local GNSS/Leveling bench marks in the target area. Fortunately, PRVI is free of the huge systematic error in the North American Vertical Datum of 1988 (NAVD88). Thus, the airborne contribution was evaluated more realistically. In addition, the airborne data picked up more detailed gravity field information in the medium wavelength band (spherical harmonic degree 200 to 600) that are largely beyond the resolution of the current satellite missions, especially along the nearby ocean trench areas. Under this circumstance (significant airborne contributions in the medium band), local surface gravity data need to be examined more carefully than before during merging with the satellite and airborne information for local geoid improvement, especially considering the well-known systematic problems in the NGS historical gravity holdings (Saleh et al 2013 JoG). Initial tests showed that it is very important to maintain high consistency between the surface data sets and the airborne enhanced reference model. In addition, a new aggregation method (Gerhards 2014, Inverse Problems) will also be tested to optimally combine the local surface data with the reference model. The data cleaning and combining procedures in the target area will be summarized here as reference for future applications.

GOCE gravity field simulation based on actual mission scenario

NASA Astrophysics Data System (ADS)

Pail, R.; Goiginger, H.; Mayrhofer, R.; Höck, E.; Schuh, W.-D.; Brockmann, J. M.; Krasbutter, I.; Fecher, T.; Gruber, T.

2009-04-01

In the framework of the ESA-funded project "GOCE High-level Processing Facility", an operational hardware and software system for the scientific processing (Level 1B to Level 2) of GOCE data has been set up by the European GOCE Gravity Consortium EGG-C. One key component of this software system is the processing of a spherical harmonic Earth's gravity field model and the corresponding full variance-covariance matrix from the precise GOCE orbit and calibrated and corrected satellite gravity gradiometry (SGG) data. In the framework of the time-wise approach a combination of several processing strategies for the optimum exploitation of the information content of the GOCE data has been set up: The Quick-Look Gravity Field Analysis is applied to derive a fast diagnosis of the GOCE system performance and to monitor the quality of the input data. In the Core Solver processing a rigorous high-precision solution of the very large normal equation systems is derived by applying parallel processing techniques on a PC cluster. Before the availability of real GOCE data, by means of a realistic numerical case study, which is based on the actual GOCE orbit and mission scenario and simulation data stemming from the most recent ESA end-to-end simulation, the expected GOCE gravity field performance is evaluated. Results from this simulation as well as recently developed features of the software system are presented. Additionally some aspects on data combination with complementary data sources are addressed.

Harmonic Kicker RF Cavity for the Jefferson Lab Electron-Ion Collider EM Simulation, Modification, and Measurements

NASA Astrophysics Data System (ADS)

Overstreet, Sarah; Wang, Haipeng

2017-09-01

An important step in the conceptual design for the future Jefferson Lab Electron-Ion Collider (JLEIC) is the development of supporting technologies for the Energy Recovery Linac (ERL) Electron Cooling Facility. The Harmonic Radiofrequency (RF) kicker cavity is one such device that is responsible for switching electron bunches in and out of the Circulator Cooling Ring (CCR) from and to the ERL, which is a critical part of the ion cooling process. Last year, a half scale prototype of the JLEIC harmonic RF kicker model was designed with resonant frequencies to support the summation of 5 odd harmonics (95.26 MHz, 285.78 MHz, 476.30 MHz, 666.82 MHz, and 857.35 MHz); however, the asymmetry of the kicker cavity gives rise to multipole components of the electric field at the electron-beam axis of the cavity. Previous attempts to symmetrize the electric field of this asymmetrical RF cavity have been unsuccessful. The aim of this study is to modify the existing prototype for a uniform electric field across the beam pathway so that the electron bunches will experience nearly zero beam current loading. In addition to this, we have driven the unmodified cavity with the harmonic sum and used the wire stretching method for an analysis of the multipole electric field components.

Lorentz drift compensation in high harmonic generation in the soft and hard X-ray regions of the spectrum

DOE PAGES

Galloway, Benjamin R.; Popmintchev, Dimitar; Pisanty, Emilio; ...

2016-09-09

Here, we present a semi-classical study of the effects of the Lorentz force on electrons during high harmonic generation in the soft and hard X-ray regions driven by near- and mid-infrared lasers with wavelengths from 0.8 to 20 μm, and at intensities below 10 15 W/cm 2. The transverse extent of the longitudinal Lorentz drift is compared for both Gaussian focus and waveguide geometries. Both geometries exhibit a longitudinal electric field component that cancels the magnetic Lorentz drift in some regions of the focus, once each full optical cycle. We show that the Lorentz force contributes a super-Gaussian scaling whichmore » acts in addition to the dominant high harmonic flux scaling of λ -(5-6) due to quantum diffusion. We predict that the high harmonic yield will be reduced for driving wavelengths > 6 μm, and that the presence of dynamic spatial mode asymmetries results in the generation of both even and odd harmonic orders. Remarkably, we show that under realistic conditions, the recollision process can be controlled and does not shut off completely even for wavelengths >10 μm and recollision energies greater than 15 keV.« less

Weak solution concept and Galerkin's matrix for the exterior of an oblate ellipsoid of revolution in the representation of the Earth's gravity potential by buried masses

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The paper is motivated by the role of boundary value problems in Earth's gravity field studies. The discussion focuses on Neumann's problem formulated for the exterior of an oblate ellipsoid of revolution as this is considered a basis for an iteration solution of the linear gravimetric boundary value problem in the determination of the disturbing potential. The approach follows the concept of the weak solution and Galerkin's approximations are applied. This means that the solution of the problem is approximated by linear combinations of basis functions with scalar coefficients. The construction of Galerkin's matrix for basis functions generated by elementary potentials (point masses) is discussed. Ellipsoidal harmonics are used as a natural tool and the elementary potentials are expressed by means of series of ellipsoidal harmonics. The problem, however, is the summation of the series that represent the entries of Galerkin's matrix. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Therefore, the straightforward application of series of ellipsoidal harmonics is complemented by deeper relations contained in the theory of ordinary differential equations of second order and in the theory of Legendre's functions. Subsequently, also hypergeometric functions and series are used. Moreover, within some approximations the entries are split into parts. Some of the resulting series may be summed relatively easily, apart from technical tricks. For the remaining series the summation was converted to elliptic integrals. The approach made it possible to deduce a closed (though approximate) form representation of the entries in Galerkin's matrix. The result rests on concepts and methods of mathematical analysis. In the paper it is confronted with a direct numerical approach applied for the implementation of Legendre's functions. The computation of the entries is more demanding in this case, but conceptually it avoids approximations. Finally, some specific features associated with function bases generated by elementary potentials in case the ellipsoidal solution domain are illustrated and discussed.

Leptogenesis from gravity waves in models of inflation.

PubMed

Alexander, Stephon H S; Peskin, Michael E; Sheikh-Jabbari, M M

2006-03-03

We present a new mechanism for creating the observed cosmic matter-antimatter asymmetry which satisfies all three Sakharov conditions from one common thread, gravitational waves. We generate lepton number through the gravitational anomaly in the lepton number current. The source term comes from elliptically polarized gravity waves that are produced during inflation if the inflaton field contains a CP-odd component. The amount of matter asymmetry generated in our model can be of realistic size for the parameters within the range of some inflationary scenarios and grand unified theories.

Impact of Tidal-Stream Turbines on the Generation of the Higher Tidal Harmonics

NASA Astrophysics Data System (ADS)

Potter, Daniel; Ilic, Suzana; Folkard, Andrew

2016-04-01

The higher tidal harmonics result from the interaction of the astronomic tides with both themselves and each other through non-linear processes. In shallower waters such as those near the coast these non-linear processes become more significant and thus, so too do the higher tidal harmonics become more significant. The interaction of the tide with tidal-stream turbines (TSTs), through thrust and drag processes will be non-linear and as such will contribute to the generation of higher tidal harmonics, thus changing the nature of the tide downstream of the turbines. The change to the tide may potentially impact on the downstream energy resource (Robins et al. 2015) and sediment transport processes (Pingree & Griffiths 1979). This paper will present analytical results, which suggest that TSTs will impact on the generation of all higher harmonics but with odd overtides being impacted more than even overtides, the most important examples of which are the M6 and M4 tides respectively, which are the first odd and even overtides of the M2 tide. Change in phase and amplitude of the M6 tide by TSTs will distort the tide but will not cause an asymmetry between the flood and ebb of the tide. Change in the phase and amplitude of the M4 can not only distort the tide but also cause asymmetry. Hence any change to the M4 tide by the turbines is more significant, despite the magnitude of change to the M6 being greater. In order to gain a fuller understanding of the way in which TSTs change the tide downstream and the significance of any change for transport processes or energy resource, a numerical modelling study will be carried out, which will be presented in a future paper. Robins, P.E., Neill, S.P., Lewis, M. & Ward, S.L., 2015. Characterising the spatial and temporal variability of the tidal-stream energy resource over the northwest European shelf seas. Applied Energy, 147: 510-522. Pingree, R.D. & Griffiths, D.K., 1979. Sand transport paths around the British Isles resulting from M2 and M4 tidal interactions. J. Mar. Biol. Ass. U.K., 59: 497-513

Interannual Variations In the Low-Degree Components of the Geopotential derived from SLR and the Connections With Geophysical/Climatic Processes

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Cox, Christopher M.; Au, Andrew Y.

2004-01-01

Recent Satellite Laser Ranging derived long wavelength gravity time series analysis has focused to a large extent on the effects of the recent large changes in the Earth s 52, and the potential causes. However, it is difficult to determine whether there are corresponding signals in the shorter wavelength zonals from the existing SLR-derived time variable gravity results, although it appears that geophysical fluid transport is being observed. For example, the recovered J3 time series shows remarkable agreement with NCEP-derived estimates of atmospheric gravity variations. Likewise, some of the non-zonal spherical harmonic coefficient series have significant interannual signal that appears to be related to mass transport. The non-zonal degree 2 terms show reasonable correlation with atmospheric signals, as well as climatic effects such as El Nino Southern Oscillation. While the formal uncertainty of these terms is significantly higher than that for J2, it is also clear that there is useful signal to be extracted. Consequently, the SLR time series is being reprocessed to improve the time variable gravity field recovery. We will present recent updates on the J2 evolution, as well as a look at other components of the interannual variations of the gravity field, complete through degree 4, and possible geophysical and climatic causes.

Combination of geodetic measurements by means of a multi-resolution representation

NASA Astrophysics Data System (ADS)

Goebel, G.; Schmidt, M. G.; Börger, K.; List, H.; Bosch, W.

2010-12-01

Recent and in particular current satellite gravity missions provide important contributions for global Earth gravity models, and these global models can be refined by airborne and terrestrial gravity observations. The most common representation of a gravity field model in terms of spherical harmonics has the disadvantages that it is difficult to represent small spatial details and cannot handle data gaps appropriately. An adequate modeling using a multi-resolution representation (MRP) is necessary in order to exploit the highest degree of information out of all these mentioned measurements. The MRP provides a simple hierarchical framework for identifying the properties of a signal. The procedure starts from the measurements, performs the decomposition into frequency-dependent detail signals by applying a pyramidal algorithm and allows for data compression and filtering, i.e. data manipulations. Since different geodetic measurement types (terrestrial, airborne, spaceborne) cover different parts of the frequency spectrum, it seems reasonable to calculate the detail signals of the lower levels mainly from satellite data, the detail signals of medium levels mainly from airborne and the detail signals of the higher levels mainly from terrestrial data. A concept is presented how these different measurement types can be combined within the MRP. In this presentation the basic principles on strategies and concepts for the generation of MRPs will be shown. Examples of regional gravity field determination are presented.

Global Gravity Field Determination by Combination of terrestrial and Satellite Gravity Data

NASA Astrophysics Data System (ADS)

Fecher, T.; Pail, R.; Gruber, T.

2011-12-01

A multitude of impressive results document the success of the satellite gravity field mission GOCE with a wide field of applications in geodesy, geophysics and oceanography. The high performance of GOCE gravity field models can be further improved by combination with GRACE data, which is contributing the long wavelength signal content of the gravity field with very high accuracy. An example for such a consistent combination of satellite gravity data are the satellite-only models GOCO01S and GOCO02S. However, only the further combination with terrestrial and altimetric gravity data enables to expand gravity field models up to very high spherical harmonic degrees and thus to achieve a spatial resolution down to 20-30 km. First numerical studies for high-resolution global gravity field models combining GOCE, GRACE and terrestrial/altimetric data on basis of the DTU10 model have already been presented. Computations up to degree/order 600 based on full normal equations systems to preserve the full variance-covariance information, which results mainly from different weights of individual terrestrial/altimetric data sets, have been successfully performed. We could show that such large normal equations systems (degree/order 600 corresponds to a memory demand of almost 1TByte), representing an immense computational challenge as computation time and memory requirements put high demand on computational resources, can be handled. The DTU10 model includes gravity anomalies computed from the global model EGM08 in continental areas. Therefore, the main focus of this presentation lies on the computation of high-resolution combined gravity field models based on real terrestrial gravity anomaly data sets. This is a challenge due to the inconsistency of these data sets, including also systematic error components, but a further step to a real independent gravity field model. This contribution will present our recent developments and progress by using independent data sets at certain land areas, which are combined with DTU10 in the ocean areas, as well as satellite gravity data. Investigations have been made concerning the preparation and optimum weighting of the different data sources. The results, which should be a major step towards a GOCO-C model, will be validated using external gravity field data and by applying different validation methods.

Recommended reference figures for geophysics and geodesy

NASA Technical Reports Server (NTRS)

Khan, M. A.; Okeefe, J. A.

1973-01-01

Specific reference figures are recommended for consistent use in geophysics and geodesy. The selection of appropriate reference figure for geophysical studies suggests a relationship between the Antarctic negative gravity anomaly and the great shrinkage of the Antarctic ice cap about 4-5 million years ago. The depression of the south polar regions relative to the north polar regions makes the Southern Hemisphere flatter than the Northern Hemisphere, thus producing the third harmonic (pear-shaped) contribution to the earth's figure.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

Global mean dynamic topography based on GOCE data and Wiener filters

NASA Astrophysics Data System (ADS)

Gilardoni, Maddalena; Reguzzoni, Mirko; Albertella, Alberta

2015-04-01

A mean dynamic ocean topography (MDT) has been computed by using a GOCE-only gravity model and a given mean sea surface (MSS) obtained from satellite altimetry. Since the used gravity model, i.e. the fifth release of the time-wise solution covering the full mission lifetime, is truncated at a maximum harmonic degree of 280, the obtained MDT has to be consistently filtered. This has been done globally by using the spherical harmonic representation and following a Wiener minimization principle. This global filtering approach is convenient from the computational point of view but requires to have MDT values all over the Earth surface and therefore to fill the continents with fictitious data. The main improvements with respect to the already presented results are in the MDT filling procedure (to guarantee that the global signal has the same covariance of the one over the oceans), in the error modelling of the input MSS and in the error estimation of the filtered MDT and of the corresponding geostrophic velocities. The impact of GOCE data in the ocean circulation global modelling has been assessed by comparing the pattern of the obtained geostrophic currents with those computed by using EGM2008. Comparisons with independent circulation data based on drifters and other MDT models have been also performed with the aim of evaluating the accuracy of the obtained results.

Inter-comparison of GRACE data over India

NASA Astrophysics Data System (ADS)

Banerjee, Chandan; Kumar, D. Nagesh

2016-05-01

The advent of satellite remote sensing and its use in hydrology has facilitated a huge leap in the understanding of the various water resources, its interaction with ecological systems and anthropogenic creations. Recently, NASA and German Aerospace Research Agency-DLR launched the Gravity Recovery and Climate Experiment (GRACE) satellite mission consisting of two satellites. They measure the time varying gravity which gives changes in the distribution of mass on the surface of the earth which after removing atmospheric and oceanic effects is majorly caused by changes in Terrestrial Water Storage (TWS) changes. GRACE data is generally available as spherical harmonic coefficients, which is difficult for hydrologists to understand and interpret. JPL's TELLUS website is now providing gridded global data set in the form of mass anomaly derived from the Level-2 data sets of spherical harmonic coefficients of 3 sources, viz. CSR, GFZ and JPL. Before using these data sets for solving hydrological problems, it is important to understand the differences and similarities between these data sets as direct calibration of GRACE data is not possible. In this study we do an inter-comparison of the Level-3 Release 05 data sets over India. We compare the data sets using Pearson, Spearman and Kendall correlation. CSR and GFZ data sets appear to be closest to each other whereas JPL and GFZ data sets are most different from each other.

Spectral analysis of the Earth's topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000

NASA Astrophysics Data System (ADS)

Rexer, Moritz; Hirt, Christian

2015-09-01

Classical degree variance models (such as Kaula's rule or the Tscherning-Rapp model) often rely on low-resolution gravity data and so are subject to extrapolation when used to describe the decay of the gravity field at short spatial scales. This paper presents a new degree variance model based on the recently published GGMplus near-global land areas 220 m resolution gravity maps (Geophys Res Lett 40(16):4279-4283, 2013). We investigate and use a 2D-DFT (discrete Fourier transform) approach to transform GGMplus gravity grids into degree variances. The method is described in detail and its approximation errors are studied using closed-loop experiments. Focus is placed on tiling, azimuth averaging, and windowing effects in the 2D-DFT method and on analytical fitting of degree variances. Approximation errors of the 2D-DFT procedure on the (spherical harmonic) degree variance are found to be at the 10-20 % level. The importance of the reference surface (sphere, ellipsoid or topography) of the gravity data for correct interpretation of degree variance spectra is highlighted. The effect of the underlying mass arrangement (spherical or ellipsoidal approximation) on the degree variances is found to be crucial at short spatial scales. A rule-of-thumb for transformation of spectra between spherical and ellipsoidal approximation is derived. Application of the 2D-DFT on GGMplus gravity maps yields a new degree variance model to degree 90,000. The model is supported by GRACE, GOCE, EGM2008 and forward-modelled gravity at 3 billion land points over all land areas within the SRTM data coverage and provides gravity signal variances at the surface of the topography. The model yields omission errors of 9 mGal for gravity (1.5 cm for geoid effects) at scales of 10 km, 4 mGal (1 mm) at 2-km scales, and 2 mGal (0.2 mm) at 1-km scales.

Source Parameter Inversion for Recent Great Earthquakes from a Decade-long Observation of Global Gravity Fields

NASA Technical Reports Server (NTRS)

Han, Shin-Chan; Riva, Ricccardo; Sauber, Jeanne; Okal, Emile

2013-01-01

We quantify gravity changes after great earthquakes present within the 10 year long time series of monthly Gravity Recovery and Climate Experiment (GRACE) gravity fields. Using spherical harmonic normal-mode formulation, the respective source parameters of moment tensor and double-couple were estimated. For the 2004 Sumatra-Andaman earthquake, the gravity data indicate a composite moment of 1.2x10(exp 23)Nm with a dip of 10deg, in agreement with the estimate obtained at ultralong seismic periods. For the 2010 Maule earthquake, the GRACE solutions range from 2.0 to 2.7x10(exp 22)Nm for dips of 12deg-24deg and centroid depths within the lower crust. For the 2011 Tohoku-Oki earthquake, the estimated scalar moments range from 4.1 to 6.1x10(exp 22)Nm, with dips of 9deg-19deg and centroid depths within the lower crust. For the 2012 Indian Ocean strike-slip earthquakes, the gravity data delineate a composite moment of 1.9x10(exp 22)Nm regardless of the centroid depth, comparing favorably with the total moment of the main ruptures and aftershocks. The smallest event we successfully analyzed with GRACE was the 2007 Bengkulu earthquake with M(sub 0) approx. 5.0x10(exp 21)Nm. We found that the gravity data constrain the focal mechanism with the centroid only within the upper and lower crustal layers for thrust events. Deeper sources (i.e., in the upper mantle) could not reproduce the gravity observation as the larger rigidity and bulk modulus at mantle depths inhibit the interior from changing its volume, thus reducing the negative gravity component. Focal mechanisms and seismic moments obtained in this study represent the behavior of the sources on temporal and spatial scales exceeding the seismic and geodetic spectrum.

Mercury's gravity field, tidal Love number k2, and spin axis orientation revealed with MESSENGER radio tracking data

NASA Astrophysics Data System (ADS)

Verma, A. K.; Margot, J. L.

2015-12-01

We are conducting an independent analysis of two-way Doppler and two-way range radio tracking data from the MESSENGER spacecraft in orbit around Mercury from 2011 to 2015. Our goals are to estimate Mercury's gravity field and to obtain independent estimates of the tidal Love number k2 and spin axis orientation. Our gravity field solution reproduces existing values with high fidelity, and prospects for recovery of the other quantities are excellent. The tidal Love number k2 provides powerful constraints on interior models of Mercury, including the mechanical properties of the mantle and the possibility of a solid FeS layer at the top of the core. Current gravity analyses cannot rule out a wide range of values (k2=43-0.50) and a variety of plausible interior models. We are seeking an independent estimate of tidal Love number k2 with improved errors to further constrain these models. Existing gravity-based solutions for Mercury's spin axis orientation differ from those of Earth-based radar and topography-based solutions. This difference may indicate an error in one of the determinations, or a real difference between the orientations about which the gravity field and the crust rotate, which can exist in a variety of plausible configuration. Securing an independent estimate of the spin axis orientation is vital because this quantity has a profound impact on the determination of the moment of inertia and interior models. We have derived a spherical harmonic solution of the gravity field to degree and order 40 as well as estimates of the tidal Love number k2 and spin axis orientation.

Mercury’s gravity field, tidal Love number k2, and spin axis orientation revealed with MESSENGER radio tracking data

NASA Astrophysics Data System (ADS)

Verma, Ashok Kumar; Margot, Jean-Luc

2015-11-01

We are conducting an independent analysis of two-way Doppler and two-way range radio tracking data from the MESSENGER spacecraft in orbit around Mercury from 2011 to 2015. Our goals are to estimate Mercury’s gravity field and to obtain independent estimates of the tidal Love number k2 and spin axis orientation. Our gravity field solution reproduces existing values with high fidelity, and prospects for recovery of the other quantities are excellent.The tidal Love number k2 provides powerful constraints on interior models of Mercury, including the mechanical properties of the mantle and the possibility of a solid FeS layer at the top of the core. Current gravity analyses cannot rule out a wide range of values (k2=43-0.50) and a variety of plausible interior models. We are seeking an independent estimate of tidal Love number k2 with improved errors to further constrain these models.Existing gravity-based solutions for Mercury's spin axis orientation differ from those of Earth-based radar and topography-based solutions. This difference may indicate an error in one of the determinations, or a real difference between the orientations about which the gravity field and the crust rotate, which can exist in a variety of plausible configuration. Securing an independent estimate of the spin axis orientation is vital because this quantity has a profound impact on the determination of the moment of inertia and interior models.We have derived a spherical harmonic solution of the gravity field to degree and order 40 as well as estimates of the tidal Love number k2 and spin axis orientation

Power laws for gravity and topography of Solar System bodies

NASA Astrophysics Data System (ADS)

Ermakov, A.; Park, R. S.; Bills, B. G.

2017-12-01

When a spacecraft visits a planetary body, it is useful to be able to predict its gravitational and topographic properties. This knowledge is important for determining the level of perturbations in spacecraft's motion as well as for planning the observation campaign. It has been known for the Earth that the power spectrum of gravity follows a power law, also known as the Kaula rule (Kaula, 1963; Rapp, 1989). A similar rule was derived for topography (Vening-Meinesz, 1951). The goal of this paper is to generalize the power law that can characterize the gravity and topography power spectra for bodies across a wide range of size. We have analyzed shape power spectra of the bodies that have either global shape and gravity field measured. These bodies span across five orders of magnitude in their radii and surface gravities and include terrestrial planets, icy moons and minor bodies. We have found that despite having different internal structure, composition and mechanical properties, the topography power spectrum of these bodies' shapes can be modeled with a similar power law rescaled by the surface gravity. Having empirically found a power law for topography, we can map it to a gravity power law. Special care should be taken for low-degree harmonic coefficients due to potential isostatic compensation. For minor bodies, uniform density can be assumed. The gravity coefficients are a linear function of the shape coefficients for close-to-spherical bodoes. In this case, the power law for gravity will be steeper than the power law of topography due to the factor (2n+1) in the gravity expansion (e.g. Eq. 10 in Wieczorek & Phillips, 1998). Higher powers of topography must be retained for irregularly shaped bodies, which breaks the linearity. Therefore, we propose the following procedure to derive an a priori constraint for gravity. First, a surface gravity needs to be determined assuming typical density for the relevant class of bodies. Second, the scaling coefficient of the power law can be found by rescaling the values known for other bodies. Third, an ensemble of synthetic shapes that follow the defined power law can be generated and gravity-from-shape can be found. The averaged power spectrum can be used as an a priori constraint for the gravity field and variance of power can be computed for individual degrees.

New Mars free-air and Bouguer gravity: Correlation with topography, geology and large impact basins

NASA Technical Reports Server (NTRS)

Frey, Herbert; Bills, Bruce G.; Kiefer, Walter S.; Nerem, R. Steven; Roark, James H.; Zuber, Maria T.

1993-01-01

Free-air and Bouguer gravity anomalies from a 50x50 field (MGM635), derived at the Goddard Space Flight Center, with global topography, geology, and the distribution of large impact basins was compared. The free-air gravity anomalies were derived from re-analysis of Viking Orbiter and Mariner 9 tracking data and have a spatial resolution of 250-300 km. Bouguer anomalies were calculated using a 50x50 expansion of the current Mars topography and the GSFC degree 50 geoid as the equipotential reference surface. Rotational flattening was removed using a moment of inertia of 0.365 and the corrections from Table B2 of Sleep and Phillips. Crustal density and mean density were assumed to be 2.9 and 3.93 gm/cm(sup 3). The spherical harmonic topography used has zero mean elevation, and differs from the USGS maps by about 2 km. Comparisons with global geology use a simplified map with about 1/3 the number of units on the current maps. For correlation with impact basins, the recent compilation by Schultz and Frey was used.

On estimating the basin-scale ocean circulation from satellite altimetry. Part 1: Straightforward spherical harmonic expansion

NASA Technical Reports Server (NTRS)

Tai, Chang-Kou

1988-01-01

Direct estimation of the absolute dynamic topography from satellite altimetry has been confined to the largest scales (basically the basin-scale) owing to the fact that the signal-to-noise ratio is more unfavorable everywhere else. But even for the largest scales, the results are contaminated by the orbit error and geoid uncertainties. Recently a more accurate Earth gravity model (GEM-T1) became available, providing the opportunity to examine the whole question of direct estimation under a more critical limelight. It is found that our knowledge of the Earth's gravity field has indeed improved a great deal. However, it is not yet possible to claim definitively that our knowledge of the ocean circulation has improved through direct estimation. Yet, the improvement in the gravity model has come to the point that it is no longer possible to attribute the discrepancy at the basin scales between altimetric and hydrographic results as mostly due to geoid uncertainties. A substantial part of the difference must be due to other factors; i.e., the orbit error, or the uncertainty of the hydrographically derived dynamic topography.

Internal gravity wave contributions to global sea surface variability

NASA Astrophysics Data System (ADS)

Savage, A.; Arbic, B. K.; Richman, J. G.; Shriver, J. F.; Buijsman, M. C.; Zamudio, L.; Wallcraft, A. J.; Sharma, H.

2016-02-01

High-resolution (1/12th and 1/25th degree) 41-layer simulations of the HYbrid Coordinate Ocean Model (HYCOM), forced by both atmospheric fields and the astronomical tidal potential, are used to construct global maps of sea-surface height (SSH). The HYCOM output has been separated into steric, non-steric, and total sea-surface height and the maps display variance in subtidal, tidal, and supertidal bands. Two of the global maps are of particular interest in planning for the upcoming Surface Water and Ocean Topography (SWOT) wide-swath satellite altimeter mission; (1) a map of the nonstationary tidal signal (estimated after removing the stationary tidal signal via harmonic analysis), and (2) a map of the steric supertidal contributions, which are dominated by the internal gravity wave continuum. Both of these maps display signals of order 1 cm2, the target accuracy for the SWOT mission. Therefore, both non-stationary internal tides and non-tidal internal gravity waves are likely to be important sources of "noise" that must be accurately removed before examination of lower-frequency phenomena can take place.

Gravity-gradient measurements down to approximately 100-km height by means of long-tethered satellites

NASA Technical Reports Server (NTRS)

Colombo, G.; Gaposchkin, E. M.; Grossi, M. D.; Weiffenbach, G. C.

1976-01-01

Long-tethered satellite systems for Shuttle flights would make measurements of the earth's gravitational field possible to a spatial resolution approaching 100 km. For instance, a subsatellite carrying a gravity gradiometer could be made to orbit at a height of 110 km by means of a 110-km tether tied to the Shuttle in a 220-km orbit. Even with an overall instrument sensitivity as poor as 1 Eotvos unit (e.u.), it would be possible to measure spatial wavelengths of approximately 600 to 700 km (i.e., harmonics of 80th to 70th degree). Also, a system of two satellites (one of which could be the Shuttle orbiter or one of its payloads) connected by a tether a few tens of kilometers long could provide a simple and sensitive means of detecting gravity anomalies characterized by wavelengths of a few hundred kilometers. In this system, the observable would be the mechanical tension on the tether, and a sensitivity up to 0.01 e.u. could be attained, provided the two satellites are tracked from the ground with sufficient accuracy.

Excitation of Earth Rotation Variations "Observed" by Time-Variable Gravity

NASA Technical Reports Server (NTRS)

Chao, Ben F.; Cox, C. M.

2005-01-01

Time variable gravity measurements have been made over the past two decades using the space geodetic technique of satellite laser ranging, and more recently by the GRACE satellite mission with improved spatial resolutions. The degree-2 harmonic components of the time-variable gravity contain important information about the Earth s length-of-day and polar motion excitation functions, in a way independent to the traditional "direct" Earth rotation measurements made by, for example, the very-long-baseline interferometry and GPS. In particular, the (degree=2, order= 1) components give the mass term of the polar motion excitation; the (2,O) component, under certain mass conservation conditions, gives the mass term of the length-of-day excitation. Combining these with yet another independent source of angular momentum estimation calculated from global geophysical fluid models (for example the atmospheric angular momentum, in both mass and motion terms), in principle can lead to new insights into the dynamics, particularly the role or the lack thereof of the cores, in the excitation processes of the Earth rotation variations.

Observations of high manganese layers by the Curiosity rover at the Kimberley, Gale crater, Mars

NASA Astrophysics Data System (ADS)

Lanza, N.; Wiens, R. C.; Fischer, W. W.; Grotzinger, J. P.; Cousin, A.; Rice, M. S.; Clark, B. C.; Arvidson, R. E.; Hurowitz, J.; Gellert, R.; McLennan, S. M.; Maurice, S.; Mangold, N.; Le Mouelic, S.; Anderson, R. B.; Nachon, M.; Ollila, A.; Schmidt, M. E.; Berger, J. A.; Blank, J. G.; Clegg, S. M.; Forni, O.; Hardgrove, C. J.; Hardy, K.; Johnson, J. R.; Melikechi, N.; Newsom, H. E.; Sautter, V.; Martín-Torres, J.; Zorzano, M. P.

2014-12-01

The Gravity Recovery and Interior Laboratory (GRAIL) spacecraft were designed to map the structure of the Moon through high-precision global gravity mapping. The mission consisted of two spacecraft with Ka-band inter-satellite tracking complemented by tracking from Earth. The mission had two phases: a primary mapping mission from March 1 until May 29, 2012 at an average altitude of 50 km, and an extended mission from August 30 until December 14, 2012, with an average altitude of 23 km before November 18, and 20 and 11 km after. High-resolution gravity field models using both these data sets have been estimated, with the current resolution being degree and order 1080 in spherical harmonics. Here, we focus on aspects of the analysis of the GRAIL data: we investigate eclipse modeling, the influence of empirical accelerations on the results, and we discuss the inversion of large-scale systems. In addition to global models we also estimated local gravity adjustments in areas of particular interest such as Mare Orientale, the south pole area, and the farside. We investigate the use of Ka-band Range Rate (KBRR) data versus numerical derivatives of KBRR data, and show that the latter have the capability to locally improve correlations with topography.

Generation and manipulation of attosecond light pulses

NASA Astrophysics Data System (ADS)

Gaarde, Mette

2006-05-01

Attosecond pulses of light can be generated in the extremely non-linear interactions between an ultrashort, intense laser pulse and a gas of atoms, via the process of high harmonic generation [1,2]. In one approach, a number of odd harmonics of rougly equal strength are combined to form a train of sub-femtosecond pulses. If the harmonics are locked in phase to each other, the train will consist of the emission of one attosecond pulse every half cycle of the driving laser field [1,3]. It is in general not trivial to ensure that the harmonics are phase-locked as they are generated with intrinsically different phases. These phases originate in the strong field dynamics of the light-matter interaction [4].We will discuss different ways of generating and manipulating attosecond pulses via high harmonic generation. We will show how the harmonics can be phase-locked and better synchronized so as to form optimal pulse trains [3]. We will also show that it is possible to generate trains of pulses separated by a full laser cycle, by combining the driving laser field with its second harmonic [5]. The strong field continuum dynamics driven by the two-color field is very different from that of the one-color field and varies strongly with the delay between the two laser fields [6]. (1) P. M. Paul et al, Science 292, 1689 (2001).(2) M. Hentschel et al, Nature 414, 509 (2001).(3) R. Lopez-Martens et al, PRL 94, 033001 (2005).(4) P. Antoine, A. L'Huillier, and M. Lewenstein, PRL 77, 1234 (1996).(5) J. Mauritsson et al, in preparation (2006).(6) M. B. Gaarde et al, in preparation (2006).

Study of Nonlinear Propagation of Ultrashort Laser Pulses and Its Application to Harmonic Generation

NASA Astrophysics Data System (ADS)

Weerawarne, Darshana L.

Laser filamentation, which is one of the exotic nonlinear optical phenomena, is self-guidance of high-power laser beams due to the dynamic balance between the optical Kerr effect (self-focusing) and other nonlinear effects such as plasma defocusing. It has many applications including supercontinuum generation (SCG), high-order harmonic generation (HHG), lightning guiding, stand-off sensing, and rain making. The main focus of this work is on studying odd-order harmonic generation (HG) (i.e., 3o, 5o, 7o, etc., where o is the angular frequency) in centrosymmetric media while a high-power, ultrashort harmonic-driving pulse undergoes nonlinear propagation such as laser filamentation. The investigation of highly-controversial nonlinear indices of refraction by measuring low-order HG in air is carried out. Furthermore, time-resolved (i.e., pump-probe) experiments and significant harmonic enhancements are presented and a novel HG mechanism based on higher-order nonlinearities is proposed to explain the experimental results. C/C++ numerical simulations are used to solve the nonlinear Schrodinger equation (NLSE) which supports the experimental findings. Another project which I have performed is selective sintering using lasers. Short-pulse lasers provide a fascinating tool for material processing, especially when the conventional oven-based techniques fail to process flexible materials for smart energy/electronics applications. I present experimental and theoretical studies on laser processing of nanoparticle-coated flexible materials, aiming to fabricate flexible electronic devices.

Frequency characteristics of standing-wave acoustooptic modulators

NASA Astrophysics Data System (ADS)

Apolonskii, A. A.; Shchebetov, S. D.

1991-10-01

Experimental data are presented on the performance of wide-aperture standing-wave acoustooptic modulators used as laser mode lockers. In particular, attention is given to the acoustooptic and electrical frequency characteristics of the modulators. The existence of a large effective diffraction frequency region below the fundamental frequency is demonstrated. Individual frequency regions of effective diffraction do not correspond to the even and odd harmonics.

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation

DOE PAGES

Li, Peng -Cheng; Sheu, Yae -Lin; Jooya, Hossein Z.; ...

2016-09-06

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories aremore » dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. As a result, it also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse.« less

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation

PubMed Central

Li, Peng-Cheng; Sheu, Yae-Lin; Jooya, Hossein Z.; Zhou, Xiao-Xin; Chu, Shih-I

2016-01-01

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories are dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. It also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse. PMID:27596056

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation.

PubMed

Li, Peng-Cheng; Sheu, Yae-Lin; Jooya, Hossein Z; Zhou, Xiao-Xin; Chu, Shih-I

2016-09-06

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories are dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. It also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse.

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

Gravity field, shape, and moment of inertia of Titan.

PubMed

Iess, Luciano; Rappaport, Nicole J; Jacobson, Robert A; Racioppa, Paolo; Stevenson, David J; Tortora, Paolo; Armstrong, John W; Asmar, Sami W

2010-03-12

Precise radio tracking of the spacecraft Cassini has provided a determination of Titan's mass and gravity harmonics to degree 3. The quadrupole field is consistent with a hydrostatically relaxed body shaped by tidal and rotational effects. The inferred moment of inertia factor is about 0.34, implying incomplete differentiation, either in the sense of imperfect separation of rock from ice or a core in which a large amount of water remains chemically bound in silicates. The equilibrium figure is a triaxial ellipsoid whose semi-axes a, b, and c differ by 410 meters (a-c) and 103 meters (b-c). The nonhydrostatic geoid height variations (up to 19 meters) are small compared to the observed topographic anomalies of hundreds of meters, suggesting a high degree of compensation appropriate to a body that has warm ice at depth.

Mapping experiment with space station

NASA Technical Reports Server (NTRS)

Wu, S. S. C.

1986-01-01

Mapping of the Earth from space stations can be approached in two areas. One is to collect gravity data for defining topographic datum using Earth's gravity field in terms of spherical harmonics. The other is to search and explore techniques of mapping topography using either optical or radar images with or without reference to ground central points. Without ground control points, an integrated camera system can be designed. With ground control points, the position of the space station (camera station) can be precisely determined at any instant. Therefore, terrestrial topography can be precisely mapped either by conventional photogrammetric methods or by current digital technology of image correlation. For the mapping experiment, it is proposed to establish four ground points either in North America or Africa (including the Sahara desert). If this experiment should be successfully accomplished, it may also be applied to the defense charting systems.

Comparison of the hydrological excitation functions HAM of polar motion for the period 1980.0-2007.0

NASA Astrophysics Data System (ADS)

Nastula, J.; Pasnicka, M.; Kolaczek, B.

2011-10-01

In this study we compared contributions of polar motion excitation determined from hydrological models and harmonic coefficients of the Earth gravity field obtained from Gravity Recovery and Climate Experiment (GRACE). Hydrological excitation function (hydrological angular momentum - HAM) has been estimated from models of global hydrology, based on the observed distribution of surface water, snow, ice and soil moisture. All of them were compared with observed Geodetic Angular Momentum (GAM), excitations of polar motion. The spectra of these excitation functions of polar motion and residual geodetic excitation function G-A-O obtained from GAM by elimination of atmospheric and oceanic excitation functions were computed too. Phasor diagrams of the seasonal components of the polar motion excitation functions of all HAM excitation functions as well as of two GRACE solutions: CSR, CNES were determined and discussed.

Gravity wave momentum flux estimation from CRISTA satellite data

NASA Astrophysics Data System (ADS)

Ern, M.; Preusse, P.; Alexander, M. J.; Offermann, D.

2003-04-01

Temperature altitude profiles measured by the CRISTA satellite were analyzed for gravity waves (GWs). Amplitudes, vertical and horizontal wavelengths of GWs are retrieved by applying a combination of maximum entropy method (MEM) and harmonic analysis (HA) to the temperature height profiles and subsequently comparing the so retrieved GW phases of adjacent altitude profiles. From these results global maps of the absolute value of the vertical flux of horizontal momentum have been estimated. Significant differences between distributions of the temperature variance and distributions of the momentum flux exist. For example, global maps of the momentum flux show a pronounced northward shift of the equatorial maximum whereas temperature variance maps of the tropics/subtropics are nearly symmetric with respect to the equator. This indicates the importance of the influence of horizontal and vertical wavelength distribution on global structures of the momentum flux.

Detection of acoustic-gravity waves in lower ionosphere by VLF radio waves

NASA Astrophysics Data System (ADS)

Nina, A.; Čadež, V. M.

2013-09-01

We present a new method to study harmonic waves in the low ionosphere (60 - 90 km) by detecting their effects on reflection of very low frequency (VLF) radio waves. Our procedure is based on amplitude analysis of reflected VLF radio waves recorded in real time, which yields an insight into the dynamics of the ionosphere at heights where VLF radio waves are being reflected. The method was applied to perturbations induced by the solar terminator motions at sunrises and sunsets. The obtained results show that typical perturbation frequencies found to exist in higher regions of the atmosphere are also present in the lower ionosphere, which indicates a global nature of the considered oscillations. In our model atmosphere, they turn out to be the acoustic and gravity waves with comparatively short and long periods, respectively.

On the Relation Between Spherical Harmonics and Simplified Spherical Harmonics Methods

NASA Astrophysics Data System (ADS)

Coppa, G. G. M.; Giusti, V.; Montagnini, B.; Ravetto, P.

2010-03-01

The purpose of the paper is, first, to recall the proof that the AN method and, therefore, the SP2N-1 method (of which AN was shown to be a variant) are equivalent to the odd order P2N-1, at least for a particular class of multi-region problems; namely the problems for which the total cross section has the same value for all the regions and the scattering is supposed to be isotropic. By virtue of the introduction of quadrature formulas representing first collision probabilities, this class is then enlarged in order to encompass the systems in which the regions may have different total cross sections. Some examples are reported to numerically validate the procedure.

Monterey Bay Geoid

DTIC Science & Technology

1994-03-01

thought to be a flat disk. The first scientific hypothesis that the earth was spherical is credited to Thales of Milet in 600 B.C. or Pythagoras in 550...acceleration can be integrated over the surface, by Gauss’s theorem and gives: 35 v1 Wv2 <v3 Figure 12. Equipotential Surfaces and Gravity: V,, V2, V3 are...continuous derivatives where they satisfy Laplace’s equation. Stokes’ theorem states that a harmonic function outside a surface is uniquely determined by

New insights into ocean tide loading corrections on tidal gravity data in Canary Islands

NASA Astrophysics Data System (ADS)

Arnoso, J.; Benavent, M.; Bos, M. S.; Montesinos, F. G.

2009-04-01

The Canary Islands are an interesting area to investigate ocean tides loading effects due to the complex coastline of the islands and the varying bathymetry. We present here the quality of five recent global oceanic tidal models, GOT00.2, GOT4.7, FES2004, TPXO.7.1 and AG2006, by comparing their predicted ocean tide loading values with results from tidal gravity observations made on three islands, Lanzarote, Tenerife and El Hierro, for the four harmonic constituents O1, K1, M2 and S2. In order to improve the accuracy of the loading corrections on the gravity tide measurements, we have used the high resolution regional oceanic model CIAM2 to supplement the global models considered here. This regional model has been obtained by assimilating TOPEX/Poseidon altimetry at crossovers and along-track points and tide gauge observations into a hydrodynamic model. The model has a 5'Ã-5' resolution and covers the area between the coordinates 26°.5N to 30°.0N and 19°.0W to 12°.5W. The gravity tide observing sites have been occupied by three different LaCoste&Romberg (LCR) spring gravimeters during different periods of observation. We considered here the most recent gravity tide observations made with LCR Graviton-EG1194 in El Hierro Island, for a period of 6 months during 2008. In the case of Tenerife and Lanzarote sites we have used observation periods of 6 months and 8 years with LCR-G665 and LCR-G434 gravimeters, respectively. The last two sites have been revisited in order to improve the previous tidal analysis results. Thus, the gravity ocean tide loading corrections, based on the five global ocean tide models supplemented with the regional model CIAM2 allowed us to review the normalization factors (scale factor and phase lag) of both two gravimeters. Also, we investigated the discrepancies of the corrected gravimetric factors with the DDW elastic and inelastic non hydrostatic body tide model (Dehant et al., 1999). The lowest values are found for inelastic model in the case of M2 and O1 waves at three sites. However, the scatter between oceanic models seen at final residual vectors does not indicate clearly if tidal observations are close to elastic or inelastic body tide model. Finally, after computing misfits of gravity tide observations and ocean tide loading calculations the level of agreement between the five global oceanic models is below 0.2 Gal (1 Gal=10-8ms-2), except for the solar harmonic K1, which reaches a large value that reflects the thermal instability at three sites because the period of K1 is very close to that of S1. None of the five global models seems to give results that are clearly better than the other models.

An introduction to wavelet analysis in oceanography and meteorology - With application to the dispersion of Yanai waves

NASA Technical Reports Server (NTRS)

Meyers, Steven D.; Kelly, B. G.; O'Brien, J. J.

1993-01-01

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an instantaneous estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumbers, possibly due to interaction with the basin boundaries.

Role of membrane stresses in the support of planetary topography

NASA Technical Reports Server (NTRS)

Turcotte, D. L.; Willemann, R. J.; Haxby, W. F.; Norberry, J.

1981-01-01

The role of membrane stresses and bending stresses in supporting topographic loads on planetary elastic lithospheres is examined. A dimensionless parameter is introduced in order to determine the ability of a spherical shell to support loads through membrane stresses. It is determined that when this parameter is large, membrane stresses can fully support topographic loads with flexure, and when it is small the influence of the membrane stresses can be neglected. Equations governing the behavior of a spherical shell are solved for a topographic load expressed in terms of spherical harmonics, and spherical harmonic expansions of the measured gravity and topography for Mars and the moon are compared with the theory. It is concluded that membrane stresses play an important role in the support of topographic loads on the moon and Mars. The correlation of observed gravitational potential anomalies with the topography on Mars is explained by membrane stresses in the elastic lithosphere.

Harmonic lasing in x-ray free electron lasers

NASA Astrophysics Data System (ADS)

Schneidmiller, E. A.; Yurkov, M. V.

2012-08-01

Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned x-ray free electron laser (FEL) facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of x-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned x-ray FEL (XFEL) facilities. In particular, Linac Coherent Light Source (LCLS) after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25-30 keV providing multigigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow one to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other x-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact x-ray FELs (driven by electron beams with a relatively low energy), allowing the use of the standard undulator technology instead of small-gap in-vacuum devices. Finally, in this paper we discover that in a part of the parameter space, corresponding to the operating range of soft x-ray beam lines of x-ray FEL facilities (like SASE3 beam line of the European XFEL), harmonics can grow faster than the fundamental wavelength. This feature can be used in some experiments, but might also be an unwanted phenomenon, and we discuss possible measures to diminish it.

Selected Gravity Models in Terms of the fit to the GOCE Kinematic Orbit in the Dynamic Orbit Determination Process

NASA Astrophysics Data System (ADS)

Bobojć, Andrzej; Drożyner, Andrzej; Rzepecka, Zofia

2017-04-01

The work includes the comparison of performance of selected geopotential models in the dynamic orbit estimation of the satellite of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. This was realized by fitting estimated orbital arcs to the official centimeter-accuracy GOCE kinematic orbit which is provided by the European Space Agency. The Cartesian coordinates of kinematic orbit were treated as observations in the orbit estimation. The initial satellite state vector components were corrected in an iterative process with respect to the J2000.0 inertial reference frame using the given geopotential model, the models describing the remaining gravitational perturbations and the solar radiation pressure. Taking the obtained solutions into account, the RMS values of orbital residuals were computed. These residuals result from the difference between the determined orbit and the reference one - the GOCE kinematic orbit. The performance of selected gravity models was also determined using various orbital arc lengths. Additionally, the RMS fit values were obtained for some gravity models truncated at given degree and order of spherical harmonic coefficients. The advantage of using the kinematic orbit is its independence from any a priori dynamical models. For the research such GOCE-independent gravity models as HUST-Grace2016s, ITU_GRACE16, ITSG-Grace2014s, ITSG-Grace2014k, GGM05S, Tongji-GRACE01, ULUX_CHAMP2013S, ITG-GRACE2010S, EIGEN-51C, EIGEN5S, EGM2008 and EGM96 were adopted.

Flyby Characterization of Lower-Degree Spherical Harmonics Around Small Bodies

NASA Technical Reports Server (NTRS)

Takahashi, Yu; Broschart, Stephen; Lantoine, Gregory

2014-01-01

Interest in studying small bodies has grown significantly in the last two decades, and there are a number of past, present, and future missions. These small body missions challenge navigators with significantly different kinds of problems than the planets and moons do. The small bodies' shape is often irregular and their gravitational field significantly weak, which make the designing of a stable orbit a complex dynamical problem. In the initial phase of spacecraft rendezvous with a small body, the determination of the gravitational parameter and lower-degree spherical harmonics are of crucial importance for safe navigation purposes. This motivates studying how well one can determine the total mass and lower-degree spherical harmonics in a relatively short time in the initial phase of the spacecraft rendezvous via flybys. A quick turnaround for the gravity data is of high value since it will facilitate the subsequent mission design of the main scientific observation campaign. We will present how one can approach the problem to determine a desirable flyby geometry for a general small body. We will work in the non-dimensional formulation since it will generalize our results across different size/mass bodies and the rotation rate for a specific combination of gravitational coefficients.

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

NASA Technical Reports Server (NTRS)

Pai, P. F.; Lee, S.-Y.

2003-01-01

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Harmonic Scalpel versus Electrocautery Dissection in Modified Radical Mastectomy for Breast Cancer: A Meta-Analysis.

PubMed

Huang, Jinbo; Yu, Yinghua; Wei, Changyuan; Qin, Qinghong; Mo, Qinguo; Yang, Weiping

2015-01-01

Despite the common use of conventional electrocautery in modified radical mastectomy for breast cancer, the harmonic scalpel is recently emerging as a dominant surgical instrument for dissection and haemostasis, which is thought to reduce the morbidity, such as seroma and blood loss. But the results of published trials are inconsistent. So we made the meta-analysis to assess the intraoperative and postoperative endpoints among women undergoing modified radical mastectomy with harmonic scalpel or electrocautery. A comprehensive literature search of case-control studies from PubMed, MEDLINE, EMBASE and Cochrane Library databases involving modified radical mastectomy with harmonic scalpel or electrocautery was performed. We carried out a meta-analysis of primary endpoints including postoperative drainage, seroma development, intraoperative blood loss and secondly endpoints including operative time and wound complications. We used odds ratios (ORs) with 95% confidence intervals (CIs) to evaluate the effect size for categorical outcomes and standardised mean differences (SMDs) for continuous outcomes. A total of 11 studies with 702 patients were included for this meta-analysis. There was significant difference in total postoperative drainage (SMD: -0.74 [95%CI: -1.31, -0.16]; P< 0.01), seroma development[OR: 0.49 (0.34, 0.70); P < 0.01], intraoperative blood loss(SMD: -1.14 [95%CI: -1.81,-0.47]; P < 0.01) and wound complications [OR: 0.38 (0.24, 0.59); P < 0.01] between harmonic scalpel dissection and standard electrocautery in modified radical mastectomy for breast cancer. No difference was found as for operative time between harmonic scalpel dissection and standard electrocautery (SMD: 0.04 [95%CI: -0.41, 0.50]; P = 0.85). Compared to standard electrocautery, harmonic scalpel dissection presents significant advantages in decreasing postoperative drainage, seroma development, intraoperative blood loss and wound complications in modified radical mastectomy for breast cancer, without increasing operative time. Harmonic scalpel can be recommended as a preferential surgical instrument in modified radical mastectomy.

Harmonic Scalpel versus Electrocautery Dissection in Modified Radical Mastectomy for Breast Cancer: A Meta-Analysis

PubMed Central

Huang, Jinbo; Yu, Yinghua; Wei, Changyuan; Qin, Qinghong; Mo, Qinguo; Yang, Weiping

2015-01-01

Background Despite the common use of conventional electrocautery in modified radical mastectomy for breast cancer, the harmonic scalpel is recently emerging as a dominant surgical instrument for dissection and haemostasis, which is thought to reduce the morbidity, such as seroma and blood loss. But the results of published trials are inconsistent. So we made the meta-analysis to assess the intraoperative and postoperative endpoints among women undergoing modified radical mastectomy with harmonic scalpel or electrocautery. Methods A comprehensive literature search of case-control studies from PubMed, MEDLINE, EMBASE and Cochrane Library databases involving modified radical mastectomy with harmonic scalpel or electrocautery was performed. We carried out a meta-analysis of primary endpoints including postoperative drainage, seroma development, intraoperative blood loss and secondly endpoints including operative time and wound complications. We used odds ratios (ORs) with 95% confidence intervals (CIs) to evaluate the effect size for categorical outcomes and standardised mean differences (SMDs) for continuous outcomes. Results A total of 11 studies with 702 patients were included for this meta-analysis. There was significant difference in total postoperative drainage (SMD: -0.74 [95%CI: -1.31, -0.16]; P< 0.01), seroma development[OR: 0.49 (0.34, 0.70); P < 0.01], intraoperative blood loss(SMD: -1.14 [95%CI: -1.81,-0.47]; P < 0.01) and wound complications [OR: 0.38 (0.24, 0.59); P < 0.01] between harmonic scalpel dissection and standard electrocautery in modified radical mastectomy for breast cancer. No difference was found as for operative time between harmonic scalpel dissection and standard electrocautery (SMD: 0.04 [95%CI: -0.41, 0.50]; P = 0.85). Conclusion Compared to standard electrocautery, harmonic scalpel dissection presents significant advantages in decreasing postoperative drainage, seroma development, intraoperative blood loss and wound complications in modified radical mastectomy for breast cancer, without increasing operative time. Harmonic scalpel can be recommended as a preferential surgical instrument in modified radical mastectomy. PMID:26544716

Effect of the Earth's inner structure on the gravity in definitions of height systems

NASA Astrophysics Data System (ADS)

Tenzer, Robert; Foroughi, Ismael; Pitoňák, Martin; Šprlák, Michal

2017-04-01

In context of the vertical datum unification, the geoid-to-quasi-geoid separation has been of significant interest in recent years, because most of existing local vertical datums are realized in the system of either normal or orthometric heights. Nevertheless, the normal-orthometric heights are still used in many other countries where the normal gravity values along leveling lines were adopted instead of the observed gravity. Whereas the conversion between the orthometric and normal heights is defined by means of the mean gravity disturbances (i.e. differences between the mean values of the actual and normal gravity) along the plumbline within the topography, differences between the normal and normal-orthometric heights can be described by means of the surface gravity disturbances. Since the normal gravity field does not reflect the topographic masses and actual mass density distribution inside the Earth, the definition of gravity represents a principal aspect for a realization of particular vertical datum. To address this issue in this study, we investigate effects of the Earth's inner density structure on the surface and mean gravity disturbances, and discuss their impact on the vertical datum realization. These two gravity field quantities are computed globally with a spectral resolution complete to a spherical harmonic degree 2160 using the global gravity, terrain, ice-thickness, inland bathymetry and crustal structure models. Our results reveal that both, the surface and mean gravity disturbances mostly comprise the gravitational signal of topography and masses distributed below the geoid surface. Moreover, in polar areas, a significant contribution comes from large glaciers. In contrast, the contributions of anomalous density distribution within the topography attributed to major lakes, sediments and bedrock density variations are much less pronounced. We also demonstrate that the mean gravity disturbances within the topography are significantly modified compared to the corresponding surface values mainly due to topographic elevation and terrain geometry as well as the presence of large glaciers in polar regions. Changes of the vertical gravity gradient within the topography attributed to the masses distributed below the geoid (dominated mainly by the isostatic signature and the long-wavelength gravitational signature of deep mantle density heterogeneities) are, on the other hand, relatively small. Despite differences between the normal and normal-orthometric heights could directly be assessed from the surface gravity disturbances only when taken along leveling lines with information about the spirit leveling height differences, our results indicate that differences between these two height systems can be significant.

Solution to the spectral filter problem of residual terrain modelling (RTM)

NASA Astrophysics Data System (ADS)

Rexer, Moritz; Hirt, Christian; Bucha, Blažej; Holmes, Simon

2018-06-01

In physical geodesy, the residual terrain modelling (RTM) technique is frequently used for high-frequency gravity forward modelling. In the RTM technique, a detailed elevation model is high-pass-filtered in the topography domain, which is not equivalent to filtering in the gravity domain. This in-equivalence, denoted as spectral filter problem of the RTM technique, gives rise to two imperfections (errors). The first imperfection is unwanted low-frequency (LF) gravity signals, and the second imperfection is missing high-frequency (HF) signals in the forward-modelled RTM gravity signal. This paper presents new solutions to the RTM spectral filter problem. Our solutions are based on explicit modelling of the two imperfections via corrections. The HF correction is computed using spectral domain gravity forward modelling that delivers the HF gravity signal generated by the long-wavelength RTM reference topography. The LF correction is obtained from pre-computed global RTM gravity grids that are low-pass-filtered using surface or solid spherical harmonics. A numerical case study reveals maximum absolute signal strengths of ˜ 44 mGal (0.5 mGal RMS) for the HF correction and ˜ 33 mGal (0.6 mGal RMS) for the LF correction w.r.t. a degree-2160 reference topography within the data coverage of the SRTM topography model (56°S ≤ φ ≤ 60°N). Application of the LF and HF corrections to pre-computed global gravity models (here the GGMplus gravity maps) demonstrates the efficiency of the new corrections over topographically rugged terrain. Over Switzerland, consideration of the HF and LF corrections reduced the RMS of the residuals between GGMplus and ground-truth gravity from 4.41 to 3.27 mGal, which translates into ˜ 26% improvement. Over a second test area (Canada), our corrections reduced the RMS of the residuals between GGMplus and ground-truth gravity from 5.65 to 5.30 mGal (˜ 6% improvement). Particularly over Switzerland, geophysical signals (associated, e.g. with valley fillings) were found to stand out more clearly in the RTM-reduced gravity measurements when the HF and LF correction are taken into account. In summary, the new RTM filter corrections can be easily computed and applied to improve the spectral filter characteristics of the popular RTM approach. Benefits are expected, e.g. in the context of the development of future ultra-high-resolution global gravity models, smoothing of observed gravity data in mountainous terrain and geophysical interpretations of RTM-reduced gravity measurements.

Hydrological signal in polar motion excitation from a combination of geophysical and gravimetric series

NASA Astrophysics Data System (ADS)

Nastula, Jolanta; Winska, Malgorzata; Salstein, David A.

2015-08-01

One can estimate the hydrological signal in polar motion excitation as a residual, namely the difference between observed geodetic excitation functions (Geodetic Angular Momentum, GAM) and the sum of Atmospheric Angular Momentum (AAM) and Oceanic Angular Momentum (OAM).The aim of this study is to find the optimal model and results for hydrological excitation functions in terms of their agreement with the computed difference between GAM and atmospheric and oceanic signals.The atmospheric and oceanic model-based data that we use in this study are the geophysical excitation functions of AAM, OAM available from the Special Bureaus for the Atmosphere and Oceans of the Geophysical Global Fluids Center (GGFC) of the International Earth Rotation and Reference Systems Service (IERS). For the atmosphere and ocean, these functions are based on the mass and motion fields of the fluids.Global models of land hydrology are used to estimate hydrological excitation functions of polar motion (Hydrological Angular Momentum - HAM). These HAM series are the mass of water substance determined from the various types of land-based hydrological reservoirs. In addition the HAM are estimated from spherical harmonic coefficients of the Earth’s gravity field. We use several sets of degree-2, order-1 harmonics of the Earth’s gravity field, derived from the Gravity Recovery and Climate Experiment (GRACE), Satellite Laser Ranging (SLR), and Global Navigation Satellite Systems (GNSS) data.Finally, these several different HAM series are used to determine the best model of hydrological excitation of polar motion. The model is found by looking for the combination of these series that fits the geodetic residuals using the least-square method.In addition, we will access model results from the Coupled Model Intercomparison Project, fifth experiment (CMIP-5) to examine atmospheric excitations from the twentieth century and estimates for the twenty-first century to see the possible signals and trends of these excitation series to help understand the potential range in the derived of hydrological excitation results.

Nonlinear Dynamics of Multi-Component Bose-Einstein Condensates ---Anti-Gravity Transport and Vortex Chaos---

NASA Astrophysics Data System (ADS)

Nakamura, K.

Bose-Einstein condensate(BEC) provides a nice stage when the nonlinearSchrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r_{ij} on short scale and logarithmic in r_{ij} on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore ``the chaos in the three-body problem" in the context of vortices with inertia.

Forward modelling of global gravity fields with 3D density structures and an application to the high-resolution ( 2 km) gravity fields of the Moon

NASA Astrophysics Data System (ADS)

Šprlák, M.; Han, S.-C.; Featherstone, W. E.

2017-12-01

Rigorous modelling of the spherical gravitational potential spectra from the volumetric density and geometry of an attracting body is discussed. Firstly, we derive mathematical formulas for the spatial analysis of spherical harmonic coefficients. Secondly, we present a numerically efficient algorithm for rigorous forward modelling. We consider the finite-amplitude topographic modelling methods as special cases, with additional postulates on the volumetric density and geometry. Thirdly, we implement our algorithm in the form of computer programs and test their correctness with respect to the finite-amplitude topography routines. For this purpose, synthetic and realistic numerical experiments, applied to the gravitational field and geometry of the Moon, are performed. We also investigate the optimal choice of input parameters for the finite-amplitude modelling methods. Fourth, we exploit the rigorous forward modelling for the determination of the spherical gravitational potential spectra inferred by lunar crustal models with uniform, laterally variable, radially variable, and spatially (3D) variable bulk density. Also, we analyse these four different crustal models in terms of their spectral characteristics and band-limited radial gravitation. We demonstrate applicability of the rigorous forward modelling using currently available computational resources up to degree and order 2519 of the spherical harmonic expansion, which corresponds to a resolution of 2.2 km on the surface of the Moon. Computer codes, a user manual and scripts developed for the purposes of this study are publicly available to potential users.

Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACE monthly solutions using an improved mascon approach

NASA Astrophysics Data System (ADS)

Ran, J.; Ditmar, P.; Klees, R.; Farahani, H. H.

2018-03-01

We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35-69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24-47%.

Saturn gravity results obtained from Pioneer 11 tracking data and earth-based Saturn satellite data

NASA Technical Reports Server (NTRS)

Null, G. W.; Lau, E. L.; Biller, E. D.; Anderson, J. D.

1981-01-01

Improved gravity coefficients for Saturn, its satellites and rings are calculated on the basis of a combination of Pioneer 11 spacecraft Doppler tracking data and earth-based determinations of Saturn natural satellite apse and node rates. Solutions are first obtained separately from the coherent Doppler tracking data obtained for the interval from August 20 to September 4, surrounding the time of closest approach, with the effects of solar plasma on radio signal propagation taken into account, and from secular rates for Mimas, Enceladus, Tethys, Dione, Rhea and Titan determined from astrometric data by Kozai (1957, 1976) and Garcia (1972). Combination of the data by the use of the Pioneer solution and corresponding unadjusted covariance matrix as a priori information for a secular rate analysis results in values for the total ring mass of essentially zero at a standard error level of 1.7 x 10 to the -6th Saturn masses, a ratio of solar mass to that of the Saturn system of 3498.09 + or - 0.22, masses of Rhea, Titan and Iapetus of 4.0 + or - 0.9, 238.8 + or - 3, and 3.4 + or - 1.3 x 10 to the -6th Saturn masses, respectively, and second and fourth zonal harmonics of 16,479 + or - 18 and -937 + or - 38, respectively. The harmonic coefficients are noted to be important as boundary conditions in the modeling of the Saturn interior.

Mascons, GRACE, and Time-variable Gravity

NASA Technical Reports Server (NTRS)

Lemoine, F.; Lutchke, S.; Rowlands, D.; Klosko, S.; Chinn, D.; Boy, J. P.

2006-01-01

The GRACE mission has been in orbit now for three years and now regularly produces snapshots of the Earth s gravity field on a monthly basis. The convenient standard approach has been to perform global solutions in spherical harmonics. Alternative local representations of mass variations using mascons show great promise and offer advantages in terms of computational efficiency, minimization of problems due to aliasing, and increased temporal resolution. In this paper, we discuss the results of processing the GRACE KBRR data from March 2003 through August 2005 to produce solutions for GRACE mass variations over mid-latitude and equatorial regions, such as South America, India and the United States, and over the polar regions (Antarctica and Greenland), with a focus on the methodology. We describe in particular mascon solutions developed on regular 4 degree x 4 degree grids, and those tailored specifically to drainage basins over these regions.

Effect of Spacecraft Rotation on Fluid Convection Under Microgravity

NASA Technical Reports Server (NTRS)

Yuferev, Valentin S.; Kolesnikova, Elvira N.; Polovko, Yuri A.; Zhmakin, Alexander I.

1996-01-01

The influence of the rotational effects on two-dimensional fluid convection in a rectangular enclosure with rigid walls during the orbital flight is considered. It is shown that the Coriolis force influence both on steady and oscillatory convection becomes significant at Ekman numbers which are quite attainable in the space orbital conditions. In the case of harmonic oscillations of the gravity force appearance of the resonance phenomena is demonstrated. Dependence of the height and shape of the resonance peak on aspect ratio of a rectangular domain and orientation of vectors of the gravity force and the angular rotation velocity is studied. Special attention is given to non-linear effects caused by convective terms of Navier-Stokes equations. The convection produced by variations of the angular rotation velocity of a spacecraft is also discussed. It is shown that in some cases the latter convection can be comparable with another kinds of convection.

Mass Anomalies on Ganymede

NASA Technical Reports Server (NTRS)

Schubert, G.; Anderson, J. D.; Jacobson, R. A.; Lau, E. L.; Moore, W. B.; Palguta, J.

2004-01-01

Radio Doppler data from two Ganymede encounters (G1 and G2) on the first two orbits in the Galileo mission have been analyzed previously for gravity information . For a satellite in hydrostatic equilibrium, its gravitational field can be modeled adequately by a truncated spherical harmonic series of degree two. However, a fourth degree field is required in order to fit the second Galileo flyby (G2). This need for a higher degree field strongly suggests that Ganymede s gravitational field is perturbed by a gravity anomaly near the G2 closest approach point (79.29 latitude, 123.68 west longitude). In fact, a plot of the Doppler residuals , after removal of the best-fit model for the zero degree term (GM) and the second degree moments (J2 and C22), suggests that if an anomaly exists, it is located downtrack of the closest approach point, closer to the equator.

Crustal thickness inversions from recent Mars Reconnaissance Orbiter gravity solutions

NASA Astrophysics Data System (ADS)

Neumann, Gregory; Zuber, Maria T.; Lemoine, Frank; Neumann, Gregory A.; Smith, David E.

Recent Mars Reconnaissance Orbiter gravity solutions from low-altitude tracking of MRO, together with previous spacecraft, have dramatically improved correlation with MOLA topography at spherical harmonic degrees up to 95. We present several updated models of crustal thickness. These models are calculated to fit the Bouguer potential anomaly following the assumptions in Neumann et al. 2004, with much weaker a priori constraints applied to the topographic corrections and the downward continuation to the martian mantle. These models are available via anonymous ftp to "ftp://lepftp.gsfc.nasa.gov/pub/exports/tharsis/marscrust3". The higher-resolution models improve on those we produced in 2004-2005. They are appropriate for modeling impacts as small as 300 km diameter, and for processes related to the hemispheric dichotomy boundary. We discuss in particular the assumption of quasi-uniform crustal density and its likely failure in volcanic regions.

Suggestions for Improvement of User Access to GOCE L2 Data

NASA Astrophysics Data System (ADS)

Tscherning, C. C.

2011-07-01

ESA's has required that most GOCE L2 products are delivered in XML format. This creates difficulties for the users because a Parser written in Perl is needed to convert the files to files without XML tags. However several products, such as the coefficients of spherical harmonic coefficients are made available on standard form through the International Center for Global Gravity Field Models. The variance-covariance information for the gravity field models is only available without XML tags. It is suggested that all XML products are made available in the Virtual Data Archive as files without tags. This will besides making the data directly usable by a FORTRAN program also reduce the size (storage requirements) of the product to about 30 %. A further reduction of used storage should be made by tuning the number of digits for the individual quantities in the products, so that it corresponds to the actual number of significant digits.

The Lunar Crustal Thickness from Analysis of the Lunar Prospector Gravity and Clementine Topography Datasets

NASA Technical Reports Server (NTRS)

Asmar, S.; Schubert, G.; Konopliv, A.; Moore, W.

1999-01-01

The Lunar Prospector spacecraft has mapped the gravity field of the Moon to a level of resolution never achieved before, and a spherical harmonic representation to degree and order 100 is available. When combined with the topography dataset produced by the Clementine mission, the resulting Bouguer anomaly map is interpreted to model the thickness of the lunar crust. Such models are crucial to understanding the lunar thermal history and the formation of geological features such as mascon basins, several more of which have been newly discovered from this dataset. A two-layer planetary model was used to compute the variations of the depth to the lunar Moho. The thickness values ranged from near 0 to 120 km. There is significant agreement with previous work using the Clementine gravitational field data with differences in specific locations such as South Pole-Aitken Basin, for example.

Global evaluation of new GRACE mascon products for hydrologic applications

NASA Astrophysics Data System (ADS)

Scanlon, Bridget R.; Zhang, Zizhan; Save, Himanshu; Wiese, David N.; Landerer, Felix W.; Long, Di; Longuevergne, Laurent; Chen, Jianli

2016-12-01

Recent developments in mascon (mass concentration) solutions for GRACE (Gravity Recovery and Climate Experiment) satellite data have significantly increased the spatial localization and amplitude of recovered terrestrial Total Water Storage anomalies (TWSA); however, land hydrology applications have been limited. Here we compare TWSA from April 2002 through March 2015 from (1) newly released GRACE mascons from the Center for Space Research (CSR-M) with (2) NASA JPL mascons (JPL-M), and with (3) CSR Tellus gridded spherical harmonics rescaled (sf) (CSRT-GSH.sf) in 176 river basins, ˜60% of the global land area. Time series in TWSA mascons (CSR-M and JPL-M) and spherical harmonics are highly correlated (rank correlation coefficients mostly >0.9). The signal from long-term trends (up to ±20 mm/yr) is much less than that from seasonal amplitudes (up to 250 mm). Net long-term trends, summed over all 176 basins, are similar for CSR and JPL mascons (66-69 km3/yr) but are lower for spherical harmonics (˜14 km3/yr). Long-term TWSA declines are found mostly in irrigated basins (-41 to -69 km3/yr). Seasonal amplitudes agree among GRACE solutions, increasing confidence in GRACE-based seasonal fluctuations. Rescaling spherical harmonics significantly increases agreement with mascons for seasonal fluctuations, but less for long-term trends. Mascons provide advantages relative to spherical harmonics, including (1) reduced leakage from land to ocean increasing signal amplitude, and (2) application of geophysical data constraints during processing with little empirical postprocessing requirements, making it easier for nongeodetic users. Results of this product intercomparison should allow hydrologists to better select suitable GRACE solutions for hydrologic applications.

Crossover between few and many fermions in a harmonic trap

NASA Astrophysics Data System (ADS)

Grining, Tomasz; Tomza, Michał; Lesiuk, Michał; Przybytek, Michał; Musiał, Monika; Moszynski, Robert; Lewenstein, Maciej; Massignan, Pietro

2015-12-01

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the nonanalytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

GTOOLS: an Interactive Computer Program to Process Gravity Data for High-Resolution Applications

NASA Astrophysics Data System (ADS)

Battaglia, M.; Poland, M. P.; Kauahikaua, J. P.

2012-12-01

An interactive computer program, GTOOLS, has been developed to process gravity data acquired by the Scintrex CG-5 and LaCoste & Romberg EG, G and D gravity meters. The aim of GTOOLS is to provide a validated methodology for computing relative gravity values in a consistent way accounting for as many environmental factors as possible (e.g., tides, ocean loading, solar constraints, etc.), as well as instrument drift. The program has a modular architecture. Each processing step is implemented in a tool (function) that can be either run independently or within an automated task. The tools allow the user to (a) read the gravity data acquired during field surveys completed using different types of gravity meters; (b) compute Earth tides using an improved version of Longman's (1959) model; (c) compute ocean loading using the HARDISP code by Petit and Luzum (2010) and ocean loading harmonics from the TPXO7.2 ocean tide model; (d) estimate the instrument drift using linear functions as appropriate; and (e) compute the weighted least-square-adjusted gravity values and their errors. The corrections are performed up to microGal ( μGal) precision, in accordance with the specifications of high-resolution surveys. The program has the ability to incorporate calibration factors that allow for surveys done using different gravimeters to be compared. Two additional tools (functions) allow the user to (1) estimate the instrument calibration factor by processing data collected by a gravimeter on a calibration range; (2) plot gravity time-series at a chosen benchmark. The interactive procedures and the program output (jpeg plots and text files) have been designed to ease data handling and archiving, to provide useful information for future data interpretation or modeling, and facilitate comparison of gravity surveys conducted at different times. All formulas have been checked for typographical errors in the original reference. GTOOLS, developed using Matlab, is open source and machine independent. We will demonstrate program use and utility with data from multiple microgravity surveys at Kilauea volcano, Hawai'i.

Self-similar gravity wave spectra resulting from the modulation of bound waves

NASA Astrophysics Data System (ADS)

Michel, Guillaume; Semin, Benoît; Cazaubiel, Annette; Haudin, Florence; Humbert, Thomas; Lepot, Simon; Bonnefoy, Félicien; Berhanu, Michaël; Falcon, Éric

2018-05-01

We experimentally study the properties of nonlinear surface gravity waves in a large-scale basin. We consider two different configurations: a one-dimensional (1D) monochromatic wave forcing, and a two-dimensional (2D) forcing with bichromatic waves satisfying resonant-wave interaction conditions. For the 1D forcing, we find a discrete wave-energy spectrum dominated at high frequencies by bound waves whose amplitudes decrease as a power law of the frequency. Bound waves (e.g., to the carrier) are harmonics superimposed on the carrier wave propagating with the same phase velocity as the one of the carrier. When a narrow frequency random modulation is applied to this carrier, the high-frequency part of the wave-energy spectrum becomes continuous with the same frequency-power law. Similar results are found for the 2D forcing when a random modulation is also applied to both carrier waves. Our results thus show that all these nonlinear gravity wave spectra are dominated at high frequencies by the presence of bound waves, even in the configuration where resonant interactions occur. Moreover, in all these configurations, the power-law exponent of the spectrum is found to depend on the forcing amplitude with the same trend as the one found in previous gravity wave turbulence experiments. Such a set of bound waves may thus explain this dependence that was previously poorly understood.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system.

PubMed

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-21

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

Polydyne displacement interferometer using frequency-modulated light

NASA Astrophysics Data System (ADS)

Arablu, Masoud; Smith, Stuart T.

2018-05-01

A radio-frequency Frequency-Modulated (FM) signal is used to diffract a He-Ne laser beam through an Acousto-Optic Modulator (AOM). Due to the modulation of the FM signal, the measured spectra of the diffracted beams comprise a series of phase-synchronized harmonics that have exact integer frequency separation. The first diffraction side-beam emerging from the AOM is selected by a slit to be used in a polydyne displacement interferometer in a Michelson interferometer topology. The displacement measurement is derived from the phase measurement of selected modulation harmonic pairs. Individual harmonic frequency amplitudes are measured using discrete Fourier transform applied to the signal from a single photodetector. Phase signals are derived from the changes in the amplitudes of different harmonic pairs (typically odd-even pairs) with the phase being extracted using a standard quadrature method. In this study, two different modulation frequencies of 5 and 10 kHz are used at different modulation depths. The measured displacements by different harmonic pairs are compared with a commercial heterodyne interferometer being used as a reference for these studies. Measurements obtained from five different harmonic pairs when the moving mirror of the interferometer is scanned over ranges up to 10 μm all show differences of less than 50 nm from the reference interferometer measurements. A drift test was also used to evaluate the differences between the polydyne interferometer and reference measurements that had different optical path lengths of approximately 25 mm and 50 mm, respectively. The drift test results indicate that about half of the differences can be attributed to temperature, pressure, and humidity variations. Other influences include Abbe and thermal expansion effects. Rough magnitude estimates using simple models for these two effects can account for remaining observed deviations.

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo; Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso

2009-06-15

It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter gravity action in four dimensions recovers the standard regularization given by the holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows one to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as T{sub j}{sup i}={+-}(l{sup 2}/8{pi}G)C{sub j}{sup i}, which has been observed in recent literature in solitonicmore » solutions and hydrodynamic models. A general procedure to generate the counterterm series for anti-de Sitter gravity in any even dimension from the corresponding Euler term is also briefly discussed.« less

Acoustic resonance frequency locked photoacoustic spectrometer

DOEpatents

Pilgrim, Jeffrey S.; Bomse, David S.; Silver, Joel A.

2003-09-09

A photoacoustic spectroscopy method and apparatus for maintaining an acoustic source frequency on a sample cell resonance frequency comprising: providing an acoustic source to the sample cell, the acoustic source having a source frequency; repeatedly and continuously sweeping the source frequency across the resonance frequency at a sweep rate; and employing an odd-harmonic of the source frequency sweep rate to maintain the source frequency sweep centered on the resonance frequency.

An Inversion of Gravity and Topography for Mantle and Crustal Structure on Mars

NASA Technical Reports Server (NTRS)

Kiefer, Walter S.; Bills, Bruce G.; Nerem, R. Steven

1996-01-01

Analysis of the gravity and topography of Mars presently provides our primary quantitative constraints on the internal structure of Mars. We present an inversion of the long-wavelength (harmonic degree less than or equal to 10) gravity and topography of Mars for lateral variations of mantle temperature and crustal thickness. Our formulation incorporates both viscous mantle flow (which most prior studies have neglected) and isostatically compensated density anomalies in the crust and lithosphere. Our nominal model has a 150-km-thick high-viscosity surface layer over an isoviscous mantle, with a core radius of 1840 km. It predicts lateral temperature variations of up to a few hundred degrees Kelvin relative to the mean mantle temperature, with high temperature under Tharsis and to a lesser extent under Elysium and cool temperatures elsewhere. Surprisingly, the model predicts crustal thinning beneath Tharsis. If correct, this implies that thinning of the crust by mantle shear stresses dominates over thickening of the crust by volcanism. The major impact basins (Hellas, Argyre, Isidis, Chryse, and Utopia) are regions of crustal thinning, as expected. Utopia is also predicted to be a region of hot mantle, which is hard to reconcile with the surface geology. An alternative model for Utopia treats it as a mascon basin. The Utopia gravity anomaly is consistent with the presence of a 1.2 to 1.6 km thick layer of uncompensated basalt, in good agreement with geologic arguments about the amount of volcanic fill in this area. The mantle thermal structure is the dominant contributor to the observed geoid in our inversion. The mantle also dominates the topography at the longest wavelengths, but shorter wavelengths (harmonic degrees greater than or equal to 4) are dominated by the crustal structure. Because of the uncertainty about the appropriate numerical values for some of the model's input parameters, we have examined the sensitivity of the model results to the planetary structural model (core radius and core and mantle densities), the mantle's viscosity stratification, and the mean crustal thickness. The model results are insensitive to the specific thickness or viscosity contrast of the high-viscosity surface layer and to the mean crustal thickness in the range 25 to 100 km. Models with a large core radius or with an upper mantle low-viscosity zone require implausibly large lateral variations in mantle temperature.

The Gravity Field, Orientation, and Ephemeris of Mercury from MESSENGER Observations After Three Years in Orbit

NASA Technical Reports Server (NTRS)

Mazarico, Erwan M.; Genova, Antonio; Goossens, Sander; Lemoine, Gregory; Neumann, Gregory A.; Zuber, Maria T.; Smith, David E.; Solomon, Sean C.

2014-01-01

We have analyzed three years of radio tracking data from the MESSENGER spacecraft in orbit around Mercury and determined the gravity field, planetary orientation, and ephemeris of the innermost planet. With improvements in spatial coverage, force modeling, and data weighting, we refined an earlier global gravity field both in quality and resolution, and we present here a spherical harmonic solution to degree and order 50. In this field, termed HgM005, uncertainties in low-degree coefficients are reduced by an order of magnitude relative to the earlier global field, and we obtained a preliminary value of the tidal Love number k(sub 2) of 0.451+/-0.014. We also estimated Mercury's pole position, and we obtained an obliquity value of 2.06 +/- 0.16 arcmin, in good agreement with analysis of Earth-based radar observations. From our updated rotation period (58.646146 +/- 0.000011 days) and Mercury ephemeris, we verified experimentally the planet's 3: 2 spin-orbit resonance to greater accuracy than previously possible. We present a detailed analysis of the HgM005 covariance matrix, and we describe some near-circular frozen orbits around Mercury that could be advantageous for future exploration.

Gravity results from Pioneer 10 Doppler data. [during Jupiter encounter

NASA Technical Reports Server (NTRS)

Anderson, J. D.; Null, G. W.; Wong, S. K.

1974-01-01

Two-way Doppler data received from Pioneer 10 during its encounter with Jupiter have been analyzed, and preliminary results have been obtained on the mass and the gravity field of Jupiter and on the masses of the four Galilean satellites. The ratios of the masses of the satellites to the mass of Jupiter are approximately 0.00004696 for Io, 0.00002565 for Europa, 0.00007845 for Ganymede, and 0.00005603 for Callisto (all error estimates presented in this paper are standard errors; those for Pioneer 10 represent our evaluation of the real errors as distinguished from formal errors). The ratio of the mass of the sun to the mass of the Jupiter system is about 1047.342, which is in good agreement with recent determinations from the motions of asteroids. The second- and fourth-degree zonal harmonic coefficients in the gravity field of Jupiter are 0.014720 and -0.00065, respectively, based on an equatorial planetary radius of 71,400 km, and the derived dynamical oblateness is 0.0647 at the same radius. The Pioneer 10 data are consistent with the assumption that Jupiter is in hydrostatic equilibrium at all levels.

The free versus fixed geodetic boundary value problem for different combinations of geodetic observables

NASA Astrophysics Data System (ADS)

Grafarend, E. W.; Heck, B.; Knickmeyer, E. H.

1985-03-01

Various formulations of the geodetic fixed and free boundary value problem are presented, depending upon the type of boundary data. For the free problem, boundary data of type astronomical latitude, astronomical longitude and a pair of the triplet potential, zero and first-order vertical gradient of gravity are presupposed. For the fixed problem, either the potential or gravity or the vertical gradient of gravity is assumed to be given on the boundary. The potential and its derivatives on the boundary surface are linearized with respect to a reference potential and a reference surface by Taylor expansion. The Eulerian and Lagrangean concepts of a perturbation theory of the nonlinear geodetic boundary value problem are reviewed. Finally the boundary value problems are solved by Hilbert space techniques leading to new generalized Stokes and Hotine functions. Reduced Stokes and Hotine functions are recommended for numerical reasons. For the case of a boundary surface representing the topography a base representation of the solution is achieved by solving an infinite dimensional system of equations. This system of equations is obtained by means of the product-sum-formula for scalar surface spherical harmonics with Wigner 3j-coefficients.

Using nonlinear programming to correct leakage and estimate mass change from GRACE observation and its application to Antarctica

NASA Astrophysics Data System (ADS)

Tang, Jingshi; Cheng, Haowen; Liu, Lin

2012-11-01

The Gravity Recovery And Climate Experiment (GRACE) mission has been providing high quality observations since its launch in 2002. Over the years, fruitful achievements have been obtained and the temporal gravity field has revealed the ongoing geophysical, hydrological and other processes. These discoveries help the scientists better understand various aspects of the Earth. However, errors exist in high degree and order spherical harmonics, which need to be processed before use. Filtering is one of the most commonly used techniques to smooth errors, yet it attenuates signals and also causes leakage of gravity signal into surrounding areas. This paper reports a new method to estimate the true mass change on the grid (expressed in equivalent water height or surface density). The mass change over the grid can be integrated to estimate regional or global mass change. This method assumes the GRACE-observed apparent mass change is only caused by the mass change on land. By comparing the computed and observed apparent mass change, the true mass change can be iteratively adjusted and estimated. The problem is solved with nonlinear programming (NLP) and yields solutions which are in good agreement with other GRACE-based estimates.

A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation

NASA Astrophysics Data System (ADS)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.

On the Variation of Zonal Gravity Coefficients of a Giant Planet Caused by Its Deep Zonal Flows

NASA Astrophysics Data System (ADS)

Kong, Dali; Zhang, Keke; Schubert, Gerald

2012-04-01

Rapidly rotating giant planets are usually marked by the existence of strong zonal flows at the cloud level. If the zonal flow is sufficiently deep and strong, it can produce hydrostatic-related gravitational anomalies through distortion of the planet's shape. This paper determines the zonal gravity coefficients, J 2n , n = 1, 2, 3, ..., via an analytical method taking into account rotation-induced shape changes by assuming that a planet has an effective uniform density and that the zonal flows arise from deep convection and extend along cylinders parallel to the rotation axis. Two different but related hydrostatic models are considered. When a giant planet is in rigid-body rotation, the exact solution of the problem using oblate spheroidal coordinates is derived, allowing us to compute the value of its zonal gravity coefficients \\bar{J}_{2n}, n=1,2,3, \\dots, without making any approximation. When the deep zonal flow is sufficiently strong, we develop a general perturbation theory for estimating the variation of the zonal gravity coefficients, \\Delta {J}_{2n}={J}_{2n}-\\bar{J}_{2n}, n=1,2,3, \\dots, caused by the effect of the deep zonal flows for an arbitrarily rapidly rotating planet. Applying the general theory to Jupiter, we find that the deep zonal flow could contribute up to 0.3% of the J 2 coefficient and 0.7% of J 4. It is also found that the shape-driven harmonics at the 10th zonal gravity coefficient become dominant, i.e., \\Delta {J}_{2n} \\,{\\ge}\\, \\bar{J}_{2n} for n >= 5.

Effect of Time Varying Gravity on DORIS processing for ITRF2013

NASA Astrophysics Data System (ADS)

Zelensky, N. P.; Lemoine, F. G.; Chinn, D. S.; Beall, J. W.; Melachroinos, S. A.; Beckley, B. D.; Pavlis, D.; Wimert, J.

2013-12-01

Computations are under way to develop a new time series of DORIS SINEX solutions to contribute to the development of the new realization of the terrestrial reference frame (c.f. ITRF2013). One of the improvements that are envisaged is the application of improved models of time-variable gravity in the background orbit modeling. At GSFC we have developed a time series of spherical harmonics to degree and order 5 (using the GOC02S model as a base), based on the processing of SLR and DORIS data to 14 satellites from 1993 to 2013. This is compared with the standard approach used in ITRF2008, based on the static model EIGEN-GL04S1 which included secular variations in only a few select coefficients. Previous work on altimeter satellite POD (c.f. TOPEX/Poseidon, Jason-1, Jason-2) has shown that the standard model is not adequate and orbit improvements are observed with application of more detailed models of time-variable gravity. In this study, we quantify the impact of TVG modeling on DORIS satellite POD, and ascertain the impact on DORIS station positions estimated weekly from 1993 to 2013. The numerous recent improvements to SLR and DORIS processing at GSFC include a more complete compliance to IERS2010 standards, improvements to SLR/DORIS measurement modeling, and improved non-conservative force modeling to DORIS satellites. These improvements will affect gravity coefficient estimates, POD, and the station solutions. Tests evaluate the impact of time varying gravity on tracking data residuals, station consistency, and the geocenter and scale reference frame parameters.

Small-scale density variations in the lunar crust revealed by GRAIL

NASA Astrophysics Data System (ADS)

Jansen, J. C.; Andrews-Hanna, J. C.; Li, Y.; Lucey, P. G.; Taylor, G. J.; Goossens, S.; Lemoine, F. G.; Mazarico, E.; Head, J. W.; Milbury, C.; Kiefer, W. S.; Soderblom, J. M.; Zuber, M. T.

2017-07-01

Data from the Gravity Recovery and Interior Laboratory (GRAIL) mission have revealed that ∼98% of the power of the gravity signal of the Moon at high spherical harmonic degrees correlates with the topography. The remaining 2% of the signal, which cannot be explained by topography, contains information about density variations within the crust. These high-degree Bouguer gravity anomalies are likely caused by small-scale (10‧s of km) shallow density variations. Here we use gravity inversions to model the small-scale three-dimensional variations in the density of the lunar crust. Inversion results from three non-descript areas yield shallow density variations in the range of 100-200 kg/m3. Three end-member scenarios of variations in porosity, intrusions into the crust, and variations in bulk crustal composition were tested as possible sources of the density variations. We find that the density anomalies can be caused entirely by changes in porosity. Characteristics of density anomalies in the South Pole-Aitken basin also support porosity as a primary source of these variations. Mafic intrusions into the crust could explain many, but not all of the anomalies. Additionally, variations in crustal composition revealed by spectral data could only explain a small fraction of the density anomalies. Nevertheless, all three sources of density variations likely contribute. Collectively, results from this study of GRAIL gravity data, combined with other studies of remote sensing data and lunar samples, show that the lunar crust exhibits variations in density by ± 10% over scales ranging from centimeters to 100‧s of kilometers.

Small-Scale Density Variations in the Lunar Crust Revealed by GRAIL

NASA Technical Reports Server (NTRS)

Jansen, J. C.; Andrews-Hanna, J. C.; Li, Y.; Lucey, P. G.; Taylor, G. J.; Goossens, S.; Lemoine, F. G.; Mazarico, E.; Head, J. W., III; Milbury, C.;

Comment on: `The quest for a consistent signal in ground and GRACE gravity time-series', by Michel Van Camp, Olivier de Viron, Laurent Metivier, Bruno Meurers and Olivier Francis

NASA Astrophysics Data System (ADS)

Crossley, D. J.; Boy, J.-P.; Hinderer, J.; Jahr, T.; Weise, A.; Wziontek, H.; Abe, M.; Förste, C.

2014-12-01

The paper in question by Van Camp and co-authors [MVC] challenges previous work showing that ground gravity data arising from hydrology can provide a consistent signal for the comparison with satellite gravity data. The data sets used are similar to those used previously, that is, the gravity field as measured by the GRACE satellites versus ground-based data from superconducting gravimeters (SGs) over the same continental area, in this case Central Europe. One of the main impediments in this paper is the presentation that is frequently confusing and misleading as to what the data analysis really shows, for example, the irregular treatment of annual components that are first subtracted then reappear in the analysis. More importantly, we disagree on specific points. Two calculations are included in our comment to illustrate where we believe that the processing in [MVC] paper is deficient. The first deals with their erroneous treatment of the global hydrology using a truncated spherical harmonic approach which explains almost a factor 2 error in their computation of the loading. The second shows the effect of making the wrong assumption in the GRACE/hydrology/surface gravity comparison by inverting the whole of the hydrology loading for underground stations. We also challenge their claims that empirical orthogonal function techniques cannot be done in the presence of periodic components, and that SG data cannot be corrected for comparisons with GRACE data. The main conclusion of their paper, that there is little coherence between ground gravity stations and this invalidates GRACE comparisons, is therefore questionable. There is nothing in [MVC] that contradicts any of the previous papers that have shown clearly a strong relation between seasonal signals obtained from both ground gravity and GRACE satellite data.

AIUB-RL02: an improved time-series of monthly gravity fields from GRACE data

NASA Astrophysics Data System (ADS)

Meyer, U.; Jäggi, A.; Jean, Y.; Beutler, G.

2016-05-01

The new release AIUB-RL02 of monthly gravity models from GRACE GPS and K-Band range-rate data is based on reprocessed satellite orbits referring to the reference frame IGb08. The release is consistent with the IERS2010 conventions. Improvements with respect to its predecessor AIUB-RL01 include the use of reprocessed (RL02) GRACE observations, new atmosphere and ocean dealiasing products (RL05), an upgraded ocean tide model (EOT11A), and the interpolation of shallow ocean tides (admittances). The stochastic parametrization of AIUB-RL02 was adapted to include daily accelerometer scale factors, which drastically reduces spurious signal at the 161 d period in C20 and at other low degree and order gravity field coefficients. Moreover, the correlation between the noise in the monthly gravity models and solar activity is considerably reduced in the new release. The signal and the noise content of the new AIUB-RL02 monthly gravity fields are studied and calibrated errors are derived from their non-secular and non-seasonal variability. The short-period time-variable signal over the oceans, mostly representing noise, is reduced by 50 per cent with respect to AIUB-RL01. Compared to the official GFZ-RL05a and CSR-RL05 monthly models, the AIUB-RL02 stands out by its low noise at high degrees, a fact emerging from the estimation of seasonal variations for selected river basins and of mass trends in polar regions. Two versions of the monthly AIUB-RL02 gravity models, with spherical harmonics resolution of degree and order 60 and 90, respectively, are available for the time period from March 2003 to March 2014 at the International Center for Global Earth Models or from ftp://ftp.unibe.ch/aiub/GRAVITY/GRACE (last accessed 22 March 2016).

Casual Set Approach to a Minimal Invariant Length

NASA Astrophysics Data System (ADS)

Raut, Usha

2007-04-01

Any attempt to quantize gravity would necessarily introduce a minimal observable length scale of the order of the Planck length. This conclusion is based on several different studies and thought experiments and appears to be an inescapable feature of all quantum gravity theories, irrespective of the method used to quantize gravity. Over the last few years there has been growing concern that such a minimal length might lead to a contradiction with the basic postulates of special relativity, in particular the Lorentz-Fitzgerald contraction. A few years ago, Rovelli et.al, attempted to reconcile an invariant minimal length with Special Relativity, using the framework of loop quantum gravity. However, the inherently canonical formalism of the loop quantum approach is plagued by a variety of problems, many brought on by separation of space and time co-ordinates. In this paper we use a completely different approach. Using the framework of the causal set paradigm, along with a statistical measure of closeness between Lorentzian manifolds, we re-examine the issue of introducing a minimal observable length that is not at odds with Special Relativity postulates.

Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,

DTIC Science & Technology

1980-02-01

the metric in spherical coordinates {X,F, rl reads ds2 = r2cos 2j dX2 + r 2d 2 + dr2 yielding the metric tensor and the associated metric tensor: {grs...leading to (3.52) would have required considerably more space if the tensor approach to this problem had been avoided, whether for pedagogical or other...useful, especially from the pedagogical point of view, since it addresses itself to large audiences and exposes the treated subject in great depth. On

A high-powered siren for stable acoustic levitation of dense materials in the earth's gravity

NASA Technical Reports Server (NTRS)

Gammel, Paul M.; Croonquist, Arvid P.; Wang, Taylor G.

1988-01-01

Levitation of large dense samples (e.g., 1-cm diameter steel balls) has been performed in a 1-g environment. A siren was used to study the effects of reflector geometry and variable-frequency operation in order to attain stable acoustic positioning. The harmonic content and spatial distribution of the acoustic field have been investigated. The best stability was obtained with an open reflector system, using a flat lower reflector and a slightly concave upper reflector while operating at a frequency slightly below resonance.

Gravity and the Spin-2 Planar Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bergshoeff, Eric A.; Rosseel, Jan; Townsend, Paul K.

2018-04-01

A Schrödinger equation proposed for the Girvin-MacDonald-Platzman gapped spin-2 mode of fractional quantum Hall states is found from a novel nonrelativistic limit, applicable only in 2 +1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3 +1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the nonlinear Einstein equations, a confining harmonic oscillator potential for the individual particles.

Vertical vibration and shape oscillation of acoustically levitated water drops

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geng, D. L.; Xie, W. J.; Yan, N.

2014-09-08

We present the vertical harmonic vibration of levitated water drops within ultrasound field. The restoring force to maintain such a vibration mode is provided by the resultant force of acoustic radiation force and drop gravity. Experiments reveal that the vibration frequency increases with the aspect ratio for drops with the same volume, which agrees with the theoretical prediction for those cases of nearly equiaxed drops. During the vertical vibration, the floating drops undergo the second order shape oscillation. The shape oscillation frequency is determined to be twice the vibration frequency.

Mars' gravity field and upper atmosphere with MGS, Mars Odyssey, and MRO radio science data

NASA Astrophysics Data System (ADS)

Genova, Antonio; Goossens, Sander J.; Lemoine, Frank G.; Mazarico, Erwan; Smith, David E.; Zuber, Maria T.

2015-04-01

The Mars exploration program conducted by NASA during the last decade has enabled continuous observations of the planet from orbit with three different missions: the Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). These spacecraft were equipped with on board instrumentation dedicated to collect radio tracking data in the X-band. The analysis of these data has provided a high-resolution gravity field model of Mars. MGS and ODY were inserted into two separate frozen sun-synchronous, near-circular, polar orbits with different local times, with their periapsis altitude at ~370 km and ~390 km, respectively. MGS was in orbit around Mars between 1999 and 2006, whereas ODY has been orbiting the planet since January 2002. Using the radio science data of these two spacecraft, gravity models with a maximum resolution of degree and order 95 in spherical harmonics (spatial resolution of 112 km) have been determined. MRO has been orbiting Mars since August 2006 in a frozen sun-synchronous orbit with a periapsis at 255 km altitude. Therefore, its radio data helped significantly improve Mars' gravity field model, up to degree and order 110 (spatial resolution of 96 km). However, mismodeling of the atmospheric drag, which is the strongest non-conservative force acting on the spacecraft at MRO's low altitude, compromises the estimation of the temporal variations of the gravity field zonal harmonics that provide crucial information on the seasonal mass of carbon dioxide in the polar caps. For this reason, we implemented the Drag Temperature Model (DTM)-Mars model (Bruinsma and Lemoine 2002) into our Precise Orbit Determination (POD) program GEODYN-II. We estimated key model parameters to adequately reproduce variations in temperatures and (partial) density along the spacecraft trajectories. Our new model allows us to directly estimate the long-term periodicity of the major constituents at MGS, ODY, and MRO altitudes (~255-450 km). In this region of the Martian upper atmosphere, CO2, O, and He represent the dominant species. MRO data primarily determine the annual and semi-annual variability of CO2 and O since these two elements are the major constituents along its orbit. MGS and ODY sample altitudes where He is the most abundant species and thus they help constrain the long-term variations of O. We will present an update on the DTM-Mars model using MGS, ODY, and MRO radio science data. The improved atmospheric model provides a better prediction of the long-term variability of the dominant species. Therefore, the inclusion of the recovered model leads to improved orbit determination and an improved gravity field model of Mars using MGS, ODY, and MRO radio tracking data. The solution will be especially based on 8 years of MRO data from August 2006 to June 2014.

A refined model of sedimentary rock cover in the southeastern part of the Congo basin from GOCE gravity and vertical gravity gradient observations

NASA Astrophysics Data System (ADS)

Martinec, Zdeněk; Fullea, Javier

2015-03-01

We aim to interpret the vertical gravity and vertical gravity gradient of the GOCE-GRACE combined gravity model over the southeastern part of the Congo basin to refine the published model of sedimentary rock cover. We use the GOCO03S gravity model and evaluate its spherical harmonic representation at or near the Earth's surface. In this case, the gradiometry signals are enhanced as compared to the original measured GOCE gradients at satellite height and better emphasize the spatial pattern of sedimentary geology. To avoid aliasing, the omission error of the modelled gravity induced by the sedimentary rocks is adjusted to that of the GOCO03S gravity model. The mass-density Green's functions derived for the a priori structure of the sediments show a slightly greater sensitivity to the GOCO03S vertical gravity gradient than to the vertical gravity. Hence, the refinement of the sedimentary model is carried out for the vertical gravity gradient over the basin, such that a few anomalous values of the GOCO03S-derived vertical gravity gradient are adjusted by refining the model. We apply the 5-parameter Helmert's transformation, defined by 2 translations, 1 rotation and 2 scale parameters that are searched for by the steepest descent method. The refined sedimentary model is only slightly changed with respect to the original map, but it significantly improves the fit of the vertical gravity and vertical gravity gradient over the basin. However, there are still spatial features in the gravity and gradiometric data that remain unfitted by the refined model. These may be due to lateral density variation that is not contained in the model, a density contrast at the Moho discontinuity, lithospheric density stratifications or mantle convection. In a second step, the refined sedimentary model is used to find the vertical density stratification of sedimentary rocks. Although the gravity data can be interpreted by a constant sedimentary density, such a model does not correspond to the gravitational compaction of sedimentary rocks. Therefore, the density model is extended by including a linear increase in density with depth. Subsequent L2 and L∞ norm minimization procedures are applied to find the density parameters by adjusting both the vertical gravity and the vertical gravity gradient. We found that including the vertical gravity gradient in the interpretation of the GOCO03S-derived data reduces the non-uniqueness of the inverse gradiometric problem for density determination. The density structure of the sedimentary formations that provide the optimum predictions of the GOCO03S-derived gravity and vertical gradient of gravity consists of a surface density contrast with respect to surrounding rocks of 0.24-0.28 g/cm3 and its decrease with depth of 0.05-0.25 g/cm3 per 10 km. Moreover, the case where the sedimentary rocks are gravitationally completely compacted in the deepest parts of the basin is supported by L∞ norm minimization. However, this minimization also allows a remaining density contrast at the deepest parts of the sedimentary basin of about 0.1 g/cm3.

High crustal density at Mafic Mound in South Pole-Aitken Basin

NASA Astrophysics Data System (ADS)

James, P. B.; Kiefer, W. S.

2017-12-01

The bulk density of a planetary surface is dependent on the porosity and composition of the crust, which are quantities of interest for exploration as well as science. We present new methods for characterizing noise in gravity data, which allow us to include more high-degree data, reduce uncertainties, and resolve smaller features. We apply these methods to an enigmatic geologic complex in the lunar South Pole-Aitken basin called "Mafic Mound". We studied Mafic Mound using GRAIL gravity [1] and the predicted gravity from a LOLA lunar shape model ("gravity-from-topography"), and these datasets are tapered within a 50-km radius. We apply a spectral taper between spherical harmonic degrees l=150 and l=585; the lower limit is selected so as to limit sensitivity to the crust-mantle interface, and the upper limit corresponds to a 2:1 signal/noise ratio [2]. A weighted linear regression of filtered gravity and gravity-from-topography reveals a density of 3190 ± 110 kg/m3 at Mafic Mound. This is a remarkably high density: similar analyses at six adjacent terrains yield densities 400-610 kg/m3 less dense than Mafic Mound. However, two lines of evidence suggest that this high estimate for bulk density may be influenced by the internal structure of Mafic Mound. First, gravity has a weaker correlation with topography in Mafic Mound than in any of the surrounding terrains, as would be expected if subsurface mass concentrations contributed heavily to the gravity anomaly. Second, a high-pass filter (l > 300) of gravity yields a lower density estimate of 2760 ± 110 kg/m3, which is only about 110 kg/m3 denser than the surrounding terrains. Forward modeling reveals that approximately half of the high-pass gravity signal energy is produced by masses at depths shallower than 3 km. We conclude that Mafic Mound is underlain at several kilometers depth by high-density crust, caused by some combination of relatively low porosity and relatively high grain densities. While alternative interpretations exist, this is consistent with intrusive magmatism and suggests a volcanic origin for Mafic Mound. An integration of LOLA-derived topography indicates a volume of 1.4×103 cubic kilometers of intrusively and extrusively placed volcanic material. [1] Konopliv, A. S. et al. (2014), GRL 41, 1452-1458 [2] James, P. B. et al. (2017), LPSC 41 #2199

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

NASA Astrophysics Data System (ADS)

Lu, Biao; Luo, Zhicai; Zhong, Bo; Zhou, Hao; Flechtner, Frank; Förste, Christoph; Barthelmes, Franz; Zhou, Rui

2017-11-01

Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components V_{xy} and V_{yz} of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7° . With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of V_{xy} and V_{yz} are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1's accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data.

Compact objects in pure Lovelock theory

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Hansraj, Sudan; Chilambwe, Brian

For static fluid interiors of compact objects in pure Lovelock gravity (involving only one Nth order term in the equation), we establish similarity in solutions for the critical odd and even d = 2N + 1, 2N + 2 dimensions. It turns out that in critical odd d = 2N + 1 dimensions, there cannot exist any bound distribution with a finite radius, while in critical even d = 2N + 2 dimensions, all solutions have similar behavior. For exhibition of similarity, we would compare star solutions for N = 1, 2 in d = 4 Einstein and d = 6 in Gauss-Bonnet theory, respectively. We also obtain the pure Lovelock analogue of the Finch-Skea model.

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-02-01

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Correcting sample drift using Fourier harmonics.

PubMed

Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L

2018-07-01

During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.

Gravity field of Venus - A preliminary analysis

NASA Technical Reports Server (NTRS)

Phillips, R. J.; Sjogren, W. L.; Abbott, E. A.; Smith, J. C.; Wimberly, R. N.; Wagner, C. A.

1979-01-01

The gravitational field of Venus obtained by tracking the Pioneer Venus Orbiter is examined. For each spacecraft orbit, two hours of Doppler data centered around periapsis were used to estimate spacecraft position and velocity and the velocity residuals obtained were spline fit and differentiated to produce line of sight gravitational accelerations. Consistent variations in line of sight accelerations from orbit to orbit reveal the presence of gravitational anomalies. A simulation of isostatic compensation for an elevated region on the surface of Venus indicates that the mean depth of compensation is no greater than about 100 km. Gravitational spectra obtained from a Fourier analysis of line of sight accelerations from selected Venus orbits are compared to the earth's gravitational spectrum and spherical harmonic gravitational potential power spectra of the earth, the moon and Mars. The Venus power spectrum is found to be remarkably similar to that of the earth, however systematic variations in the harmonics suggest differences in dynamic processes or lithospheric behavior.

A relativistic gravity train

NASA Astrophysics Data System (ADS)

Parker, Edward

2017-08-01

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.

The relation between degree-2160 spectral models of Earth's gravitational and topographic potential: a guide on global correlation measures and their dependency on approximation effects

NASA Astrophysics Data System (ADS)

Hirt, Christian; Rexer, Moritz; Claessens, Sten; Rummel, Reiner

2017-10-01

Comparisons between high-degree models of the Earth's topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (quantifying the amount of topographic signal contained in the gravitational potential) are indicators used in a number of contemporary studies. However, depending on the modelling techniques and underlying levels of approximation, the correlation at high degrees may vary significantly, as do the conclusions drawn. The present paper addresses this problem by attempting to provide a guide on global correlation measures with particular emphasis on approximation effects and variants of topographic potential modelling. We investigate and discuss the impact of different effects (e.g., truncation of series expansions of the topographic potential, mass compression, ellipsoidal versus spherical approximation, ellipsoidal harmonic coefficient versus spherical harmonic coefficient (SHC) representation) on correlation measures. Our study demonstrates that the correlation coefficients are realistic only when the model's harmonic coefficients of a given degree are largely independent of the coefficients of other degrees, permitting degree-wise evaluations. This is the case, e.g., when both models are represented in terms of SHCs and spherical approximation (i.e. spherical arrangement of field-generating masses). Alternatively, a representation in ellipsoidal harmonics can be combined with ellipsoidal approximation. The usual ellipsoidal approximation level (i.e. ellipsoidal mass arrangement) is shown to bias correlation coefficients when SHCs are used. Importantly, gravity models from the International Centre for Global Earth Models (ICGEM) are inherently based on this approximation level. A transformation is presented that enables a transformation of ICGEM geopotential models from ellipsoidal to spherical approximation. The transformation is applied to generate a spherical transform of EGM2008 (sphEGM2008) that can meaningfully be correlated degree-wise with the topographic potential. We exploit this new technique and compare a number of models of topographic potential constituents (e.g., potential implied by land topography, ocean water masses) based on the Earth2014 global relief model and a mass-layer forward modelling technique with sphEGM2008. Different to previous findings, our results show very significant short-scale correlation between Earth's gravitational potential and the potential generated by Earth's land topography (correlation +0.92, and 60% of EGM2008 signals are delivered through the forward modelling). Our tests reveal that the potential generated by Earth's oceans water masses is largely unrelated to the geopotential at short scales, suggesting that altimetry-derived gravity and/or bathymetric data sets are significantly underpowered at 5 arc-min scales. We further decompose the topographic potential into the Bouguer shell and terrain correction and show that they are responsible for about 20 and 25% of EGM2008 short-scale signals, respectively. As a general conclusion, the paper shows the importance of using compatible models in topographic/gravitational potential comparisons and recommends the use of SHCs together with spherical approximation or EHCs with ellipsoidal approximation in order to avoid biases in the correlation measures.

The evens and odds of CMB anomalies

NASA Astrophysics Data System (ADS)

Gruppuso, A.; Kitazawa, N.; Lattanzi, M.; Mandolesi, N.; Natoli, P.; Sagnotti, A.

2018-06-01

The lack of power of large-angle CMB anisotropies is known to increase its statistical significance at higher Galactic latitudes, where a string-inspired pre-inflationary scale Δ can also be detected. Considering the Planck 2015 data, and relying largely on a Bayesian approach, we show that the effect is mostly driven by the even - ℓ harmonic multipoles with ℓ ≲ 20, which appear sizably suppressed in a way that is robust with respect to Galactic masking, along with the corresponding detections of Δ. On the other hand, the first odd - ℓ multipoles are only suppressed at high Galactic latitudes. We investigate this behavior in different sky masks, constraining Δ through even and odd multipoles, and we elaborate on possible implications. We include low- ℓ polarization data which, despite being noise-limited, help in attaining confidence levels of about 3 σ in the detection of Δ. We also show by direct forecasts that a future all-sky E-mode cosmic-variance-limited polarization survey may push the constraining power for Δ beyond 5 σ.

Three-wave and four-wave interactions in gravity wave turbulence

NASA Astrophysics Data System (ADS)

Aubourg, Quentin; Campagne, Antoine; Peureux, Charles; Ardhuin, Fabrice; Sommeria, Joel; Viboud, Samuel; Mordant, Nicolas

2017-11-01

Weak-turbulence theory is a statistical framework to describe a large ensemble of nonlinearly interacting waves. The archetypal example of such system is the ocean surface that is made of interacting surface gravity waves. Here we describe a laboratory experiment dedicated to probe the statistical properties of turbulent gravity waves. We set up an isotropic state of interacting gravity waves in the Coriolis facility (13-m-diam circular wave tank) by exciting waves at 1 Hz by wedge wave makers. We implement a stereoscopic technique to obtain a measurement of the surface elevation that is resolved in both space and time. Fourier analysis shows that the laboratory spectra are systematically steeper than the theoretical predictions and the field observations in the Black Sea by Leckler et al. [F. Leckler et al., J. Phys. Oceanogr. 45, 2484 (2015), 10.1175/JPO-D-14-0237.1]. We identify a strong impact of surface dissipation on the scaling of the Fourier spectrum at the scales that are accessible in the experiments. We use bicoherence and tricoherence statistical tools in frequency and/or wave-vector space to identify the active nonlinear coupling. These analyses are also performed on the field data by Leckler et al. for comparison with the laboratory data. Three-wave coupling is characterized by and shown to involve mostly quasiresonances of waves with second- or higher-order harmonics. Four-wave coupling is not observed in the laboratory but is evidenced in the field data. We discuss temporal scale separation to explain our observations.

Mars Gravity Field Model Development from Mars Global Surveyor Tracking Data

NASA Technical Reports Server (NTRS)

Lemoine, F. G.; Zuber, M. T.

1999-01-01

Since Feb. 99 the MGS spacecraft has been in a near circular orbit at about 400 km altitude. The MGS has been regularly tracked by the Deep Space Network (DSN) at X-band and for a 3 week period in February was tracked almost continuously for an intensive gravity modeling activity that would form the basis of the orbital computations for the rest of the mission. The data collected during this calibration period and the earlier SPO and Hiatus periods have now been used to develop a new gravity field model for Mars that is showing considerable new detail in both the northern and southern hemispheres. Until February no data at 400 km altitude or lower had been acquired on any previous mission south of about 35S and all the previous data were of significantly lower quality. Low altitude data (-170 km) were obtained over the higher latitudes of the northern hemisphere during the SPO periods but because of the high eccentricity of the orbit nothing of similar quality was obtainable for the southern hemisphere. The new models are of spherical harmonic degree and order 70 or higher and are suggesting large anomalies are often associated with the large impact features. Gravity data have also been obtained over both the northern and southern polar ice caps. The MGS orbit quality resulting from the use of these newer models is better than any previous Mars missions and is approaching the ten's of meter level that had been hoped would be eventually realizable.

Introduction to TAFI - A Matlab® toolbox for analysis of flexural isostasy

NASA Astrophysics Data System (ADS)

Jha, S.; Harry, D. L.; Schutt, D.

2016-12-01

The isostatic response of vertical tectonic loads emplaced on thin elastic plates overlying inviscid substrate and the corresponding gravity anomalies are commonly modeled using well established theories and methodologies of flexural analysis. However, such analysis requires some mathematical and coding expertise on part of users. With that in mind, we designed a new interactive Matlab® toolbox called Toolbox for Analysis of Flexural Isostasy (TAFI). TAFI allows users to create forward models (2-D and 3-D) of flexural deformation of the lithosphere and resulting gravity anomaly. TAFI computes Green's Functions for flexure of the elastic plate subjected to point or line loads, and analytical solution for harmonic loads. Flexure due to non-impulsive, distributed 2-D or 3-D loads are computed by convolving the appropriate Green's function with a user-supplied spatially discretized load function. The gravity anomaly associated with each density interface is calculated by using the Fourier Transform of flexural deflection of these interfaces and estimating the gravity in the wavenumber domain. All models created in TAFI are based on Matlab's intrinsic functions and do not require any specialized toolbox, function or library except those distributed with TAFI. Modeling functions within TAFI can be called from Matlab workspace, from within user written programs or from the TAFI's graphical user interface (GUI). The GUI enables the user to model the flexural deflection of lithosphere interactively, enabling real time comparison of model fit with observed data constraining the flexural deformation and gravity, facilitating rapid search for best fitting flexural model. TAFI is a very useful teaching and research tool and have been tested rigorously in graduate level teaching and basic research environment.

ORBSIM- ESTIMATING GEOPHYSICAL MODEL PARAMETERS FROM PLANETARY GRAVITY DATA

NASA Technical Reports Server (NTRS)

Sjogren, W. L.

1994-01-01

The ORBSIM program was developed for the accurate extraction of geophysical model parameters from Doppler radio tracking data acquired from orbiting planetary spacecraft. The model of the proposed planetary structure is used in a numerical integration of the spacecraft along simulated trajectories around the primary body. Using line of sight (LOS) Doppler residuals, ORBSIM applies fast and efficient modelling and optimization procedures which avoid the traditional complex dynamic reduction of data. ORBSIM produces quantitative geophysical results such as size, depth, and mass. ORBSIM has been used extensively to investigate topographic features on the Moon, Mars, and Venus. The program has proven particulary suitable for modelling gravitational anomalies and mascons. The basic observable for spacecraft-based gravity data is the Doppler frequency shift of a transponded radio signal. The time derivative of this signal carries information regarding the gravity field acting on the spacecraft in the LOS direction (the LOS direction being the path between the spacecraft and the receiving station, either Earth or another satellite). There are many dynamic factors taken into account: earth rotation, solar radiation, acceleration from planetary bodies, tracking station time and location adjustments, etc. The actual trajectories of the spacecraft are simulated using least squares fitted to conic motion. The theoretical Doppler readings from the simulated orbits are compared to actual Doppler observations and another least squares adjustment is made. ORBSIM has three modes of operation: trajectory simulation, optimization, and gravity modelling. In all cases, an initial gravity model of curved and/or flat disks, harmonics, and/or a force table are required input. ORBSIM is written in FORTRAN 77 for batch execution and has been implemented on a DEC VAX 11/780 computer operating under VMS. This program was released in 1985.

Monthly gravity field solutions based on GRACE observations generated with the Celestial Mechanics Approach

NASA Astrophysics Data System (ADS)

Meyer, Ulrich; Jäggi, Adrian; Beutler, Gerhard

2012-09-01

The main objective of the Gravity Recovery And Climate Experiment (GRACE) satellite mission consists of determining the temporal variations of the Earth's gravity field. These variations are captured by time series of gravity field models of limited resolution at, e.g., monthly intervals. We present a new time series of monthly models, which was computed with the so-called Celestial Mechanics Approach (CMA), developed at the Astronomical Institute of the University of Bern (AIUB). The secular and seasonal variations in the monthly models are tested for statistical significance. Calibrated errors are derived from inter-annual variations. The time-variable signal can be extracted at least up to degree 60, but the gravity field coefficients of orders above 45 are heavily contaminated by noise. This is why a series of monthly models is computed up to a maximum degree of 60, but only a maximum order of 45. Spectral analysis of the residual time-variable signal shows a distinctive peak at a period of 160 days, which shows up in particular in the C20 spherical harmonic coefficient. Basic filter- and scaling-techniques are introduced to evaluate the monthly models. For this purpose, the variability over the oceans is investigated, which serves as a measure for the noisiness of the models. The models in selected regions show the expected seasonal and secular variations, which are in good agreement with the monthly models of the Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ). The results also reveal a few small outliers, illustrating the necessity for improved data screening. Our monthly models are available at the web page of the International Centre for Global Earth Models (ICGEM).

On the generation of internal wave modes by surface waves

NASA Astrophysics Data System (ADS)

Harlander, Uwe; Kirschner, Ian; Maas, Christian; Zaussinger, Florian

2016-04-01

Internal gravity waves play an important role in the ocean since they transport energy and momentum and the can lead to mixing when they break. Surface waves and internal gravity waves can interact. On the one hand, long internal waves imply a slow varying shear current that modifies the propagation of surface waves. Surface waves generated by the atmosphere can, on the other hand, excite internal waves by nonlinear interaction. Thereby a surface wave packet consisting of two close frequencies can resonate with a low frequency internal wave (Phillips, 1966). From a theoretical point of view, the latter has been studied intensively by using a 2-layer model, i.e. a surface layer with a strong density contrast and an internal layer with a comparable weak density contrast (Ball, 1964; Craig et al., 2010). In the present work we analyse the wave coupling for a continuously stratified fluid using a fully non-linear 2D numerical model (OpenFoam) and compare this with laboratory experiments (see Lewis et al. 1974). Surface wave modes are used as initial condition and the time development of the dominant surface and internal waves are studied by spectral and harmonic analysis. For the simple geometry of a box, the results are compared with analytical spectra of surface and gravity waves. Ball, F.K. 1964: Energy transfer between external and internal gravity waves. J. Fluid Mech. 19, 465. Craig, W., Guyenne, P., Sulem, C. 2010: Coupling between internal and surface waves. Natural Hazards 57, 617-642. Lewis, J.E., Lake, B.M., Ko, D.R.S 1974: On the interaction of internal waves and surfacr gravity waves, J. Fluid Mech. 63, 773-800. Phillips, O.M. 1966: The dynamics of the upper ocean, Cambridge University Press, 336pp.

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

The OSIRIS-REx Radio Science Experiment at Bennu

NASA Astrophysics Data System (ADS)

McMahon, J. W.; Scheeres, D. J.; Hesar, S. G.; Farnocchia, D.; Chesley, S.; Lauretta, D.

2018-02-01

The OSIRIS-REx mission will conduct a Radio Science investigation of the asteroid Bennu with a primary goal of estimating the mass and gravity field of the asteroid. The spacecraft will conduct proximity operations around Bennu for over 1 year, during which time radiometric tracking data, optical landmark tracking images, and altimetry data will be obtained that can be used to make these estimates. Most significantly, the main Radio Science experiment will be a 9-day arc of quiescent operations in a 1-km nominally circular terminator orbit. The pristine data from this arc will allow the Radio Science team to determine the significant components of the gravity field up to the fourth spherical harmonic degree. The Radio Science team will also be responsible for estimating the surface accelerations, surface slopes, constraints on the internal density distribution of Bennu, the rotational state of Bennu to confirm YORP estimates, and the ephemeris of Bennu that incorporates a detailed model of the Yarkovsky effect.

A refined gravity model from Lageos /GEM-L2/

NASA Technical Reports Server (NTRS)

Lerch, F. J.; Klosko, S. M.; Patel, G. B.

1982-01-01

Lageos satellite laser ranging (SLR) data taken over a 2.5 yr period were employed to develop the Goddard Earth Model GEM-L2, a refined gravity field model. Additional data was gathered with 30 other satellites, resulting in spherical harmonics through degree and order 20, based on over 600,000 measurements. The Lageos data was accurate down to 10 cm, after which the GEM 9 data were used to make adjustments past order 7. The resolution of long wavelength activity, through degree and order 4, was made possible by the Lageos data. The GEM-L2 model features a 20 x 20 geopotential, tracking station coordinates (20), 5-day polar motion and A1-UT1 values, and a GM value of 398,600.607 cu km/sq sec. The accuracy of station positioning has been raised to within 6 cm total position globally and within 1.8 cm in baselines. It is concluded that SLR is useful for measuring tectonic plate motions and inter-plate deformations.

On a Continuum Limit for Loop Quantum Cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corichi, Alejandro; Center for Fundamental Theory, Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park PA 16802; Vukasinac, Tatjana

2008-03-06

The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and, in particular, the passage to the limit in which the auxiliary parameter (interpreted as ''quantum geometry discreetness'') is sent to zeromore » in hope to get rid of this 'regulator' that dictates the LQC dynamics at each 'scale'. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator.« less

Influence of Partial Solar Eclipse 2016 on the surface gravity acceleration using photogate sensor on Kater's reversible pendulum

NASA Astrophysics Data System (ADS)

Nugraha, M. G.; Saepuzaman, D.; Sholihat, F. N.; Ramayanti, S.; Setyadin, A. H.; Ferahenki, A. R.; Samsudin, A.; Utama, J. A.; Susanti, H.; Kirana, K. H.

2016-11-01

This study was conducted to determine the Earth's surface gravitational acceleration (g) prior to, during, and after a partial solar eclipse. Data was collected in Basic Physics Laboratory Universitas Pendidikan Indonesia, Bandung with coordinates S 6°51'48", E 107°35'40" for three days on March 8 - 10, 2016, in time interval measurement from 6 a.m. to 9 a.m. This research used a standard pendulum, Kater's reversible pendulum, which deviated less than 3° so that the motion can be regarded harmonics oscillation. The period of pendulum oscillation motion is measured by a light sensor (photogate sensor) with accuracy until 10-13 seconds. The data analysis shows that there is small difference value of gravity acceleration at the Earth's surface from three days of observation, i.e. in the order of 10-3 ms-2. It means, there is a changes in the Earth's surface gravitational acceleration (g) due to the partial solar eclipse but not significant.

The gravity field and interior structure of Enceladus.

PubMed

Iess, L; Stevenson, D J; Parisi, M; Hemingway, D; Jacobson, R A; Lunine, J I; Nimmo, F; Armstrong, J W; Asmar, S W; Ducci, M; Tortora, P

2014-04-04

The small and active Saturnian moon Enceladus is one of the primary targets of the Cassini mission. We determined the quadrupole gravity field of Enceladus and its hemispherical asymmetry using Doppler data from three spacecraft flybys. Our results indicate the presence of a negative mass anomaly in the south-polar region, largely compensated by a positive subsurface anomaly compatible with the presence of a regional subsurface sea at depths of 30 to 40 kilometers and extending up to south latitudes of about 50°. The estimated values for the largest quadrupole harmonic coefficients (10(6)J2 = 5435.2 ± 34.9, 10(6)C22 = 1549.8 ± 15.6, 1σ) and their ratio (J2/C22 = 3.51 ± 0.05) indicate that the body deviates mildly from hydrostatic equilibrium. The moment of inertia is around 0.335MR(2), where M is the mass and R is the radius, suggesting a differentiated body with a low-density core.

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity.

PubMed

Biasi, Anxo F; Mas, Javier; Paredes, Angel

2017-03-01

We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscillations in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in anti de Sitter space where collapse corresponds to black-hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On the one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the other hand, Gross-Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of anti de Sitter instability.

Global excitation of wave phenomena in a dissipative multiconstituent medium. I - Transfer function of the earth's thermosphere. II - Impulsive perturbations in the earth's thermosphere

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Herrero, F. A.; Varosi, F.

1984-01-01

A transfer function approach is taken in constructing a spectral model of the acoustic-gravity wave response in a multiconstituent thermosphere. The model is then applied to describing the thermospheric response to various sources around the globe. Zonal spherical harmonics serve to model the horizontal variations in propagating waves which, when integrated with respect to height, generate a transfer function for a vertical source distribution in the thermosphere. Four wave components are characterized as resonance phenomena and are associated with magnetic activity and ionospheric disturbances. The waves are either trapped or propagate, the latter becoming significant when possessing frequencies above 3 cycles/day. The energy input is distributed by thermospheric winds. The disturbances decay slowly, mainly due to heat conduction and diffusion. Gravity waves appear abruptly and are connected to a sudden switching on or off of a source. Turn off of a source coincides with a reversal of the local atmospheric circulation.

A dynamic model of Venus's gravity field

NASA Technical Reports Server (NTRS)

Kiefer, W. S.; Richards, M. A.; Hager, B. H.; Bills, B. G.

1984-01-01

Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage.

Macromolecular Origins of Harmonics Higher than the Third in Large-Amplitude Oscillatory Shear Flow

NASA Astrophysics Data System (ADS)

Giacomin, Alan; Jbara, Layal; Gilbert, Peter; Chemical Engineering Department Team

2016-11-01

In 1935, Andrew Gemant conceived of the complex viscosity, a rheological material function measured by "jiggling" an elastic liquid in oscillatory shear. This test reveals information about both the viscous and elastic properties of the liquid, and about how these properties depend on frequency. The test gained popularity with chemists when John Ferry perfected instruments for measuring both the real and imaginary parts of the complex viscosity. In 1958, Cox and Merz discovered that the steady shear viscosity curve was easily deduced from the magnitude of the complex viscosity, and today oscillatory shear is the single most popular rheological property measurement. With oscillatory shear, we can control two things: the frequency (Deborah number) and the shear rate amplitude (Weissenberg number). When the Weissenberg number is large, the elastic liquids respond with a shear stress over a series of odd-multiples of the test frequency. In this lecture we will explore recent attempts to deepen our understand of the physics of these higher harmonics, including especially harmonics higher than the third. Canada Research Chairs program of the Government of Canada for the Natural Sciences and Engineering Research Council of Canada (NSERC) Tier 1 Canada Research Chair in Rheology.

Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator

NASA Astrophysics Data System (ADS)

Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan

2018-01-01

The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.

Improved linearity using harmonic error rejection in a full-field range imaging system

NASA Astrophysics Data System (ADS)

Payne, Andrew D.; Dorrington, Adrian A.; Cree, Michael J.; Carnegie, Dale A.

2008-02-01

Full field range imaging cameras are used to simultaneously measure the distance for every pixel in a given scene using an intensity modulated illumination source and a gain modulated receiver array. The light is reflected from an object in the scene, and the modulation envelope experiences a phase shift proportional to the target distance. Ideally the waveforms are sinusoidal, allowing the phase, and hence object range, to be determined from four measurements using an arctangent function. In practice these waveforms are often not perfectly sinusoidal, and in some cases square waveforms are instead used to simplify the electronic drive requirements. The waveforms therefore commonly contain odd harmonics which contribute a nonlinear error to the phase determination, and therefore an error in the range measurement. We have developed a unique sampling method to cancel the effect of these harmonics, with the results showing an order of magnitude improvement in the measurement linearity without the need for calibration or lookup tables, while the acquisition time remains unchanged. The technique can be applied to existing range imaging systems without having to change or modify the complex illumination or sensor systems, instead only requiring a change to the signal generation and timing electronics.

Symmetry-controlled time structure of high-harmonic carrier fields from a solid

PubMed Central

Langer, F.; Hohenleutner, M.; Huttner, U.; Koch, S. W.; Kira, M.; Huber, R.

2017-01-01

High-harmonic (HH) generation in crystalline solids1–6 marks an exciting development, with potential applications in high-efficiency attosecond sources7, all-optical bandstructure reconstruction8,9, and quasiparticle collisions10,11. Although the spectral1–4 and temporal shape5 of the HH intensity has been described microscopically1–6,12, the properties of the underlying HH carrier wave have remained elusive. Here we analyse the train of HH waveforms generated in a crystalline solid by consecutive half cycles of the same driving pulse. Extending the concept of frequency combs13–15 to optical clock rates, we show how the polarization and carrier-envelope phase (CEP) of HH pulses can be controlled by crystal symmetry. For some crystal directions, we can separate two orthogonally polarized HH combs mutually offset by the driving frequency to form a comb of even and odd harmonic orders. The corresponding CEP of successive pulses is constant or offset by π, depending on the polarization. In the context of a quantum description of solids, we identify novel capabilities for polarization- and phase-shaping of HH waveforms that cannot be accessed with gaseous sources. PMID:28572835

Water mass changes inferred by gravity field variations with GRACE

NASA Astrophysics Data System (ADS)

Fagiolini, Elisa; Gruber, Christian; Apel, Heiko; Viet Dung, Nguyen; Güntner, Andreas

2013-04-01

Since 2002 the Gravity Recovery And Climate Experiment (GRACE) mission has been measuring temporal variations of Earth's gravity field depicting with extreme accuracy how mass is distributed and varies around the globe. Advanced signal separation techniques enable to isolate different sources of mass such as atmospheric and oceanic circulation or land hydrology. Nowadays thanks to GRACE, floods, droughts, and water resources monitoring are possible on a global scale. At GFZ Potsdam scientists have been involved since 2000 in the initiation and launch of the GRACE precursor CHAMP satellite mission, since 2002 in the GRACE Science Data System and since 2009 in the frame of ESÁs GOCE High Processing Facility as well as projected GRACE FOLLOW-ON for the continuation of time variable gravity field determination. Recently GFZ has reprocessed the complete GRACE time-series of monthly gravity field spherical harmonic solutions with improved standards and background models. This new release (RL05) already shows significantly less noise and spurious artifacts. In order to monitor water mass re-distribution and fast moving water, we still need to reach a higher resolution in both time and space. Moreover, in view of disaster management applications we need to act with a shorter latency (current latency standard is 2 months). For this purpose, we developed a regional method based on radial base functions that is capable to compute models in regional and global representation. This new method localizes the gravity observation to the closest regions and omits spatial correlations with farther regions. Additionally, we succeeded to increase the temporal resolution to sub-monthly time scales. Innovative concepts such as Kalman filtering and regularization, along with sophisticated regional modeling have shifted temporal and spatial resolution towards new frontiers. We expect global hydrological models as WHGM to profit from such accurate outcomes. First results comparing the mass changes over the Mekong Delta observed with GRACE with spatial explicit hydraulic simulations of the large scale annual inundation volume during the flood season are presented and discussed.

Venus geology, geochemistry, and geophysics - Research results from the USSR

NASA Astrophysics Data System (ADS)

Barsukov, V. L.; Basilevsky, A. T.; Volkov, V. P.; Zharkov, V. N.

The book includes papers on the Venusian volcanism, hot-spot structures, the Lakshmi phenomenon, tesserae, ridge belts on plains, impact craters, evidence on the crustal dichotomy, the global tectonic style, resurfacing, and Venusian igneous rocks. Special attention is given to volatiles in the atmosphere and crust, the expansion of topography into spherical harmonics, rotation, statistical properties of topography and the gravity field, a physical model of Venus, and models of the thermal evolution of Venus. Also presented are an atlas of Venusian surface images and a table listing topographic features on Venus and their coordinates.

The Downward Continuation to the Earth’s Surface of Truncated Spherical and Ellipsoidal Harmonic Series of the Gravity and Height Anomalies,

DTIC Science & Technology

1981-12-01

triangle OBQ, we obtain r c =COtI ose + sine (411) Hence with (4.10) e 2 sinecose (412)tan ip = (__o__2)_ 1 - e 2sin2 0 Pythagoras ’ theorem then easily...coordinate system. Strictly, this theorem tinds no application in our physical world since it guarantees convergence only outside the sphere enclosing...Junq, 1956, p.54 3 ; Moritz, 1980, p.52) is found, using the above theorem , to be f =E, the focal distance of the ellipsoid, shoving also that the

Electrical torques on the electrostatic gyro in the gyro relativity experiment

NASA Technical Reports Server (NTRS)

Eby, P.; Darbo, W.

1980-01-01

A comprehensive discussion and calculation of electrical torques on an electrostatic gyro as they relate to the gyroscope experiment to test general relativity is presented. Drift rates were computed for some typical state of the art rotors, including higher harmonics in the rotor shape. The effect of orbital averaging of gravity gradient forces, roll averaging of torques, and the effect of spin averaging on the effective shape of the rotor were considered. The electrical torques are reduced sufficiently in a low g environment to permit a measurement of the relativistic drifts predicted by general relativity.

Quantum gravity in the Southern Cone Conference. Proceedings. Conference, Bariloche (Argentina), 7 - 10 Jan 1998.

NASA Astrophysics Data System (ADS)

1999-04-01

The following topics are discussed: Black hole formation by canonical dynamics of gravitating shells; canonical quantum gravity; Vassiliev invariants; midisuperspace models; quantum spacetime; large-N limit of superconformal field theories and supergravity; world-volume fields and background coupling of branes; gauge enhancement and chirality changes in nonperturbative orbifold models; chiral p-forms; formally renormalizable gravitationally self-interacting string models; gauge supergravities for all odd dimensions; black hole radiation and S-matrix; primordial black holes; fluctuations in a thermal field and dissipation of a black hole spacetime in far-field limit; adiabatic interpretation of particle creation in a de Sitter universe; nonequilibrium dynamics of quantum fields in inflationary cosmology; magnetic fields in the early Universe; classical regime of a quantum universe obtained through a functional method; decoherence and correlations in semiclassical cosmology; fluid of primordial fluctuations; causal statistical mechanics calculation of initial cosmic entropy and quantum gravity prospects and black hole-D-brane correspondence.

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2017-04-01

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

Gravity model development for TOPEX/POSEIDON: Joint gravity models 1 and 2

NASA Technical Reports Server (NTRS)

Nerem, R. S.; Lerch, F. J.; Marshall, J. A.; Pavlis, E. C.; Putney, B. H.; Tapley, B. D.; Eanes, R. J.; Ries, J. C.; Schutz, B. E.; Shum, C. K.

1994-01-01

The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-1) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being +/- 25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3-4 cm root mean square (RMS), a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

Rosetta at comet 67P/Churyumov-Gerasimenko: Spacecraft orbit modeling

NASA Astrophysics Data System (ADS)

Hahn, Matthias; Paetzold, Martin; Tellmann, Silvia; Haeusler, Bernd; Andert, Thomas

The Rosetta spacecraft has been successfully launched on 2nd March 2004 to its target comet 67P/Churyumov-Gerasimenko. The science objectives of the Rosetta Radio Science Investiga-tions (RSI) experiment addresses fundamental aspects of cometary science such as the deter-minations of the nucleus mass and bulk density, its size and shape, its gravity field and internal structure, and its perturbed interplanetary orbit. The radio carrier links at X-band (8.4 GHz) and S-band (2.3 GHz) between the Rosetta spacecraft and the Earth will be used for these investigations. The motion of the spacecraft will be perturbed near the comet nucleus. The Doppler frequency shifts of the transmitted radio signals can be used to reconstruct the flown orbit. In order to extract small changes of the Doppler frequency, a prediction of the orbit is needed which includes best known estimates for all forces acting on the spacecraft. These forces are the nucleus gravity field, third body perturbations, the solar radiation pressure, the solar wind pressure, the cometary outgassing, etc. It is then possible to determine iteratively low degree and order harmonic coefficients of the nucleus gravity field or the gas pressure force and the gas production rate from outgassing from the differences between the predicted and the observed frequency shifts.

Simple lock-in detection technique utilizing multiple harmonics for digital PGC demodulators.

PubMed

Duan, Fajie; Huang, Tingting; Jiang, Jiajia; Fu, Xiao; Ma, Ling

2017-06-01

A simple lock-in detection technique especially suited for digital phase-generated carrier (PGC) demodulators is proposed in this paper. It mixes the interference signal with rectangular waves whose Fourier expansions contain multiple odd or multiple even harmonics of the carrier to recover the quadrature components needed for interference phase demodulation. In this way, the use of a multiplier is avoided and the efficiency of the algorithm is improved. Noise performance with regard to light intensity variation and circuit noise is analyzed theoretically for both the proposed technique and the traditional lock-in technique, and results show that the former provides a better signal-to-noise ratio than the latter with proper modulation depth and average interference phase. Detailed simulations were conducted and the theoretical analysis was verified. A fiber-optic Michelson interferometer was constructed and the feasibility of the proposed technique is demonstrated.

Clutter suppression and classification using twin inverted pulse sonar in ship wakes.

PubMed

Leighton, T G; Finfer, D C; Chua, G H; White, P R; Dix, J K

2011-11-01

Twin inverted pulse sonar (TWIPS) is here deployed in the wake of a moored rigid inflatable boat (RIB) with propeller turning, and then in the wake of a moving tanker of 4580 dry weight tonnage (the Whitchallenger). This is done first to test its ability to distinguish between scatter from the wake and scatter from the seabed, and second to test its ability to improve detectability of the seabed through the wake, compared to conventional sonar processing techniques. TWIPS does this by distinguishing between linear and nonlinear scatterers and has the further property of distinguishing those nonlinear targets which scatter energy at the even-powered harmonics from those which scatter in the odd-powered harmonics. TWIPS can also, in some manifestations, require no range correction (and therefore does not require the a priori environment knowledge necessary for most remote detection technologies).

Laser under ultrastrong light-matter interaction: Qualitative aspects and quantitative influences by level and mode truncations

NASA Astrophysics Data System (ADS)

Bamba, Motoaki; Ogawa, Tetsuo

2016-03-01

We investigate theoretically the light amplification by stimulated emission of radiation (laser) in the ultrastrong light-matter interaction regime under the two-level and single-mode approximations. The conventional picture of the laser is broken under the ultrastrong interaction. Instead, we must explicitly discuss the dynamics of the electric field and of the magnetic one distinctively, which make the "laser" qualitatively different from the conventional laser. We found that the laser generally accompanies odd-order harmonics of the electromagnetic fields both inside and outside the cavity and a synchronization with an oscillation of atomic population. A bistability is also demonstrated. However, since our model is quite simplified, we got quantitatively different results from the Hamiltonians in the velocity and length forms of the light-matter interaction, while the appearance of the multiple harmonics and the bistability is qualitatively reliable.

On the Application of Euler Deconvolution to the Analytic Signal

NASA Astrophysics Data System (ADS)

Fedi, M.; Florio, G.; Pasteka, R.

2005-05-01

In the last years papers on Euler deconvolution (ED) used formulations that accounted for the unknown background field, allowing to consider the structural index (N) an unknown to be solved for, together with the source coordinates. Among them, Hsu (2002) and Fedi and Florio (2002) independently pointed out that the use of an adequate m-order derivative of the field, instead than the field itself, allowed solving for both N and source position. For the same reason, Keating and Pilkington (2004) proposed the ED of the analytic signal. A function being analyzed by ED must be homogeneous but also harmonic, because it must be possible to compute its vertical derivative, as well known from potential field theory. Huang et al. (1995), demonstrated that analytic signal is a homogeneous function, but, for instance, it is rather obvious that the magnetic field modulus (corresponding to the analytic signal of a gravity field) is not a harmonic function (e.g.: Grant & West, 1965). Thus, it appears that a straightforward application of ED to the analytic signal is not possible because a vertical derivation of this function is not correct by using standard potential fields analysis tools. In this note we want to theoretically and empirically check what kind of error are caused in the ED by such wrong assumption about analytic signal harmonicity. We will discuss results on profile and map synthetic data, and use a simple method to compute the vertical derivative of non-harmonic functions measured on a horizontal plane. Our main conclusions are: 1. To approximate a correct evaluation of the vertical derivative of a non-harmonic function it is useful to compute it with finite-difference, by using upward continuation. 2. We found that the errors on the vertical derivative computed as if the analytic signal was harmonic reflects mainly on the structural index estimate; these errors can mislead an interpretation even though the depth estimates are almost correct. 3. Consistent estimates of depth and S.I. are instead obtained by using a finite-difference vertical derivative of the analytic signal. 4. Analysis of a case history confirms the strong error in the estimation of structural index if the analytic signal is treated as an harmonic function.

Cosmological rotating black holes in five-dimensional fake supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nozawa, Masato; Maeda, Kei-ichi; Waseda Research Institute for Science and Engineering, Okubo 3-4-1, Shinjuku, Tokyo 169-8555

2011-01-15

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order 'Killing spinor'more » equation in 'fake supergravity' coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial 'Killing spinor', which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.« less

Biomechanical analysis of INFINITY rehabilitation method for treatment of low back pain

PubMed Central

Daniel, Matej; Tomanová, Michaela; Hornová, Jana; Novotná, Iva; Lhotská, Lenka

2017-01-01

[Purpose] Low back pain is a pervasive problem in modern societies. Physical rehabilitation in treatment of low back pain should reduce pain, muscle tension and restore spine stability and balance. The INFINITY® rehabilitation method that is based on a figure of eight movement pattern was proved to be effective in low back pain treatment. The aim of the paper is to estimate the effect of a figure of eight motion on the L5/S1 load and lumbar spine muscle activation in comparison to other motion patterns. [Subjects and Methods] Three-dimensional model of lumbar spine musculoskeletal system is used to simulate effect of various load motion pattern induced by displacement of the center of gravity of the upper body. Four motion patterns were examined: lateral and oblique pendulum-like motion, elliptical motion and figure of eight motion. [Results] The simple pendulum-like and elliptical-like patterns induce harmonic muscle activation and harmonic spinal load. The figure of eight motion pattern creates high-frequency spinal loading that activates remodeling of bones and tendons. The figure of eight pattern also requires muscle activity that differs from harmonic frequency and is more demanding on muscle control and could also improve muscle coordination. [Conclusion] The results of the study indicate that complex motion pattern during INFINITY® rehabilitation might enhance the spine stability by influencing its passive, active and neural components. PMID:28603355

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

PubMed Central

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-01

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer’s Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26-cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients. PMID:28033119

Mars Gravity Field and Upper Atmosphere from MGS, Mars Odyssey, and MRO

NASA Astrophysics Data System (ADS)

Genova, A.; Goossens, S. J.; Lemoine, F. G.; Mazarico, E.; Neumann, G. A.; Smith, D. E.; Zuber, M. T.

2015-12-01

The NASA orbital missions Mars Global Surveyor (MGS), Mars Odyssey (ODY), and Mars Reconnaissance Orbiter (MRO) have been exploring and monitoring the planet Mars since 1997. MGS executed its mapping mission between 1999 and 2006 in a frozen sun-synchronous, near-circular, polar orbit with the periapsis altitude at ~370 km and the dayside equatorial crossing at 2 pm Local Solar Time (LST). The spacecraft was equipped with onboard instrumentation to acquire radio science data and to measure spacecraft ranges to the Martian surface (Mars Orbiter Laser Altimeter). These measurements resulted in static and time-varying gravity field and high-resolution global topography of the planet. ODY and MRO are still orbiting about Mars in two different sun-synchronous orbits, providing radio tracking data that indirectly measure both the static and time-varying gravity field and the atmospheric density. The orbit of ODY has its periapsis at ~390 km altitude and descending node at 4-5 pm LST. However, the spacecraft also collected measurements at lower altitudes (~220 km) in 2002 prior to the mapping phase. Since November 2006, MRO is in a low-altitude orbit with a periapsis altitude of 255 km and descending node at 3 pm LST. Radio data from MRO help improve the resolution of the static gravity field and measure the mass distribution of the polar caps, but the atmospheric drag at those altitudes may limit the benefits of these radio tracking observations. We present a combined solution of the Martian gravity field to degree and order 110 and atmospheric density profiles with radio tracking data from MGS, ODY and MRO. The gravity field solution is combined with the MOLA topography yielding an updated map of Mars crustal thickness. We also show our solution of the Love number k2 and time-variable gravity zonal harmonics (C20 and C30, in particular). The recovered atmospheric density profiles may be used in atmospheric models to constrain the long-term variability of the constituents in the upper atmosphere.

Measurement and Interpretation of Temporal Variations of the Earths Gravity Field Using GPS and SLR Data

NASA Technical Reports Server (NTRS)

Nerem, R. Steven; Leuliette, Eric; Russell, Gary

2003-01-01

This investigation has had four main thrusts: 1) The analysis of seasonal variations of the Earth's gravitational field using Lageos 1 and 2 SLR data and comparisons to geophysical models. We have estimated the annual variation of the gravity field via a spherical harmonic expansion complete to degree and order 4. We have also constructed a similar model using models of the annual variation in the gravity field due to atmospheric, hydrologic, and ocean mass redistribution. These three models, when combined together, are in excellent agreement with the variations observed by satellite laser ranging. An article on these results was published in the journal Geophysical Research Letters. 2) The second thrust of our investigation has been to analyze the output of a Global Climate Model (GCM) to determine if the GRACE gravity mission can be expected to detect climate change signals. Working with Gary Russell at the Goddard Institute for Space Studies (GISS), we have determined that there are several large secular signals that GRACE might be able to detect, including secular changes in snow cover, sea ice, polar ice, ocean mass, and other variables. It is possible that some of these signals could be detected with 5 years of GRACE measurements - its hard to judge this because the interannual variability in the GCM, which could mask the climate signals, is unreliable. Certainly a follow-on GRACE mission could detect these signals when compared to the data from the initial GRACE mission.). An article on these results will be published in the journal Journal of Geophysical Research. 3) In the last year of the investigation, we developed a new technique for analyzing temporal gravity variations using "geophysical fingerprints", which was successfully demonstrated on 20 years of satellite laser ranging data [Nerem et al., 20031. 4]. We also participated in a workshop on future satellite gravity measurements, which resulted in paper on measuring ocean mass variations using GRACE [Nerem et al., 20031 and on using laser interferometry for future gravity missions [Bender et al., 20031].

Determination of Eros Physical Parameters for Near Earth Asteroid Rendezvous Orbit Phase Navigation

NASA Technical Reports Server (NTRS)

Miller, J. K.; Antreasian, P. J.; Georgini, J.; Owen, W. M.; Williams, B. G.; Yeomans, D. K.

1995-01-01

Navigation of the orbit phase of the Near Earth steroid Rendezvous (NEAR) mission will re,quire determination of certain physical parameters describing the size, shape, gravity field, attitude and inertial properties of Eros. Prior to launch, little was known about Eros except for its orbit which could be determined with high precision from ground based telescope observations. Radar bounce and light curve data provided a rough estimate of Eros shape and a fairly good estimate of the pole, prime meridian and spin rate. However, the determination of the NEAR spacecraft orbit requires a high precision model of Eros's physical parameters and the ground based data provides only marginal a priori information. Eros is the principal source of perturbations of the spacecraft's trajectory and the principal source of data for determining the orbit. The initial orbit determination strategy is therefore concerned with developing a precise model of Eros. The original plan for Eros orbital operations was to execute a series of rendezvous burns beginning on December 20,1998 and insert into a close Eros orbit in January 1999. As a result of an unplanned termination of the rendezvous burn on December 20, 1998, the NEAR spacecraft continued on its high velocity approach trajectory and passed within 3900 km of Eros on December 23, 1998. The planned rendezvous burn was delayed until January 3, 1999 which resulted in the spacecraft being placed on a trajectory that slowly returns to Eros with a subsequent delay of close Eros orbital operations until February 2001. The flyby of Eros provided a brief glimpse and allowed for a crude estimate of the pole, prime meridian and mass of Eros. More importantly for navigation, orbit determination software was executed in the landmark tracking mode to determine the spacecraft orbit and a preliminary shape and landmark data base has been obtained. The flyby also provided an opportunity to test orbit determination operational procedures that will be used in February of 2001. The initial attitude and spin rate of Eros, as well as estimates of reference landmark locations, are obtained from images of the asteroid. These initial estimates are used as a priori values for a more precise refinement of these parameters by the orbit determination software which combines optical measurements with Doppler tracking data to obtain solutions for the required parameters. As the spacecraft is maneuvered; closer to the asteroid, estimates of spacecraft state, asteroid attitude, solar pressure, landmark locations and Eros physical parameters including mass, moments of inertia and gravity harmonics are determined with increasing precision. The determination of the elements of the inertia tensor of the asteroid is critical to spacecraft orbit determination and prediction of the asteroid attitude. The moments of inertia about the principal axes are also of scientific interest since they provide some insight into the internal mass distribution. Determination of the principal axes moments of inertia will depend on observing free precession in the asteroid's attitude dynamics. Gravity harmonics are in themselves of interest to science. When compared with the asteroid shape, some insight may be obtained into Eros' internal structure. The location of the center of mass derived from the first degree harmonic coefficients give a direct indication of overall mass distribution. The second degree harmonic coefficients relate to the radial distribution of mass. Higher degree harmonics may be compared with surface features to gain additional insight into mass distribution. In this paper, estimates of Eros physical parameters obtained from the December 23,1998 flyby will be presented. This new knowledge will be applied to simplification of Eros orbital operations in February of 2001. The resulting revision to the orbit determination strategy will also be discussed.

Associations between paternal urinary phthalate metabolite concentrations and reproductive outcomes among couples seeking fertility treatment

PubMed Central

Dodge, LE; Williams, PL; Williams, MA; Missmer, SA; Souter, I; Calafat, AM; Hauser, R

2015-01-01

INTRODUCTION Limited evidence suggests that male exposure to ubiquitous environmental phthalates may result in poor reproductive outcomes among female partners. METHODS This analysis included male-female couples undergoing in vitro fertilization (IVF) and/or intrauterine insemination (IUI). We evaluated associations between the geometric mean of paternal specific gravity-adjusted urinary phthalate concentrations prior to the female partners’ cycle and fertilization, embryo quality, implantation, and live birth using generalized linear mixed models. RESULTS Two-hundred eighteen couples underwent 211 IVF and 195 IUI cycles. Trends were observed between paternal urinary mono-3-carboxypropyl phthalate (MCPP; P=0.01) and mono(carboxyoctyl) phthalate (MCOP; P=0.01) and decreased odds of implantation. MCPP and MCOP were also associated with decreased odds of live birth following IVF (P=0.01 and P=0.04, respectively), and monobutyl phthalate above the first quartile was significantly associated with decreased odds of live birth following IUI (P=0.04). However, most urinary phthalate metabolites were not associated with these reproductive outcomes. CONCLUSION Selected phthalates were associated with decreased odds of implantation and live birth. PMID:26456810

High-Precision Simulation of the Gravity Field of Rapidly-Rotating Barotropes in Hydrostatic Equilibrium

NASA Astrophysics Data System (ADS)

Hubbard, W. B.

2013-12-01

The so-called theory of figures (TOF) uses potential theory to solve for the structure of highly distorted rotating liquid planets in hydrostatic equilibrium. TOF is noteworthy both for its antiquity (Maclaurin 1742) and its mathematical complexity. Planned high-precision gravity measurements near the surfaces of Jupiter and Saturn (possibly detecting signals ~ microgal) will place unprecedented requirements on TOF, not because one expects hydrostatic equilibrium to that level, but because nonhydrostatic components in the surface gravity, at expected levels ~ 1 milligal, must be referenced to precise hydrostatic-equilibrium models. The Maclaurin spheroid is both a useful test of numerical TOF codes (Hubbard 2012, ApJ Lett 756:L15), and an approach to an efficient TOF code for arbitrary barotropes of variable density (Hubbard 2013, ApJ 768:43). For the latter, one trades off vertical resolution by replacing a continuous barotropic pressure-density relation with a stairstep relation, corresponding to N concentric Maclaurin spheroids (CMS), each of constant density. The benefit of this trade-off is that two-dimensional integrals over the mass distributions at each interface are reduced to one-dimensional integrals, quickly and accurately evaluated by Gaussian quadrature. The shapes of the spheroids comprise N level surfaces within the planet and at its surface, are gravitationally coupled to each other, and are found by self-consistent iteration, relaxing to a final configuration to within the computer's precision limits. The angular and radial variation of external gravity (using the usual geophysical expansion in multipole moments) can be found to the limit of typical floating point precision (~ 1.e-14), much better than the expected noise/signal for either the Juno or Cassini gravity experiments. The stairstep barotrope can be adjusted to fit a prescribed continuous or discontinuous interior barotrope, and can be made to approximate it to any required precision by increasing N. One can insert a higher density of CMSs toward the surface of an interior model in order to more accurately model high-order gravitational moments. The magnitude of high-order moments predicted by TOF declines geometrically with order number, and falls below the magnitude of expected non-hydrostatic terms produced by interior dynamics at ~ order 10 and above. Juno's sensitivity is enough to detect tidal gravity signals from Galilean satellites. The CMS method can be generalized to predict tidal zonal and tesseral terms consistent with an interior model fitted to measured zonal harmonics. For this purpose, two-dimensional Gaussian quadrature is necessary at each CMS interface. However, once the model is relaxed to equilibrium, one need not refit the model to the average zonal harmonics because of the smallness of the tidal terms. I will describe how the CMS method has been validated through comparisons with standard TOF models for which fully or partially analytic solutions exist, as well as through consistency checks. At this stage in software development in preparation for Jupiter orbit, we are focused on increasing the speed of the code in order to more efficiently search the parameter space of acceptable Jupiter interior models, as well as to interface it with advanced hydrogen-helium equations of state.

Heterogeneity of the North Atlantic oceanic lithosphere based on integrated analysis of GOCE satellite gravity and geological data

NASA Astrophysics Data System (ADS)

Barantseva, Olga; Artemieva, Irina; Thybo, Hans; Herceg, Matija

2015-04-01

We present the results from modelling the gravity and density structure of the upper mantle for the off-shore area of the North Atlantic region. The crust and upper mantle of the region is expected to be anomalous: Part of the region affected by the Icelandic plume has an anomalously shallow bathymetry, whereas the northern part of the region is characterized by ultraslow spreading. In order to understand the links between deep geodynamical processes that control the spreading rate, on one hand, and their manifestations such as oceanic floor bathymetry and heat flow, on the other hand, we model the gravity and density structure of the upper mantle from satellite gravity data. The calculations are based on interpretation of GOCE gravity satellite data for the North Atlantics. To separate the gravity signal responsible for density anomalies within the crust and upper mantle, we subtract the lower harmonics caused by deep density structure of the Earth (the core and the lower mantle). The gravity effect of the upper mantle is calculated by subtracting the gravity effect of the crust for two crustal models. We use a recent regional seismic model for the crustal structure (Artemieva and Thybo, 2013) based om seismic data together with borehole data for sediments. For comparison, similar results are presented for the global CRUST 1.0 model as well (Laske, 2013). The conversion of seismic velocity data for the crustal structure to crustal density structure is crucial for the final results. We use a combination of Vp-to-density conversion based on published laboratory measurements for the crystalline basement (Ludwig, Nafe, Drake, 1970; Christensen and Mooney, 1995) and for oceanic sediments and oceanic crust based on laboratory measurements for serpentinites and gabbros from the Mid-Atlantic Ridge (Kelemen et al., 2004). Also, to overcome the high degree of uncertainty in Vp-to-density conversion, we account for regional tectonic variations in the Northern Atlantics as constrained by numerous published seismic profiles and potential-field models across the Norwegian off-shore crust (e.g. Breivik et al., 2005, 2007). The results demonstrate the presence of strong gravity and density heterogeneity of the upper mantle in the North Atlantic region. In particular, there is a sharp contrast at the continent-ocean transition, which also allows for recognising mantle gravity anomalies associated with continental fragments and with anomalous oceanic lithosphere.

Estimating lithospheric properties at Atla Regio, Venus

NASA Technical Reports Server (NTRS)

Phillips, Roger J.

1994-01-01

Magellan spehrical harmonic gravity and topography models are used to estimate lithospheric properties at Alta Regio, Venus, a proposed hotspot with dynamic support from mantle plume(s). Global spherical harmonic and local representations of the gravity field share common properties in the Atla region interms of their spectral behavior over a wavelength band from approximately 2100 to approximately 700 km. The estimated free-air admittance spectrum displays a rather featureless long-wavelength portion followed by a sharp rise at wavelengths shorter than about 1000 km. This sharp rise requires significant flexural support of short-wavelength structures. The Bouguer coherence also displays a sharp drop in this wavelength band, indicating a finite flexural rigidity of the lithosphere. A simple model for lithospheric loading from above and below is introduced (D. W. Forsyth, 1985) with four parameters: f, the ratio of bottom loading to top loading; z(sub m), crustal thickness; z(sub l) depth to bottom loading source; and T(sub e) elastic lithosphere thickness. A dual-mode compensation model is introduced in which the shorter wavelengths (lambda approximately less than 1000 km) might be explained best by a predominance of top loading by the large shield volcanoes Maat Mons, Ozza Mons, and Sapas Mons, and the longer wavelengths (lambda approximately greater than 1500 km) might be explained best by a deep depth of compensation, possibly representing bottom loading by a dynamic source. A Monte Carlo inversion technique is introduced to thoroughly search out the four-space of the model parameters and to examine parameter correlation in the solutions. Venus either is a considerabe deficient in heat sources relative to Earth, or the thermal lithosphere is overthickened in response to an earlier episode of significant heat loss from the planet.

Isostatic compensation of equatorial highlands on Venus

NASA Technical Reports Server (NTRS)

Kucinskas, Algis B.; Turcotte, Donald L.

1994-01-01

Spherical harmonic models for Venus' global topography and gravity incorporating Magellan data are used to test isostatic compensation models in five 30 deg x 30 deg regions representative of the main classes of equatorial highlands. The power spectral density for the harmonic models obeys a power-law scaling with spectral slope Beta approximately 2 (Brown noise) for the topography and Beta approximately 3 (Kaula's law) for the geoid, similar to what is observed for Earth. The Venus topography spectrum has lower amplitudes than Earth's which reflects the dominant lowland topography on Venus. Observed degree geoid to topography ratios (GTRs) on Venus are significantly smaller than degree GTRs for uncompensated topography, indicative of substantial compensation. Assuming a global Airy compensation, most of the topography is compensated at depths greater than 100 km, suggesting a thick lithosphere on Venus. For each region considered we obtain a regional degree of compensation C from a linear regression of Bouguer anomaly versus Bouguer gravity data. Geoid anomaly (N) versus topography variation (h) data for each sample were compared, in the least-squares sense, to theoretical correlations for Pratt, Airy, and thermal thinning isostasy models yielding regional GTR, zero-elevation crustal thickness (H), and zero elevation thermal lithosphere thickness (y(sub L(sub 0)), respectively. We find the regional compensation to be substantial (C approximately 52-80%), and the h, N data correlations in the chosen areas can be explained by isostasy models applicable on the Earth and involving variations in crustal thickness (Airy) and/or lithospheric (thermal thinning) thickness. However, a thick crust and lithosphere (y(sub L(sub 0)) approximately 300 km) must be assumed for Venus.

Influence of parameterized small-scale gravity waves on the migrating diurnal tide in Earth's thermosphere

NASA Astrophysics Data System (ADS)

Yiǧit, Erdal; Medvedev, Alexander S.

2017-04-01

Effects of subgrid-scale gravity waves (GWs) on the diurnal migrating tides are investigated from the mesosphere to the upper thermosphere for September equinox conditions, using a general circulation model coupled with the extended spectral nonlinear GW parameterization of Yiğit et al. (). Simulations with GW effects cut off above the turbopause and included in the entire thermosphere have been conducted. GWs appreciably impact the mean circulation and cool the thermosphere down by up to 12-18%. GWs significantly affect the winds modulated by the diurnal migrating tide, in particular, in the low-latitude mesosphere and lower thermosphere and in the high-latitude thermosphere. These effects depend on the mutual correlation of the diurnal phases of the GW forcing and tides: GWs can either enhance or reduce the tidal amplitude. In the low-latitude MLT, the correlation between the direction of the deposited GW momentum and the tidal phase is positive due to propagation of a broad spectrum of GW harmonics through the alternating winds. In the Northern Hemisphere high-latitude thermosphere, GWs act against the tide due to an anticorrelation of tidal wind and GW momentum, while in the Southern high-latitudes they weakly enhance the tidal amplitude via a combination of a partial correlation of phases and GW-induced changes of the circulation. The variable nature of GW effects on the thermal tide can be captured in GCMs provided that a GW parameterization (1) considers a broad spectrum of harmonics, (2) properly describes their propagation, and (3) correctly accounts for the physics of wave breaking/saturation.

Long-term and seasonal Caspian Sea level change from satellite gravity and altimeter measurements

NASA Astrophysics Data System (ADS)

Chen, J. L.; Wilson, C. R.; Tapley, B. D.; Save, H.; Cretaux, Jean-Francois

2017-03-01

We examine recent Caspian Sea level change by using both satellite radar altimetry and satellite gravity data. The altimetry record for 2002-2015 shows a declining level at a rate that is approximately 20 times greater than the rate of global sea level rise. Seasonal fluctuations are also much larger than in the world oceans. With a clearly defined geographic region and dominant signal magnitude, variations in the sea level and associated mass changes provide an excellent way to compare various approaches for processing satellite gravity data. An altimeter time series derived from several successive satellite missions is compared with mass measurements inferred from Gravity Recovery and Climate Experiment (GRACE) data in the form of both spherical harmonic (SH) and mass concentration (mascon) solutions. After correcting for spatial leakage in GRACE SH estimates by constrained forward modeling and accounting for steric and terrestrial water processes, GRACE and altimeter observations are in complete agreement at seasonal and longer time scales, including linear trends. This demonstrates that removal of spatial leakage error in GRACE SH estimates is both possible and critical to improving their accuracy and spatial resolution. Excellent agreement between GRACE and altimeter estimates also provides confirmation of steric Caspian Sea level change estimates. GRACE mascon estimates (both the Jet Propulsion Laboratory (JPL) coastline resolution improvement version 2 solution and the Center for Space Research (CSR) regularized) are also affected by leakage error. After leakage corrections, both JPL and CSR mascon solutions also agree well with altimeter observations. However, accurate quantification of leakage bias in GRACE mascon solutions is a more challenging problem.

Methods for removal of unwanted signals from gravity time-series: Comparison using linear techniques complemented with analysis of system dynamics

NASA Astrophysics Data System (ADS)

Valencio, Arthur; Grebogi, Celso; Baptista, Murilo S.

2017-10-01

The presence of undesirable dominating signals in geophysical experimental data is a challenge in many subfields. One remarkable example is surface gravimetry, where frequencies from Earth tides correspond to time-series fluctuations up to a thousand times larger than the phenomena of major interest, such as hydrological gravity effects or co-seismic gravity changes. This work discusses general methods for the removal of unwanted dominating signals by applying them to 8 long-period gravity time-series of the International Geodynamics and Earth Tides Service, equivalent to the acquisition from 8 instruments in 5 locations representative of the network. We compare three different conceptual approaches for tide removal: frequency filtering, physical modelling, and data-based modelling. Each approach reveals a different limitation to be considered depending on the intended application. Vestiges of tides remain in the residues for the modelling procedures, whereas the signal was distorted in different ways by the filtering and data-based procedures. The linear techniques employed were power spectral density, spectrogram, cross-correlation, and classical harmonics decomposition, while the system dynamics was analysed by state-space reconstruction and estimation of the largest Lyapunov exponent. Although the tides could not be completely eliminated, they were sufficiently reduced to allow observation of geophysical events of interest above the 10 nm s-2 level, exemplified by a hydrology-related event of 60 nm s-2. The implementations adopted for each conceptual approach are general, so that their principles could be applied to other kinds of data affected by undesired signals composed mainly by periodic or quasi-periodic components.

Nocturnal Air Seiches in the Arizona Meteor Crater

NASA Astrophysics Data System (ADS)

Muschinski, A.; Fritts, D. C.; Zhong, S.; Oncley, S. P.

2011-12-01

The Arizona Meteor Crater near Winslow, AZ is 170 m deep, has a diameter of 1.2 km, and it has a nearly circular shape. The motivation of the Meteor Crater Experiment (METCRAX), conducted in October 2006, was to use the Meteor Crater as a natural laboratory to study atmospheric phenomena that are typical for small basins. Among other observations, high-resolution wind, temperature and pressure measurements were collected with sonics and microbarometers, respectively, during the entire month. The sensors were mounted between 0.5 m and 8.5 m AGL on seven portable towers, five of which were located within the crater and two on the crater rim. Here we report observations of nocturnal air seiches, that is, standing gravity waves associated with the time-harmonic sloshing of the cold-air pool that forms at the bottom of the crater due to radiative cooling at night. We present time series, spectra, and spectrograms of temperature, wind and pressure fluctuations that characterize those air seiches. Typical seiche periods were 15 min. We compare the observations with the time-harmonic solutions of the shallow-water equation and with numerical simulations.

Evaluation of Rotor Structural and Aerodynamic Loads using Measured Blade Properties

NASA Technical Reports Server (NTRS)

Jung, Sung N.; You, Young-Hyun; Lau, Benton H.; Johnson, Wayne; Lim, Joon W.

2012-01-01

The structural properties of Higher harmonic Aeroacoustic Rotor Test (HART I) blades have been measured using the original set of blades tested in the wind tunnel in 1994. A comprehensive rotor dynamics analysis is performed to address the effect of the measured blade properties on airloads, blade motions, and structural loads of the rotor. The measurements include bending and torsion stiffness, geometric offsets, and mass and inertia properties of the blade. The measured properties are correlated against the estimated values obtained initially by the manufacturer of the blades. The previously estimated blade properties showed consistently higher stiffnesses, up to 30% for the flap bending in the blade inboard root section. The measured offset between the center of gravity and the elastic axis is larger by about 5% chord length, as compared with the estimated value. The comprehensive rotor dynamics analysis was carried out using the measured blade property set for HART I rotor with and without HHC (Higher Harmonic Control) pitch inputs. A significant improvement on blade motions and structural loads is obtained with the measured blade properties.

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: Numerical method of studying nonlinear interactions between long waves and multiple short waves

NASA Astrophysics Data System (ADS)

Xie, Tao; Kuang, Hai-Lan; William, Perrie; Zou, Guang-Hui; Nan, Cheng-Feng; He, Chao; Shen, Tao; Chen, Wei

2009-07-01

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.

Generalized Gödel universes in higher dimensions and pure Lovelock gravity

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Molina, Alfred; Pons, Josep M.

2017-10-01

The Gödel universe is a homogeneous rotating dust with negative Λ which is a direct product of a three-dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity with only one N th-order term. For higher-dimensional generalization, we have to include more rotations in the metric, and hence we shall begin with the corresponding pure rotation odd (d =2 n +1 )-dimensional metric involving n rotations, which eventually can be extended by a direct product with a line or a space of constant curvature for yielding a higher-dimensional Gödel universe. The considerations of n rotations and also of constant curvature spaces is a new line of generalization and is being considered for the first time.

Controlling plasma properties under differing degrees of electronegativity using odd harmonic dual frequency excitation

NASA Astrophysics Data System (ADS)

Gibson, Andrew R.; Gans, Timo

2017-11-01

The charged particle dynamics in low-pressure oxygen plasmas excited by odd harmonic dual frequency waveforms (low frequency of 13.56 MHz and high frequency of 40.68 MHz) are investigated using a one-dimensional numerical simulation in regimes of both low and high electronegativity. In the low electronegativity regime, the time and space averaged electron and negative ion densities are approximately equal and plasma sustainment is dominated by ionisation at the sheath expansion for all combinations of low and high frequency and the phase shift between them. In the high electronegativity regime, the negative ion density is a factor of 15-20 greater than the low electronegativity cases. In these cases, plasma sustainment is dominated by ionisation inside the bulk plasma and at the collapsing sheath edge when the contribution of the high frequency to the overall voltage waveform is low. As the high frequency component contribution to the waveform increases, sheath expansion ionisation begins to dominate. It is found that the control of the average voltage drop across the plasma sheath and the average ion flux to the powered electrode are similar in both regimes of electronegativity, despite the differing electron dynamics using the considered dual frequency approach. This offers potential for similar control of ion dynamics under a range of process conditions, independent of the electronegativity. This is in contrast to ion control offered by electrically asymmetric waveforms where the relationship between the ion flux and ion bombardment energy is dependent upon the electronegativity.

Unimodular Gravity and General Relativity UV divergent contributions to the scattering of massive scalar particles

NASA Astrophysics Data System (ADS)

Gonzalez-Martin, S.; Martin, C. P.

2018-01-01

We work out the one-loop and order κ2 mphi2 UV divergent contributions, coming from Unimodular Gravity and General Relativity, to the S matrix element of the scattering process phi + phi→ phi + phi in a λ phi4 theory with mass mphi. We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contributions in Dimensional Regularization. This seems to be at odds with the known result that in a multiplicative MS dimensional regularization scheme the General Relativity corrections, in the de Donder gauge, to the beta function, βλ, of the λ coupling do not vanish, whereas the Unimodular Gravity corrections, in a certain gauge, do vanish. Actually, by comparing the UV divergent contributions calculated in this paper with those which give rise to the non-vanishing gravitational corrections to βλ, one readily concludes that the UV divergent contributions that yield the just mentioned non-vanishing gravitational corrections to βλ do not contribute to the UV divergent behaviour of the S matrix element of phi + phi→ phi + phi. This shows that any physical consequence—such as the existence of asymptotic freedom due to gravitational interactions—drawn from the value of βλ is not physically meaningful.

Quantum statistical relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miskovic, Olivera; Olea, Rodrigo

2011-03-15

We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of a Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics. These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti-de Sitter/conformal field theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy of the system, manifested as the vacuum energy for global AdS spacetime in odd dimensions. Because of this reason, wemore » derive a quantum statistical relation directly from the Euclidean action and not from the integration of the first law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists, in addition to the bulk action, of counterterms that depend on both extrinsic and intrinsic curvatures of the boundary (Kounterterm series). This procedure results in a consistent inclusion of the vacuum energy and chemical potential in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless of the explicit form of the nonlinear electrodynamics Lagrangian.« less

Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.

A solution of the geodetic boundary value problem to order e3

NASA Technical Reports Server (NTRS)

Mather, R. S.

1973-01-01

A solution is obtained for the geodetic boundary value problem which defines height anomalies to + or - 5 cm, if the earth were rigid. The solution takes into account the existence of the earth's topography, together with its ellipsoidal shape and atmosphere. A relation is also established between the commonly used solution of Stokes and a development correct to order e cubed. The data requirements call for a complete definition of gravity anomalies at the surface of the earth and a knowledge of elevation characteristics at all points exterior to the geoid. In addition, spherical harmonic representations must be based on geocentric rather than geodetic latitudes.

Comments on X. Yin, A. Wen, Y. Chen, and T. Wang, `Studies in an optical millimeter-wave generation scheme via two parallel dual-parallel Mach-Zehnder modulators', Journal of Modern Optics, 58(8), 2011, pp. 665-673

NASA Astrophysics Data System (ADS)

Hasan, Mehedi; Maldonado-Basilio, Ramón; Hall, Trevor J.

2015-04-01

Yin et al. have described an innovative filter-less optical millimeter-wave generation scheme for octotupling of a 10 GHz RF oscillator, or sedecimtupling of a 5 GHz RF oscillator using two parallel dual-parallel Mach-Zehnder modulators (DP-MZMs). The great merit of their design is the suppression of all harmonics except those of order ? (octotupling) or all harmonics except those of order ? (sedecimtupling), where ? is an integer. A demerit of their scheme is the requirement to set a precise RF signal modulation index in order to suppress the zeroth order optical carrier. The purpose of this comment is to show that, in the case of the octotupling function, all harmonics may be suppressed except those of order ?, where ? is an odd integer, by the simple addition of an optical ? phase shift between the two DP-MZMs and an adjustment of the RF drive phases. Since the carrier is suppressed in the modified architecture, the octotupling circuit is thereby released of the strict requirement to set the drive level to a precise value without any significant increase in circuit complexity.

An Approximate Model for the Performance and Acoustic Predictions of Counterrotating Propeller Configurations. M.S. Thesis

NASA Technical Reports Server (NTRS)

Denner, Brett William

1989-01-01

An approximate method was developed to analyze and predict the acoustics of a counterrotating propeller configuration. The method employs the analytical techniques of Lock and Theodorsen as described by Davidson to predict the steady performance of a counterrotating configuration. Then, a modification of the method of Lesieutre is used to predict the unsteady forces on the blades. Finally, the steady and unsteady loads are used in the numerical method of Succi to predict the unsteady acoustics of the propeller. The numerical results are compared with experimental acoustic measurements of a counterrotating propeller configuration by Gazzaniga operating under several combinations of advance ratio, blade pitch, and number of blades. In addition, a constant-speed commuter-class propeller configuration was designed with the Davidson method and the acoustics analyzed at three advance ratios. Noise levels and frequency spectra were calculated at a number of locations around the configuration. The directivity patterns of the harmonics in both the horizontal and vertical planes were examined, with the conclusion that the noise levels of the even harmonics are relatively independent of direction whereas the noise levels of the odd harmonics are extremely dependent on azimuthal direction in the horizontal plane. The equations of Succi are examined to explain this behavior.

Investigation of an Ultrafast Harmonic Resonant RF Kicker

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Yulu

An Energy Recovery Linac (ERL) based multi-turn electron Circulator Cooler Ring (CCR) is envisaged in the proposed Jefferson Lab Electron Ion Collider (JLEIC) to cool the ion bunches with high energy (55 MeV), high current (1.5 A), high repetition frequency (476.3 MHz), high quality magnetized electron bunches. A critical component in this scheme is a pair of ultrafast kickers for the exchange of electron bunches between the ERL and the CCR. The ultrafast kicker should operate with the rise and fall time in less than 2.1 ns, at the repetition rate of ~10s MHz, and should be able to runmore » continuously during the whole period of cooling. These -and-fall time being combined together, are well beyond the state-of-art of traditional pulsed power supplies and magnet kickers. To solve this technical challenge, an alternative method is to generate this high repetition rate, fast rise-and-fall time short pulse continuous waveform by summing several finite number of (co)sine waves at harmonic frequencies of the kicking repetition frequency, and these harmonic modes can be generated by the Quarter Wave Resonater (QWR) based multifrequency cavities. Assuming the recirculator factor is 10, 10 harmonic modes (from 47.63 MHz to 476.3 MHz) with proper amplitudes and phases, plus a DC offset are combined together, a continuous short pulse waveform with the rise-and-fall time in less than 2.1 ns, repetition rate of 47.63 MHz waveform can be generated. With the compact and matured technology of QWR cavities, the total cost of both hardware development and operation can be reduced to a modest level. Focuse on the technical scheme, three main topics will be discussed in this thesis: the synthetization of the kicking pulse, the design and optimization of the deflecting QWR multi-integer harmonic frequency resonator and the fabrication and bench measurements of a half scale copper prototype. In the kicking pulse synthetization part, we begin with the Fourier Series expansion of an ideal square pulse, and get a Flat-Top waveform which will give a uniform kick over the bunch length of the kicked electron bunches, thus the transverse emittance of these kicked electron bunches can be maintained. By using two identical kickers with the betatron phase advance of 180 degree or its odd multiples, the residual kick voltage wave slopes at the unkicked bunch position will be totally cancelled out. Flat-Top waveform combined with two kicker scheme, the transverse emittance of the cooling electron bunches will be conserved during the whole injection, recirculation, and ejection processes. In the cavity design part, firstly, the cavity geometry is optimized to get high transverse shunt impedance thus less than 100 W of RF losses on the cavity wall can be achieved for all these 10 harmonic modes. To support all these 10 harmonic modes, group of four QWRs are adopted with the mode distribution of 5:3:1:1. In the multi-frequency cavities such as the five-mode-cavity and the three-mode-cavity, tunings are required to achieve the design frequencies for each mode. Slight segments of taper design on the inner conductor help to get the frequencies to be exactly on the odd harmonic modes. Stub tuners equal to the number of resonant modes are inserted to the outer conductor wall to compensate the frequency shifts due manufacturing errors and other perturbations during the operation such as the change of the cavity temperature. Single loop couple is designed for all harmonic modes in each cavity. By adjusting its loop size, position and rotation, it is possible to get the fundamental mode critical coupled and other higher harmonic modes slightly over coupled. A broadband circulator will be considered for absorbing the reflected power. Finally in this part, multipole field components due to the asymmetric cylindrical structure around the beam axis of the cavity as well as the beam-induced higher order mode (HOM) issues will be analyzed and discussed in this thesis. A half-scale copper prototype cavity (resonant frequencies from 95.26 MHz to 857.34 MHz) was fabricated to validate the electromagnetic characteristics. With this half scale prototype, the tuning processes of multiple harmonic frequencies, unloaded quality factor measurements of each mode, and bead-pull measurements are performed. The bench measurement results matched well with the simulation results, which have validated our cavity design and construction methods. Finally, a simple mode combining experiment with five separate signal generators was performed on this prototype cavity and the desired fast rise/fall time (1.2 ns), high repetition rate (95.26 MHz) waveform was captured, which finally proved our design of this ultrafast harmonic kicker.« less

Gravity Before Einstein and Schwinger Before Gravity

NASA Astrophysics Data System (ADS)

Trimble, Virginia L.

2012-05-01

Julian Schwinger was a child prodigy, and Albert Einstein distinctly not; Schwinger had something like 73 graduate students, and Einstein very few. But both thought gravity was important. They were not, of course, the first, nor is the disagreement on how one should think about gravity that is being highlighted here the first such dispute. The talk will explore, first, several of the earlier dichotomies: was gravity capable of action at a distance (Newton), or was a transmitting ether required (many others). Did it act on everything or only on solids (an odd idea of the Herschels that fed into their ideas of solar structure and sunspots)? Did gravitational information require time for its transmission? Is the exponent of r precisely 2, or 2 plus a smidgeon (a suggestion by Simon Newcomb among others)? And so forth. Second, I will try to say something about Scwinger's lesser known early work and how it might have prefigured his "source theory," beginning with "On the Interaction of Several Electrons (the unpublished, 1934 "zeroth paper," whose title somewhat reminds one of "On the Dynamics of an Asteroid," through his days at Berkeley with Oppenheimer, Gerjuoy, and others, to his application of ideas from nuclear physics to radar and of radar engineering techniques to problems in nuclear physics. And folks who think good jobs are difficult to come by now might want to contemplate the couple of years Schwinger spent teaching elementary physics at Purdue before moving on to the MIT Rad Lab for war work.

Modeling Wave Driven Non-linear Flow Oscillations: The Terrestrial QBO and a Solar Analog

NASA Technical Reports Server (NTRS)

Mayr, Hans G.; Bhartia, P. K. (Technical Monitor)

2001-01-01

The Quasi Biennial Oscillation (QBO) of the zonal circulation observed in the terrestrial atmosphere at low latitudes is driven by wave mean flow interaction as was demonstrated first by Lindzen and Holton (1968), shown in a laboratory experiment by Plumb and McEwan (1978), and modeled by others (e.g., Plumb, Dunkerton). Although influenced by the seasonal cycle of solar forcing, the QBO, in principle, represents a nonlinear flow oscillation that can be maintained by a steady source of upward propagating waves. The wave driven non-linearity is of third or odd order in the flow velocity, which regenerates the fundamental harmonic itself to keep the oscillation going - the fluid dynamical analog of the displacement mechanism in the mechanical clock. Applying Hines' Doppler Spread Parameterization (DSP) for gravity waves (GW), we discuss with a global-scale spectral model numerical experiments that elucidate some properties of the QBO and its possible effects on the climatology of the atmosphere. Depending on the period of the QBO, wave filtering can cause interaction with the seasonal variations to produce pronounced oscillations with beat periods around 10 years. Since the seasonal cycle and its variability influence the period of the QBO, it may also be a potent conduit of solar activity variations to lower altitudes. Analogous to the terrestrial QBO, we propose that a flow oscillation may account for the 22-year periodicity of the solar magnetic cycle, potentially answering Dicke (1978) who asked, "Is there a chronometer hidden deep inside the Sun?" The oscillation would occur below the convection region, where gravity waves can propagate. Employing a simplified, analytic model, Hines' DSP is applied to estimate the flow oscillation. Depending on the adopted horizontal wavelengths of GW's, wave amplitudes less than 10 m/s can be made to produce oscillating zonal flows of about 20 m/s that should be large enough to generate a significant oscillation in the magnetic field. For the large length scales of the Sun, the flow cycle period tends to be very long. The period, however, can be made to be 22 years, provided the buoyancy frequency (stability) is sufficiently small, thus placing the proposed flow near the base of the convection zone where a dynamo is now believed to operate.

The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96

NASA Technical Reports Server (NTRS)

Lemoine, F. G.; Kenyon, S.C.; Factor, J. K.; Trimmer, R. G.; Pavlis, N. K.; Chinn, D. S.; Cox, C. M.; Klosko, S. M.; Luthcke, S. B.; Torrence, M. H.;

Intercomparison of Satellite Derived Gravity Time Series with Inferred Gravity Time Series from TOPEX/POSEIDON Sea Surface Heights and Climatological Model Output

NASA Technical Reports Server (NTRS)

Cox, C.; Au, A.; Klosko, S.; Chao, B.; Smith, David E. (Technical Monitor)

2001-01-01

The upcoming GRACE mission promises to open a window on details of the global mass budget that will have remarkable clarity, but it will not directly answer the question of what the state of the Earth's mass budget is over the critical last quarter of the 20th century. To address that problem we must draw upon existing technologies such as SLR, DORIS, and GPS, and climate modeling runs in order to improve our understanding. Analysis of long-period geopotential changes based on SLR and DORIS tracking has shown that addition of post 1996 satellite tracking data has a significant impact on the recovered zonal rates and long-period tides. Interannual effects such as those causing the post 1996 anomalies must be better characterized before refined estimates of the decadal period changes in the geopotential can be derived from the historical database of satellite tracking. A possible cause of this anomaly is variations in ocean mass distribution, perhaps associated with the recent large El Nino/La Nina. In this study, a low-degree spherical harmonic gravity time series derived from satellite tracking is compared with a TOPEX/POSEIDON-derived sea surface height time series. Corrections for atmospheric mass effects, continental hydrology, snowfall accumulation, and ocean steric model predictions will be considered.

Orbit determination and gravity field recovery from Doppler tracking data to the Lunar Reconnaissance Orbiter

NASA Astrophysics Data System (ADS)

Maier, Andrea; Baur, Oliver

2016-03-01

We present results for Precise Orbit Determination (POD) of the Lunar Reconnaissance Orbiter (LRO) based on two-way Doppler range-rates over a time span of ~13 months (January 3, 2011 to February 9, 2012). Different orbital arc lengths and various sets of empirical parameters were tested to seek optimal parametrization. An overlap analysis covering three months of Doppler data shows that the most precise orbits are obtained using an arc length of 2.5 days and estimating arc-wise constant empirical accelerations in along track direction. The overlap analysis over the entire investigated time span of 13 months indicates an orbital precision of 13.79 m, 14.17 m, and 1.28 m in along track, cross track, and radial direction, respectively, with 21.32 m in total position. We compare our orbits to the official science orbits released by the US National Aeronautics and Space Administration (NASA). The differences amount to 9.50 m, 6.98 m, and 1.50 m in along track, cross track, and radial direction, respectively, as well as 12.71 m in total position. Based on the reconstructed LRO orbits, we estimated lunar gravity field coefficients up to spherical harmonic degree and order 60. The results are compared to gravity field solutions derived from data collected by other lunar missions.

Time-Variable Gravity from Satellite-Laser-Ranging and Doppler Measurements: An Update on the Low-degree components as well as the connections with Geophysical/Climatic Processes

NASA Technical Reports Server (NTRS)

Cox, Christopher M.; Chao, Benjamin F.; Au, Andrew Y.; Boy, J.-P.

2003-01-01

The oblateness of the Earth's gravity field, 52, has long been observed to undergo a slight decrease due to post-glacial rebound of the mantle. Sometime around 1998 this trend reversed quite suddenly. This reversal persisted until 2001, at which point the atmosphere-corrected time series appears to have reversed yet again. Presently, the time series appears to be returning to the value that would nominally have been reached had the anomaly not occurred. This anomaly signifies a large interannual change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound over such timescales. A number of possible causes have been considered, with oceanic mass redistribution as the leading candidate although other effects, such as glacial melting and core effects may be contributing. The amount by which J2 returns to it's nominal value provides a valuable constraint on the separation of the causes, and will be considered. We will present our latest Satellite Laser Ranging and DORIS Doppler derived time series for J2, and various other low-degree harmonic terms, as well as our investigations into the causes. In addition, we will show the comparison of the J2 results with those derived from CHAMP, as computed at NASA GSFC, and the recently released GRACE gravity model.

Short note: the experimental geopotential model XGM2016

NASA Astrophysics Data System (ADS)

Pail, R.; Fecher, T.; Barnes, D.; Factor, J. F.; Holmes, S. A.; Gruber, T.; Zingerle, P.

2018-04-01

As a precursor study for the upcoming combined Earth Gravitational Model 2020 (EGM2020), the Experimental Gravity Field Model XGM2016, parameterized as a spherical harmonic series up to degree and order 719, is computed. XGM2016 shares the same combination methodology as its predecessor model GOCO05c (Fecher et al. in Surv Geophys 38(3): 571-590, 2017. doi: 10.1007/s10712-016-9406-y). The main difference between these models is that XGM2016 is supported by an improved terrestrial data set of 15^' × 15^' gravity anomaly area-means provided by the United States National Geospatial-Intelligence Agency (NGA), resulting in significant upgrades compared to existing combined gravity field models, especially in continental areas such as South America, Africa, parts of Asia, and Antarctica. A combination strategy of relative regional weighting provides for improved performance in near-coastal ocean regions, including regions where the altimetric data are mostly unchanged from previous models. Comparing cumulative height anomalies, from both EGM2008 and XGM2016 at degree/order 719, yields differences of 26 cm in Africa and 40 cm in South America. These differences result from including additional information of satellite data, as well as from the improved ground data in these regions. XGM2016 also yields a smoother Mean Dynamic Topography with significantly reduced artifacts, which indicates an improved modeling of the ocean areas.

The Effect of Seasonal and Long-Period Geopotential Variations on the GPS Orbits

NASA Technical Reports Server (NTRS)

Melachroinos, Stavros A.; Lemoine, Frank G.; Chinn, Douglas S.; Zelensky, Nikita P.; Nicholas, Joseph B.; Beckley, Brian D.

2013-01-01

We examine the impact of using seasonal and long-period time-variable gravity field (TVG) models on GPS orbit determination, through simulations from 1994 to 2012. The models of time-variable gravity that we test include the GRGS release RL02 GRACE-derived 10-day gravity field models up to degree and order 20 (grgs20x20), a 4 x 4 series of weekly coefficients using GGM03S as a base derived from SLR and DORIS tracking to 11 satellites (tvg4x4), and a harmonic fit to the above 4 x 4 SLR-DORIS time series (goco2s_fit2). These detailed models are compared to GPS orbit simulations using a reference model (stdtvg) based on the International Earth Rotation Service (IERS) and International GNSS Service (IGS) repro1 standards. We find that the new TVG modeling produces significant along, cross-track orbit differences as well as annual, semi-annual, draconitic and long-period effects in the Helmert translation parameters (Tx, Ty, Tz) of the GPS orbits with magnitudes of several mm. We show that the simplistic TVG modeling approach used by all of the IGS Analysis Centers, which is based on the models provided by the IERS standards, becomes progressively less adequate following 2006 when compared to the seasonal and long-period TVG models.

Degree of dispersion monitoring by ultrasonic transmission technique and excitation of the transducer's harmonics

NASA Astrophysics Data System (ADS)

Schober, G.; Heidemeyer, P.; Kretschmer, K.; Bastian, M.; Hochrein, T.

2014-05-01

The degree of dispersion of filled polymer compounds is an important quality parameter for various applications. For instance, there is an influence on the chroma in pigment colored plastics or on the mechanical properties of filled or reinforced compounds. Most of the commonly used offline methods are work-intensive and time-consuming. Moreover, they do not allow an all-over process monitoring. In contrast, the ultrasonic technique represents a suitable robust and process-capable inline method. Here, we present inline ultrasonic measurements on polymer melts with a fundamental frequency of 1 MHz during compounding. In order to extend the frequency range we additionally excite the fundamental and the odd harmonics vibrations at 3 and 5 MHz. The measurements were carried out on a compound consisting of polypropylene and calcium carbonate. For the simulation of agglomerates calcium carbonate with a larger particle size was added with various rates. The total filler content was kept constant. The frequency selective analysis shows a linear correlation between the normalized extinction and the rate of agglomerates simulated by the coarser filler. Further experiments with different types of glass beads with a well-defined particle size verify these results. A clear correlation between the normalized extinction and the glass bead size as well as a higher damping with increasing frequency corresponds to the theoretical assumption. In summary the dispersion quality can be monitored inline by the ultrasonic technique. The excitation of the ultrasonic transducer's harmonics generates more information about the material as the usage of the pure harmonic vibration.

Relativistic satellite orbits: central body with higher zonal harmonics

NASA Astrophysics Data System (ADS)

Schanner, Maximilian; Soffel, Michael

2018-06-01

Satellite orbits around a central body with arbitrary zonal harmonics are considered in a relativistic framework. Our starting point is the relativistic Celestial Mechanics based upon the first post-Newtonian approximation to Einstein's theory of gravity as it has been formulated by Damour et al. (Phys Rev D 43:3273-3307, 1991; 45:1017-1044, 1992; 47:3124-3135, 1993; 49:618-635, 1994). Since effects of order (GM/c^2R) × J_k with k ≥ 2 for the Earth are very small (of order 7 × 10^{-10} × J_k) we consider an axially symmetric body with arbitrary zonal harmonics and a static external gravitational field. In such a field the explicit J_k/c^2-terms (direct terms) in the equations of motion for the coordinate acceleration of a satellite are treated first with first-order perturbation theory. The derived perturbation theoretical results of first order have been checked by purely numerical integrations of the equations of motion. Additional terms of the same order result from the interaction of the Newtonian J_k-terms with the post-Newtonian Schwarzschild terms (relativistic terms related to the mass of the central body). These `mixed terms' are treated by means of second-order perturbation theory based on the Lie-series method (Hori-Deprit method). Here we concentrate on the secular drifts of the ascending node <{\\dot{Ω }}> and argument of the pericenter <{\\dot{ω }}>. Finally orders of magnitude are given and discussed.

Quantifying the resolution level where the GRACE satellites can separate Greenland's glacial mass balance from surface mass balance

NASA Astrophysics Data System (ADS)

Bonin, J. A.; Chambers, D. P.

2015-09-01

Mass change over Greenland can be caused by either changes in the glacial dynamic mass balance (DMB) or the surface mass balance (SMB). The GRACE satellite gravity mission cannot directly separate the two physical causes because it measures the sum of the entire mass column with limited spatial resolution. We demonstrate one theoretical way to indirectly separate cumulative SMB from DMB with GRACE, using a least squares inversion technique with knowledge of the location of the glaciers. However, we find that the limited 60 × 60 spherical harmonic representation of current GRACE data does not provide sufficient resolution to adequately accomplish the task. We determine that at a maximum degree/order of 90 × 90 or above, a noise-free gravity measurement could theoretically separate the SMB from DMB signals. However, current GRACE satellite errors are too large at present to separate the signals. A noise reduction of a factor of 10 at a resolution of 90 × 90 would provide the accuracy needed for the interannual cumulative SMB and DMB to be accurately separated.

Quantifying the resolution level where the GRACE satellites can separate Greenland's glacial mass balance from surface mass balance

NASA Astrophysics Data System (ADS)

Bonin, J. A.; Chambers, D. P.

2015-02-01

Mass change over Greenland can be caused by either changes in the glacial mass balance (GMB) or the precipitation-based surface mass balance (SMB). The GRACE satellite gravity mission cannot directly separate the two physical causes because it measures the sum of the entire mass column with limited spatial resolution. We demonstrate one theoretical way to indirectly separate SMB from GMB with GRACE, using a least squares inversion technique with knowledge of the location of the glacier. However, we find that the limited 60 × 60 spherical harmonic representation of current GRACE data does not provide sufficient resolution to adequately accomplish the task. We determine that at a maximum degree/order of 90 × 90 or above, a noise-free gravity measurement could theoretically separate the SMB from GMB signals. However, current GRACE satellite errors are too large at present to separate the signals. A noise reduction of a factor of 9 at a resolution of 90 × 90 would provide the accuracy needed for the interannual SMB and GMB to be accurately separated.

Analysis of the Effect of UTI-UTC to High Precision Orbit

NASA Astrophysics Data System (ADS)

Shin, Dongseok; Kwak, Sunghee; Kim, Tag-Gon

1999-12-01

As the spatial resolution of remote sensing satellites becomes higher, very accurate determination of the position of a LEO (Low Earth Orbit) satellite is demanding more than ever. Non-symmetric Earth gravity is the major perturbation force to LEO satellites. Since the orbit propagation is performed in the celestial frame while Earth gravity is defined in the terrestrial frame, it is required to convert the coordinates of the satellite from one to the other accurately. Unless the coordinate conversion between the two frames is performed accurately the orbit propagation calculates incorrect Earth gravitational force at a specific time instant, and hence, causes errors in orbit prediction. The coordinate conversion between the two frames involves precession, nutation, Earth rotation and polar motion. Among these factors, unpredictability and uncertainty of Earth rotation, called UTI-UTC, is the largest error source. In this paper, the effect of UTI-UTC on the accuracy of the LEO propagation is introduced, tested and analzed. Considering the maximum unpredictability of UTI-UTC, 0.9 seconds, the meaningful order of non-spherical Earth harmonic functions is derived.

Radio science investigations with Mars Observer

NASA Technical Reports Server (NTRS)

Tyler, G. L.; Balmino, Georges; Hinson, David P.; Sjogren, William L.; Smith, David E.; Woo, Richard; Asmar, Sami W.; Connally, Michael J.; Hamilton, Carole L.; Simpson, Richard A.

1992-01-01

Mars Observer radio science investigations focus on two major areas of study: the gravity field and the atmosphere of Mars. Measurement accuracies expressed as an equivalent spacecraft velocity are expected to be of the order of 100 microns/s (for both types of investigations) from use of an improved radio transponder for two-way spacecraft tracking and a highly stable on-board oscillator for atmospheric occultation measurements. Planned gravity investigations include a combination of classical and modern elements. A spherical harmonic (or equivalent) field model of degree and order in the range 30-50 will be obtained, while interpretation will be in terms of internal stress and density models for the planet, using the topography to be obtained from the Mars Observer laser altimeter. Atmospheric investigations will emphasize precision measurement of the thermal structure and dynamics in the polar regions, which are regularly accessible as a result of the highly inclined orbit. Studies based on the measurements will include polar processes, cycling of the atmosphere between the poles, traveling baroclinic disturbances, small-scale waves and turbulence, the planetary boundary layer, and (possibly) the variability and altitude of the ionosphere.

Using satellite laser ranging to measure ice mass change in Greenland and Antarctica

NASA Astrophysics Data System (ADS)

Bonin, Jennifer A.; Chambers, Don P.; Cheng, Minkang

2018-01-01

A least squares inversion of satellite laser ranging (SLR) data over Greenland and Antarctica could extend gravimetry-based estimates of mass loss back to the early 1990s and fill any future gap between the current Gravity Recovery and Climate Experiment (GRACE) and the future GRACE Follow-On mission. The results of a simulation suggest that, while separating the mass change between Greenland and Antarctica is not possible at the limited spatial resolution of the SLR data, estimating the total combined mass change of the two areas is feasible. When the method is applied to real SLR and GRACE gravity series, we find significantly different estimates of inverted mass loss. There are large, unpredictable, interannual differences between the two inverted data types, making us conclude that the current 5×5 spherical harmonic SLR series cannot be used to stand in for GRACE. However, a comparison with the longer IMBIE time series suggests that on a 20-year time frame, the inverted SLR series' interannual excursions may average out, and the long-term mass loss estimate may be reasonable.

Relationship between low and high frequencies in the \\delta Scuti star KIC 9764965

NASA Astrophysics Data System (ADS)

Rostopchina, A.; Breger, M.

2014-10-01

Two years of Kepler spacecraft data of the \\delta Sct/\\gamma Dor star KIC 9764965 revealed 67 statistically significant frequencies from 0.45 to 59.17 c d-1 (0.005 to 0.685 mHz). The 19 low frequencies do not show equidistant period spacing predicted for gravity modes of successive radial order. We note a favored frequency spacing of 2.053 c d-1 that appears in both the low-frequency (gravity mode) region and high-frequency (pressure mode) regions. The value of this frequency spacing also occurs as a dominant low frequency and in a high-frequency triplet. A peak at exactly twice the value of the 2.053 c d-1 mode is shown not to be a Fourier harmonic of the low-frequency peak due to a different amplitude variability. This behavior is also seen in other \\delta Sct stars. The test for resonant mode coupling between low and high frequencies could not be carried out due to the small amplitudes of the peaks, making it difficult to separate the parent and child modes.

Asymptotic Charges at Null Infinity in Any Dimension

NASA Astrophysics Data System (ADS)

Campoleoni, Andrea; Francia, Dario; Heissenberg, Carlo

2018-03-01

We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing non-linear Yang-Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin.

3rd IAGA/ICMA Workshop on Vertical Coupling in the Atmosphere/Ionosphere System/ Abstract

DTIC Science & Technology

2007-01-10

energy and momentum from the lower atmosphere to the upper atmosphere and ionosphere and vice versa. The programme focussed on various aspects and...ICMA Workshop Vertical Coupling in the Atmosphere/Ionosphere System - 6 - The influence of global dependence of gravity wave energy in the troposphere...transport during the polar night of thermospheric odd nitrogen produced by lower- energy electron precipitation and solar extreme UV fluxes. However, at low

Atmospheric effect in three-space scenario for the Stokes-Helmert method of geoid determination

NASA Astrophysics Data System (ADS)

Yang, H.; Tenzer, R.; Vanicek, P.; Santos, M.

2004-05-01

: According to the Stokes-Helmert method for the geoid determination by Vanicek and Martinec (1994) and Vanicek et al. (1999), the Helmert gravity anomalies are computed at the earth surface. To formulate the fundamental formula of physical geodesy, Helmert's gravity anomalies are then downward continued from the earth surface onto the geoid. This procedure, i.e., the inverse Dirichlet's boundary value problem, is realized by solving the Poisson integral equation. The above mentioned "classical" approach can be modified so that the inverse Dirichlet's boundary value problem is solved in the No Topography (NT) space (Vanicek et al., 2004) instead of in the Helmert (H) space. This technique has been introduced by Vanicek et al. (2003) and was used by Tenzer and Vanicek (2003) for the determination of the geoid in the region of the Canadian Rocky Mountains. According to this new approach, the gravity anomalies referred to the earth surface are first transformed into the NT-space. This transformation is realized by subtracting the gravitational attraction of topographical and atmospheric masses from the gravity anomalies at the earth surface. Since the NT-anomalies are harmonic above the geoid, the Dirichlet boundary value problem is solved in the NT-space instead of the Helmert space according to the standard formulation. After being obtained on the geoid, the NT-anomalies are transformed into the H-space to minimize the indirect effect on the geoidal heights. This step, i.e., transformation from NT-space to H-space is realized by adding the gravitational attraction of condensed topographical and condensed atmospheric masses to the NT-anomalies at the geoid. The effects of atmosphere in the standard Stokes-Helmert method was intensively investigated by Sjöberg (1998 and 1999), and Novák (2000). In this presentation, the effect of the atmosphere in the three-space scenario for the Stokes-Helmert method is discussed and the numerical results over Canada are shown. Key words: Atmosphere - Geoid - Gravity

Geodesy at Mercury with MESSENGER

NASA Technical Reports Server (NTRS)

Smith, David E.; Zuber, Maria t.; Peale, Stanley J.; Phillips, Roger J.; Solomon, Sean C.

2006-01-01

In 2011 the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft will enter Mercury orbit and begin the mapping phase of the mission. As part of its science objectives the MESSENGER mission will determine the shape and gravity field of Mercury. These observations will enable the topography and the crustal thickness to be derived for the planet and will determine the small libration of the planet about its axis, the latter critical to constraining the state of the core. These measurements require very precise positioning of the MESSENGER spacecraft in its eccentric orbit, which has a periapsis altitude as low as 200 km, an apoapsis altitude near 15,000 km, and a closest approach to the surface varying from latitude 60 to about 70 N. The X-band tracking of MESSENGER and the laser altimetry are the primary data that will be used to measure the planetary shape and gravity field. The laser altimeter, which has an expected range of 1000 to 1200 km, is expected to provide significant data only over the northern hemisphere because of MESSENGER's eccentric orbit. For the southern hemisphere, radio occultation measurements obtained as the spacecraft passes behind the planet as seen from Earth and images obtained with the imaging system will be used to provide the long-wavelength shape of the planet. Gravity, derived from the tracking data, will also have greater resolution in the northern hemisphere, but full global models for both topography and gravity will be obtained at low harmonic order and degree. The limiting factor for both gravity and topography is expected to be knowledge of the spacecraft location. Present estimations are that in a combined tracking, altimetry, and occultation solution the spacecraft position uncertainty is likely to be of order 10 m. This accuracy should be adequate for establishing an initial geodetic coordinate system for Mercury that will enable positioning of imaged features on the surface, determination of the planet's obliquity, and detection of the librational motion of the planet about its axis.

Advances and Best Practices in Airborne Gravimetry from the U.S. GRAV-D Project

NASA Astrophysics Data System (ADS)

Diehl, Theresa; Childers, Vicki; Preaux, Sandra; Holmes, Simon; Weil, Carly

2013-04-01

The Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project, an official policy of the U.S. National Geodetic Survey as of 2007, is working to survey the entire U.S. and its holdings with high-altitude airborne gravimetry. The goal of the project is to provide a consistent, high-quality gravity dataset that will become the cornerstone of a new gravimetric geoid and national vertical datum in 2022. Over the last five years, the GRAV-D project has surveyed more than 25% of the country, accomplishing almost 500 flights on six different aircraft platforms and producing more than 3.7 Million square km of data thus far. This wealth of experience has led to advances in the collection, processing, and evaluation of high-altitude (20,000 - 35,000 ft) airborne gravity data. This presentation will highlight the most important practical and theoretical advances of the GRAV-D project, giving an introduction to each. Examples of innovation include: 1. Use of navigation grade inertial measurement unit data and precise lever arm measurements for positioning; 2. New quality control tests and software for near real-time analysis of data in the field; 3. Increased accuracy of gravity post-processing by reexamining assumptions and simplifications that were inconsistent with a goal of 1 mGal precision; and 4. Better final data evaluation through crossovers, additional statistics, and inclusion of airborne data into harmonic models that use EGM08 as a base model. The increases in data quality that resulted from implementation of the above advances (and others) will be shown with a case study of the GRAV-D 2008 southern Alaska survey near Anchorage, over Cook Inlet. The case study's statistics and comparisons to global models illustrate the impact that these advances have had on the final airborne gravity data quality. Finally, the presentation will summarize the best practices identified by the project from its last five years of experience.

Earth's structure and evolution inferred from topography, gravity, and seismicity.

NASA Astrophysics Data System (ADS)

Watkinson, A. J.; Menard, J.; Patton, R. L.

2016-12-01

Earth's wavelength-dependent response to loading, reflected in observed topography, gravity, and seismicity, can be interpreted in terms of a stack of layers under the assumption of transverse isotropy. The theory of plate tectonics holds that the outermost layers of this stack are mobile, produced at oceanic ridges, and consumed at subduction zones. Their toroidal motions are generally consistent with those of several rigid bodies, except in the world's active mountain belts where strains are partitioned and preserved in tectonite fabrics. Even portions of the oceanic lithosphere exhibit non-rigid behavior. Earth's gravity-topography cross-spectrum exhibits notable variations in signal amplitude and character at spherical harmonic degrees l=13, 116, 416, and 1389. Corresponding Cartesian wavelengths are approximately equal to the respective thicknesses of Earth's mantle, continental mantle lithosphere, oceanic thermal lithosphere, and continental crust, all known from seismology. Regional variations in seismic moment release with depth, derived from the global Centroid Moment Tensor catalog, are also evident in the crust and mantle lithosphere. Combined, these observations provide powerful constraints for the structure and evolution of the crust, mantle lithosphere, and mantle as a whole. All that is required is a dynamically consistent mechanism relating wavelength to layer thickness and shear-strain localization. A statistically-invariant 'diharmonic' relation exhibiting these properties appears as the leading order approximation to toroidal motions on a self-gravitating body of differential grade-2 material. We use this relation, specifically its predictions of weakness and rigidity, and of folding and shear banding response as a function of wavelength-to-thickness ratio, to interpret Earth's gravity, topography, and seismicity in four-dimensions. We find the mantle lithosphere to be about 255-km thick beneath the Himalaya and the Andes, and the long-wavelength (l < 14) low-amplitude portion of Earth's gravity field to be consistent with loading of the mesosphere by subducted slabs. The Earth that emerges from this work might be characterized as a self-gravitating, self-peeling onion.

High-degree Gravity Models from GRAIL Primary Mission Data

NASA Technical Reports Server (NTRS)

Lemoine, Frank G.; Goossens, Sander J.; Sabaka, Terence J.; Nicholas, Joseph B.; Mazarico, Erwan; Rowlands, David D.; Loomis, Bryant D.; Chinn, Douglas S.; Caprette, Douglas S.; Neumann, Gregory A.;

Combination of monthly gravity field solutions from different processing centers

NASA Astrophysics Data System (ADS)

Jean, Yoomin; Meyer, Ulrich; Jäggi, Adrian

2015-04-01

Currently, the official GRACE Science Data System (SDS) monthly gravity field solutions are generated independently by the Centre for Space Research (CSR) and the German Research Centre for Geosciences (GFZ). Additional GRACE SDS monthly fields are provided by the Jet Propulsion Laboratory (JPL) for validation and outside the SDS by a number of other institutions worldwide. Although the adopted background models and processing standards have been harmonized more and more by the various processing centers during the past years, notable differences still exist and the users are more or less left alone with a decision which model to choose for their individual applications. Combinations are well-established in the area of other space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Very Long Baseline Interferometry (VLBI), where regular comparisons and combinations of space-geodetic products have tremendously increased the usefulness of the products in a wide range of disciplines and scientific applications. In the frame of the recently started Horizon 2020 project European Gravity Service for Improved Emergency Management (EGSIEM), a scientific combination service shall therefore be established to deliver the best gravity products for applications in Earth and environmental science research based on the unified knowledge of the European GRACE community. In a first step the large variety of available monthly GRACE gravity field solutions shall be mutually compared spatially and spectrally. We assess the noise of the raw as well as filtered solutions and compare the secular and seasonal periodic variations fitted to the monthly solutions. In a second step we will explore ways to generate combined solutions, e.g., based on a weighted average of the individual solutions using empirical weights derived from pair-wise comparisons. We will also assess the quality of such a combined solution and discuss the potential benefits for the GRACE and GRACE-FO user community.

Mach-Zehnder modulator modulated radio-over-fiber transmission system using dual wavelength linearization

NASA Astrophysics Data System (ADS)

Zhu, Ran; Hui, Ming; Shen, Dongya; Zhang, Xiupu

2017-02-01

In this paper, dual wavelength linearization (DWL) technique is studied to suppress odd and even order nonlinearities simultaneously in a Mach-Zehnder modulator (MZM) modulated radio-over-fiber (RoF) transmission system. A theoretical model is given to analyze the DWL employed for MZM. In a single-tone test, the suppressions of the second order harmonic distortion (HD2) and third order harmonic distortion (HD3) at the same time are experimentally verified at different bias voltages of the MZM. The measured spurious-free dynamic ranges (SFDRs) with respect to the HD2 and HD3 are improved simultaneously compared to using a single laser. The output P1 dB is also improved by the DWL technique. Moreover, a WiFi signal is transmitted in the RoF system to test the linearization for broadband signal. The result shows that more than 1 dB improvement of the error vector magnitude (EVM) is obtained by the DWL technique.

Comparison of intense electrostatic waves near f/sub UHR/ with linear instability theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurth, W.S.; Frank, L.A.; Gurnett, D.A.

1979-06-01

Intense electrostatic waves beyond the plasmapause have recently been identified at frequencies near the upper hybrid resonance frequency. In addition, the waves occur within a band at an odd, half-harmonic of the local electron gyrofrequency. These bands of electrostatic turbulence are among the most intense waves detected within the earth's magnetosphere. Measurements obtained with the ISEE 1 plasma wave receiver show that the intense waves appear to be intensifications of an electrostatic cyclotron harmonic band near the upper hybrid resonance frequency. A straightforward explanation of intense waves at the upper hybrid resonance frequency exists in the electrostatic multi-cyclotron emission theory.more » For a broad range of plasma parameters nonconvective instability or large spatial growth rates occur within the cyclotron band encompassing the cold upper hybrid frequency. Comparison of spatial growth rate spectra with measured wave spectra shows that there is excellent qualitative agreement between the linear theory and the observed wave characteristics.« less

What can be learned about the lunar mantle from the Gravity Recovery and Interior Laboratory (GRAIL)?

NASA Astrophysics Data System (ADS)

Zuber, M. T.; Smith, D. E.; Asmar, S. W.; Konopliv, A. S.; Lemoine, F. G.; Melosh, J.; Neumann, G. A.; Phillips, R. J.; Solomon, S. C.; Watkins, M. M.; Wieczorek, M. A.; Williams, J. G.; Andrews-Hanna, J. C.; Garrick-Bethell, I.; Head, J. W.; Kiefer, W. S.; Matsuyama, I.; McGovern, P. J.; Nimmo, F.; Soderblom, J. M.; Taylor, J.; Weber, R. C.; Goossens, S. J.; Kruizinga, G. L.; Mazarico, E.; Park, R. S.; Yuan, D.

2013-12-01

The Gravity Recovery and Interior Laboratory (GRAIL), a dual-spacecraft, gravity-mapping mission that is a component of NASA's Discovery Program, has successfully concluded its Primary and Extended Missions, and is currently in the science analysis phase. In order to safely navigate the dual spacecraft at an average altitude of 22.5 km above the lunar surface during the Extended Mission phase in the fall of 2012, and to derive the greatest information from the full mission data set, the focus had been on the production of gravitational fields with the highest-possible resolution. Spherical harmonic models of the Moon's gravitational field, produced by separate software systems at the Goddard Space Flight Center and the Jet Propulsion Laboratory, now include observations from both the Primary and Extended Missions. The highest-resolution models to date are to degree and order 900, corresponding to a spatial block size of 6 km, and are ideally suited to study the structure of the Moon's crust in extraordinary detail. GRAIL has achieved all measurement objectives for the Primary Mission, enabling all science investigations to be addressed. One of these investigations is to study the lunar hemispherical asymmetry, i.e., the difference between the nearside and farside. In this study we explore the nearside and farside mantle by isolating the long-wavelength gravity field. We accomplish this objective by removing plausible short-wavelength contributions from the crust that were based on the full resolution of high-degree and -order models, and by considering constraints from crustal compositions and volumes of mare basalt deposits. We localize the power spectral contributions of the nearside and farside to constrain lateral density variations, such as those associated with melting from the source regions of the mare basalts.

Height unification using GOCE

NASA Astrophysics Data System (ADS)

Rummel, R.

2012-12-01

With the gravity field and steady-state ocean circulation explorer (GOCE) (preferably combined with the gravity field and climate experiment (GRACE)) a new generation of geoid models will become available for use in height determination. These models will be globally consistent, accurate (<3 cm) and with a spatial resolution up to degree and order 200, when expressed in terms of a spherical harmonic expansion. GOCE is a mission of the European Space Agency (ESA). It is the first satellite equipped with a gravitational gradiometer, in the case of GOCE it measures the gradient components Vxx , Vyy, Vzzand Vxz. The GOCE gravitational sensor system comprises also a geodetic global positioning system (GPS)-receiver, three star sensors and ion-thrusters for drag compensation in flight direction. GOCE was launched in March 2009 and will fly till the end of 2013. Several gravity models have been derived from its data, their maximum degree is typically between 240 and 250. In summer 2012 a first re-processing of all level-1b data took place. One of the science objectives of GOCE is the unification of height systems. The existing height offsets among the datum zones can be determined by least-squares adjustment. This requires several precise geodetic reference points available in each height datum zone, physical heights from spirit levelling (plus gravimetry), the GOCE geoid and, in addition, short wavelength geoid refinement from terrestrial gravity anomalies. GOCE allows for important simplifications of the functional and stochastic part of the adjustment model. The future trend will be the direct determination of physical heights (orthometric as well as normal) from precise global navigation satellite system (GNSS)-positioning in combination with a next generation combined satellite-terrestrial high-resolution geoid model.

The Determination of Titan Gravity Field from Doppler Tracking of the Cassini Spacecraft

NASA Technical Reports Server (NTRS)

Iess, L.; Armstrong, J. W.; Aamar, S. W.; DiBenedetto, M.; Graziani, A.; Mackenzie, R.; Racioppa, P.; Rappaport, N.; Tortora, P.

2007-01-01

In its tour of the Saturnian system, the spacecraft Cassini is carrying out measurements of the gravity field of Titan, whose knowledge is crucial for constraining the internal structure of the satellite. In the five flybys devoted to gravity science, the spacecraft is tracked in X (8.4 GHz) and Ka band (32.5 GHz) from the antennas of NASA's Deep Space Network. The use of a dual frequency downlink is used to mitigate the effects of interplanetary plasma, the largest noise source affecting Doppler measurements. Variations in the wet path delay are effectively compensated by means of advanced water vapor radiometers placed close to the ground antennas. The first three flybys occurred on February 27, 2006, December 28, 2006, and June 29, 2007. Two additional flybys are planned in July 2008 and May 2010. This paper presents the estimation of the mass and quadrupole field of Titan from the first two flybys, carried out by the Cassini Radio Science Team using a short arc orbit determination. The data from the two flybys are first independently fit using a dynamical model of the spacecraft and the bodies of the Saturnian system, and then combined in a multi-arc solution. Under the assumption that the higher degree harmonics are negligible, the estimated values of the gravity parameters from the combined, multi-arc solution are GM = 8978.1337 +/- 0.0025 km(exp 3) / s(exp 2), J (sub 2) = (2.7221 +/- 0.0185) 10 (exp -5) and C (sub 22) = (1.1159 +/- 0.0040) 10 (exp -5) The excellent agreement (within 1.7 sigma) of the results from the two flybys further increases the confidence in the solution and provides an a posteriori validation of the dynamical model.

The role of topography in geodetic gravity field modelling

NASA Technical Reports Server (NTRS)

Forsberg, R.; Sideris, M. G.

1989-01-01

Masses associated with the topography, bathymetry, and its isostatic compensation are a dominant source of gravity field variations, especially at shorter wavelengths. On global scales the topographic/isostatic effects are also significant, except for the lowest harmonics. In practice, though, global effects need not be taken into account as such effects are included in the coefficients of the geopotential reference fields. On local scales, the short-wavelength gravity variations due to the topography may, in rugged terrain, be an order of magnitude larger than other effects. In such cases, explicit or implicit terrain reduction procedures are mandatory in order to obtain good prediction results. Such effects may be computed by space-domain integration or by fast Fourier transformation (FFT) methods. Numerical examples are given for areas of the Canadian Rockies. In principle, good knowledge of the topographic densities is required to produce the smoothest residual field. Densities may be determined from sample measurements or by gravimetric means, but both are somewhat troublesome methods in practice. The use of a standard density, e.g., 2.67 g/cu cm, may often yield satisfactory results and may be put within a consistent theoretical framework. The independence of density assumptions is the key point of the classical Molodensky approach to the geodetic boundary value problem. The Molodensky solutions take into account that land gravity field observations are done on a non-level surface. Molodensky's problem may be solved by integral expansions or more effective FFT methods, but the solution should not be intermixed with the use of terrain reductions. The methods are actually complimentary and may both be required in order to obtain the smoothest possible signal, least prone to aliasing and other effects coming from sparse data coverage, typical of rugged topography.

Spatial gravity wave characteristics obtained from multiple OH(3-1) airglow temperature time series

NASA Astrophysics Data System (ADS)

Wachter, Paul; Schmidt, Carsten; Wüst, Sabine; Bittner, Michael

2015-12-01

We present a new approach for the detection of gravity waves in OH-airglow observations at the measurement site Oberpfaffenhofen (11.27°E, 48.08°N), Germany. The measurements were performed at the German Remote Sensing Data Center (DFD) of the German Aerospace Center (DLR) during the period from February 4th, 2011 to July 6th, 2011. In this case study the observations were carried out by three identical Ground-based Infrared P-branch Spectrometers (GRIPS). These instruments provide OH(3-1) rotational temperature time series, which enable spatio-temporal investigations of gravity wave characteristics in the mesopause region. The instruments were aligned in such a way that their fields of view (FOV) formed an equilateral triangle in the OH-emission layer at a height of 87 km. The Harmonic Analysis is applied in order to identify joint temperature oscillations in the three individual datasets. Dependent on the specific gravity wave activity in a single night, it is possible to detect up to four different wave patterns with this method. The values obtained for the waves' periods and phases are then used to derive further parameters, such as horizontal wavelength, phase velocity and the direction of propagation. We identify systematic relationships between periods and amplitudes as well as between periods and horizontal wavelengths. A predominant propagation direction towards the East and North-North-East characterizes the waves during the observation period. There are also indications of seasonal effects in the temporal development of the horizontal wavelength and the phase velocity. During late winter and early spring the derived horizontal wavelengths and the phase velocities are smaller than in the subsequent period from early April to July 2011.

On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

NASA Astrophysics Data System (ADS)

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

2017-03-01

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1-2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA's satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock-Water-Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30-40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.

Reducing errors in the GRACE gravity solutions using regularization

NASA Astrophysics Data System (ADS)

Save, Himanshu; Bettadpur, Srinivas; Tapley, Byron D.

2012-09-01

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth's monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003-Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE.

Comments on, Xuan Li, Shanghong Zhao, Zihang Zhu, Bing Gong, Xingchun Chu, Yongjun Li, Jing Zhao and Yun Liu `an optical millimeter-wave generation scheme based on two parallel dual-parallel Mach-Zehnder modulators and polarization multiplexing', Journal of Modern Optics, 2015

NASA Astrophysics Data System (ADS)

Hasan, Mehedi; Hall, Trevor

2016-11-01

In the title paper, Li et al. have presented a scheme for filter-less photonic millimetre-wave (mm-wave) generation based on two polarization multiplexed parallel dual-parallel Mach-Zehnder modulators (DP-MZMs). For frequency octo-tupling, all the harmonics are suppressed except those of order 4l, where l is the integer. The carrier is then suppressed by the polarization multiplexing technique, which is the principal innovative step in their design. Frequency 12-tupling and 16-tupling is also described following a similar method. The two DP-MZM are similarly driven and provide identical outputs for the same RF modulation indices. Consequently, a demerit of their design is the requirement to apply two different RF signal modulation indexes in a particular range and set the polarizer to a precise angle which depends on the pair of modulation indices used in order to suppress the unwanted harmonics (e.g. the carrier) without simultaneously suppressing the wanted harmonics. The aim of this comment is to show that, an adjustment of the RF drive phases with a fixed polarizer angle with the design presented by Li, all harmonics can be suppressed except those of order4l, where l is an odd integer. Hence, a filter-less frequency octo-tupling can be generated whose performance is not limited by the careful adjustment of the RF drive signal, rather it can be operated for a wide range of modulation indexes (m 2.5 → 7.5). If the modulation index is adjusted to suppress 4th harmonics, then the design can be used to perform frequency 24-tupling. Since, the carrier is suppressed by design in the modified architecture, the strict requirement to adjust the RF drive (and polarizer angle) can be avoided without any significant change to the circuit complexity.

Discrete mathematical physics and particle modeling

NASA Astrophysics Data System (ADS)

Greenspan, D.

The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed.

Detailed gravimetric geoid for the United States.

NASA Technical Reports Server (NTRS)

Strange, W. E.; Vincent, S. F.; Berry, R. H.; Marsh, J. G.

1972-01-01

A detailed gravimetric geoid was computed for the United States using a combination of satellite-derived spherical harmonic coefficients and 1 by 1 deg mean gravity values from surface gravimetry. Comparisons of this geoid with astrogeodetic geoid data indicate that a precision of plus or minus 2 meters has been obtained. Translations only were used to convert the NAD astrogeodetic geoid heights to geocentric astrogeodetic heights. On the basis of the agreement between the geocentric astrogeodetic geoid heights and the gravimetric geoid heights, no evidence is found for rotation in the North American datum. The value of the zero-order undulation can vary by 10 to 20 meters, depending on which investigator's station positions are used to establish it.

Mantle rheology and satellite signatures from present-day glacial forcings

NASA Technical Reports Server (NTRS)

Sabadini, Roberto; Yuen, David A.; Gasperini, Paolo

1988-01-01

Changes in the long-wavelength region of the earth's gravity field resulting from both present-day glacial discharges and the possible growth of the Antarctic ice sheet are considered. Significant differences in the responses between the Maxell and Burger body rheologies are found for time spans of less than 100 years. The quantitative model for predicting the secular variations of the gravitational potential, and means for incorporating glacial forcings, are described. Results are given for the excitation of the degree two harmonics. It is suggested that detailed satellite monitoring of present-day ice movements in conjunction with geodetic satellite missions may provide a reasonable alternative for the esimation of deep mantle viscosity.

Application of Classical and Lie Transform Methods to Zonal Perturbation in the Artificial Satellite

NASA Astrophysics Data System (ADS)

San-Juan, J. F.; San-Martin, M.; Perez, I.; Lopez-Ochoa, L. M.

2013-08-01

A scalable second-order analytical orbit propagator program is being carried out. This analytical orbit propagator combines modern perturbation methods, based on the canonical frame of the Lie transform, and classical perturbation methods in function of orbit types or the requirements needed for a space mission, such as catalog maintenance operations, long period evolution, and so on. As a first step on the validation of part of our orbit propagator, in this work we only consider the perturbation produced by zonal harmonic coefficients in the Earth's gravity potential, so that it is possible to analyze the behaviour of the perturbation methods involved in the corresponding analytical theories.

New approaches to probing Minkowski functionals

NASA Astrophysics Data System (ADS)

Munshi, D.; Smidt, J.; Cooray, A.; Renzi, A.; Heavens, A.; Coles, P.

2013-10-01

We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of cosmic microwave background (CMB) maps in several domains: in real space (where they are commonly known as cumulant-correlators), and in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using a perturbative series to construct the Minkowski functionals (MFs), we provide a pseudo-C_ℓ based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise, we present approximate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of next-order corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology.

Lutetia: an example of prediction of polyhedra in shapes of small cosmic bodies

NASA Astrophysics Data System (ADS)

Kochemasov, G. G.

2011-10-01

The following prediction based on rules of the wave planetology [1-12] was published before the Rosetta spacecraft imaged asteroid Lutetia [13]. "A 100 km long flattened asteroid 21-Lutetia will be imaged by the "Ros etta' s pacecraft in July 2010. Knowing that heavenly bodies are effectively structurized by warping inertia -gravity waves one might expect that Lutetia will not be an exclusion out of a row of bodies subjected to an action of these waves [1-9]. The elliptical keplerian orbits with periodically changing bodies 'accelerations imply inertia -gravity forces applied to any body notwithstanding its size, mass, density, chemical composition, and physical state. These forces produce inertia-gravity waves having in rotating bodied standing character and four direct ions of propagation (orthogonal and diagonal). Interfering these waves produce in bodies three (five) kinds of tectonic blocks: uprising s trongly and moderately (++, +), subsiding deeply and moderately (--, -), and neutral (0) where + and - are compensated. Lengths and amplitudes of warping waves form the harmonic sequence. The fundamental wave1 (long 2πR) ma kes ubiquitous tectonic dichotomy (two antipodean segments or hemispheres: one risen, another fallen). In small bodies this structurization is expressed in their convexo-concave shape: one hemisphere is bulged, another one pressed in. Bulging hemisphere is extended, pressed in hemisphere contracted. This wave shaping tends to transform a globular body into a tetrahedron - the ess entially dichotomous s imp les t Plato's figure. In this polyhedron always there is an oppos ition of extension (a face) to contraction (a vertex). The firs t overtone wave2 (long πR) ma kes tectonic s ectors , als o ris en and fallen, and regularly disposed on (and in) a globe. This regularity is expressed in an octahedron form. The octahedron (diamond) or its parts are often observed in shapes of small bodies with small gravities. Larger bodies with rather strong gravity tend to smooth polyhedron vertices and edges but a polyhedron structurization is always present inside their globes a nd is shown in their tectonics, geomorphology and geophysical fields. The shorter warping waves are also present but because of their comparatively small lengths and amplitudes they are not so important in distorting globes. The presented main harmonic row is complicated by superimposed individual waves lengths of which are inversely proportional to orbital frequencies: higher frequency - smaller wave, and, vice versa, lower frequency - larger wave. In the main asteroid belt the fundamental wave of the ma in s equence and the individual wave (a ls o long 2π R) a re in the s tron gest 1:1 resonance what prohibits an accretion of a real planet because of prevailing debris scattering. Thus, the Lutetia shape can support the main point of the wave planetology - "orbits make s tructures ." [13]. Below are some examples of cosmic polyhedra belonging to small bodies of various classes (asteroids, satellites, comets), s izes and compos itions . Thus , the prediction of Lutetia' s hape (s trengthened by the later Tempel's images ) was bas ed on rathe r representative observations.

Waiting for 21-Lutetia "Rosetta" images as a final proof of structurizing force of inertia-gravity waves

NASA Astrophysics Data System (ADS)

Kochemasov, Gennady G.

2010-05-01

The 100 km long flattened asteroid 21-Lutetia will be imaged by the "Rosetta' spacecraft in July 2010. Knowing that heavenly bodies are effectively structurized by warping inertia-gravity waves one might expect that Lutetia will not be an exclusion out of a row of bodies subjected to an action of these waves [1-9]. The elliptical keplerian orbits with periodically changing bodies' accelerations imply inertia-gravity forces applied to any body notwithstanding its size, mass, density, chemical composition, and physical state. These forces produce inertia-gravity waves having in rotating bodied standing character and four directions of propagation (orthogonal and diagonal). Interfering these waves produce in bodies three (five) kinds of tectonic blocks: uprising strongly and moderately (++, +), subsiding deeply and moderately (--, -), and neutral (0) where + and - are compensated. Lengths and amplitudes of warping waves form the harmonic sequence. The fundamental wave1 (long 2πR) makes ubiquitous tectonic dichotomy (two antipodean segments or hemispheres: one risen, another fallen). In small bodies this structurization is expressed in their convexo-concave shape: one hemisphere is bulged, another one pressed in. Bulging hemisphere is extended, pressed in hemisphere contracted. This wave shaping tends to transform a globular body into a tetrahedron - the essentially dichotomous simplest Plato's figure. In this polyhedron always there is an opposition of extension (a face) to contraction (a vertex). The first overtone wave2 (long πR) makes tectonic sectors, also risen and fallen, and regularly disposed on (and in) a globe. This regularity is expressed in an octahedron form. The octahedron (diamond) or its parts are often observed in shapes of small bodies with small gravities. Larger bodies with rather strong gravity tend to smooth polyhedron vertices and edges but a polyhedron structurization is always present inside their globes and is shown in their tectonics, geomorphology and geophysical fields. The shorter warping waves are also present but because of their comparatively small lengths and amplitudes they are not so important in distorting globes. The presented main harmonic row is complicated by superimposed individual waves lengths of which are inversely proportional to orbital frequencies: higher frequency - smaller wave, and, vice versa, lower frequency - larger wave. In the main asteroid belt the fundamental wave of the main sequence and the individual wave (also long 2πR) are in the strongest 1:1 resonance what prohibits an accretion of a real planet because of prevailing debris scattering. Thus, the Lutetia shape can support the main point of the wave planetology - «orbits make structures». [1] Kochemasov G.G. (1999) "Diamond" and "dumb-bells"-like shapes of celestial bodies induced by inertia-gravity waves // 30th Vernadsky-Brown microsymposium on comparative planetology, Abstracts, Moscow, Vernadsky Inst., 49-50. [2] -"- (1999) On convexo-concave shape of small celestial bodies // Asteroids, Comets, Meteors. Cornell Univ., July 26-30, 1999, Abstr. # 24.22. [3] -"- (2006) The wave planetology illustrated - I: dichotomy, sectoring // 44th Vernadsky-Brown microsymposium "Topics in Comparative Planetology", Oct. 9-11, 2006, Moscow, Vernadsky Inst., Abstr. m44_39, CD-ROM; [4] -"- (2006) Theorems of the wave planetology imprinted in small bodies // Geophys. Res. Abstracts, Vol. 8, EGU06-A-01098, CD-ROM. [5] -"- (2007) Plato's polyhedra in space // EPSC Abstracts, Vol. 2, EPSC2007-A-00014, 2007. [6] -"-(2007) Wave shaping of small saturnian satellites and wavy granulation of saturnian rings // Geophys. Res. Abstracts, Vol. 9, EGU2007-A-01594, CD-ROM. [7] -"- (2007) Plato's polyhedra as shapes of small satellites in the outer Solar system // New Concepts in Global Tectonics Newsletter, # 44, 43-45. [8] -"- (2008) Plato' polyhedra as shapes of small icy satellites // Geophys. Res. Abstracts, Vol. 10, EGU2008-A-01271, CD-ROM. [9] -"- (2008) A wave geometrization of small heavenly bodies // GRA, Vol. 10, EGU2008-A-01275, CD-ROM.

Geoid undulation accuracy

NASA Technical Reports Server (NTRS)

Rapp, Richard H.

1993-01-01

The determination of the geoid and equipotential surface of the Earth's gravity field, has long been of interest to geodesists and oceanographers. The geoid provides a surface to which the actual ocean surface can be compared with the differences implying information on the circulation patterns of the oceans. For use in oceanographic applications the geoid is ideally needed to a high accuracy and to a high resolution. There are applications that require geoid undulation information to an accuracy of +/- 10 cm with a resolution of 50 km. We are far from this goal today but substantial improvement in geoid determination has been made. In 1979 the cumulative geoid undulation error to spherical harmonic degree 20 was +/- 1.4 m for the GEM10 potential coefficient model. Today the corresponding value has been reduced to +/- 25 cm for GEM-T3 or +/- 11 cm for the OSU91A model. Similar improvements are noted by harmonic degree (wave-length) and in resolution. Potential coefficient models now exist to degree 360 based on a combination of data types. This paper discusses the accuracy changes that have taken place in the past 12 years in the determination of geoid undulations.

Digital hum filtering

USGS Publications Warehouse

Knapp, R.W.; Anderson, N.L.

1994-01-01

Data may be overprinted by a steady-state cyclical noise (hum). Steady-state indicates that the noise is invariant with time; its attributes, frequency, amplitude, and phase, do not change with time. Hum recorded on seismic data usually is powerline noise and associated higher harmonics; leakage from full-waveform rectified cathodic protection devices that contain the odd higher harmonics of powerline frequencies; or vibrational noise from mechanical devices. The fundamental frequency of powerline hum may be removed during data acquisition with the use of notch filters. Unfortunately, notch filters do not discriminate signal and noise, attenuating both. They also distort adjacent frequencies by phase shifting. Finally, they attenuate only the fundamental mode of the powerline noise; higher harmonics and frequencies other than that of powerlines are not removed. Digital notch filters, applied during processing, have many of the same problems as analog filters applied in the field. The method described here removes hum of a particular frequency. Hum attributes are measured by discrete Fourier analysis, and the hum is canceled from the data by subtraction. Errors are slight and the result of the presence of (random) noise in the window or asynchrony of the hum and data sampling. Error is minimized by increasing window size or by resampling to a finer interval. Errors affect the degree of hum attenuation, not the signal. The residual is steady-state hum of the same frequency. ?? 1994.

Lunar Gravity Field Determination Using SELENE Same-Beam Differential VLBI Tracking Data

NASA Technical Reports Server (NTRS)

Goossens, S.; Matsumoto, K.; Liu, Q.; Kikuchi, F.; Sato, K.; Hanada, H.; Ishihara, Y.; Noda, H.; Kawano, N.; Namiki, N.;

Lithospheric Stress Tensor from Gravity and Lithospheric Structure Models

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Tenzer, Robert

2017-07-01

In this study we investigate the lithospheric stresses computed from the gravity and lithospheric structure models. The functional relation between the lithospheric stress tensor and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of stresses inside the lithosphere, while assuming the horizontal shear stress components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the stress spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear stress tensor components globally at the Moho interface. The results reveal that most of the lithospheric stresses are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest stresses within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced stresses (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading stresses along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated stress spectrum (between the degrees from 13 to 180).

High-resolution CSR GRACE RL05 mascons

NASA Astrophysics Data System (ADS)

Save, Himanshu; Bettadpur, Srinivas; Tapley, Byron D.

2016-10-01

The determination of the gravity model for the Gravity Recovery and Climate Experiment (GRACE) is susceptible to modeling errors, measurement noise, and observability issues. The ill-posed GRACE estimation problem causes the unconstrained GRACE RL05 solutions to have north-south stripes. We discuss the development of global equal area mascon solutions to improve the GRACE gravity information for the study of Earth surface processes. These regularized mascon solutions are developed with a 1° resolution using Tikhonov regularization in a geodesic grid domain. These solutions are derived from GRACE information only, and no external model or data is used to inform the constraints. The regularization matrix is time variable and will not bias or attenuate future regional signals to some past statistics from GRACE or other models. The resulting Center for Space Research (CSR) mascon solutions have no stripe errors and capture all the signals observed by GRACE within the measurement noise level. The solutions are not tailored for specific applications and are global in nature. This study discusses the solution approach and compares the resulting solutions with postprocessed results from the RL05 spherical harmonic solutions and other global mascon solutions for studies of Arctic ice sheet processes, ocean bottom pressure variation, and land surface total water storage change. This suite of comparisons leads to the conclusion that the mascon solutions presented here are an enhanced representation of the RL05 GRACE solutions and provide accurate surface-based gridded information that can be used without further processing.

The Density of the North Polar Layered Deposit from Gravity and Topography

NASA Astrophysics Data System (ADS)

Ojha, L.; Lewis, K. W.

2017-12-01

The North Polar Layered Deposit (NPLD) of Mars is a vast reservoir of water ice with a volume of 1.14 million km3. Radar data indicates that the ice in the NPLD is extremely pure with dust content between 5 % to 10 %, however the radar data has not been able to put a direct constraint on the density of the NPLD. Here, we localize the gravity and topography signature of the NPLD and place a direct constraint on its density. We performed a grid search by generating admittance spectrum at each latitude and longitude between 75° N to 90° N and 0° E to 360° E, using a spherical cap of angular radius () of 7°, and a harmonic-bandwidth of the localization window Lwin of 37°. A region between Gemina Lingula and Planum Boreum was found to possesss an adequate correlation between gravity and topography. The estimated admittance spectra were compared with synthetic admittance spectra to constrain the load-density and the elastic thickness of the lithosphere. We constructed forward models by assuming that the lithosphere is a thin shell that deforms elastically in response to surface loads. We find that the bulk density of the NPLD ranges between 1000 to 1100 kg.m-3. Assuming a grain density of 3000 kg.m-3 for dust, the NPLD region within our localized window can contain dust content between 3 - 8 %, which is in an excellent agreement with the radar data.

Crustal structure of Mars from gravity and topography

NASA Technical Reports Server (NTRS)

Neumann, G. A.; Zuber, M. T.; Wieczorek, M. A.; McGovern, P. J.; Lemoine, F. G.; Smith, D. E.

2004-01-01

Mars Orbiter Laser Altimeter (MOLA) topography and gravity models from 5 years of Mars Global Surveyor (MGS) spacecraft tracking provide a window into the structure of the Martian crust and upper mantle. We apply a finite-amplitude terrain correction assuming uniform crustal density and additional corrections for the anomalous densities of the polar caps, the major volcanos, and the hydrostatic flattening of the core. A nonlinear inversion for Moho relief yields a crustal thickness model that obeys a plausible power law and resolves features as small as 300 km wavelength. On the basis of petrological and geophysical constraints, we invoke a mantle density contrast of 600 kg m-3; with this assumption, the Isidis and Hellas gravity anomalies constrain the global mean crustal thickness to be >45 km. The crust is characterized by a degree 1 structure that is several times larger than any higher degree harmonic component, representing the geophysical manifestation of the planet's hemispheric dichotomy. It corresponds to a distinction between modal crustal thicknesses of 32 km and 58 km in the northern and southern hemispheres, respectively. The Tharsis rise and Hellas annulus represent the strongest components in the degree 2 crustal thickness structure. A uniform highland crustal thickness suggests a single mechanism for its formation, with subsequent modification by the Hellas impact, erosion, and the volcanic construction of Tharsis. The largest surviving lowland impact, Utopia, post-dated formation of the crustal dichotomy. Its crustal structure is preserved, making it unlikely that the northern crust was subsequently thinned by internal processes.

Black hole perturbation under a 2 +2 decomposition in the action

NASA Astrophysics Data System (ADS)

Ripley, Justin L.; Yagi, Kent

2018-01-01

Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2 +2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two-dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two-dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two-dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well-studied physical system: the metric perturbations of a static black hole. The 2 +2 formalism we present can be generalized to m +n -dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of m +n formalism for vacuum spacetime splittings.

Three-dimensional fractional-spin gravity

NASA Astrophysics Data System (ADS)

Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio

2014-02-01

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ , ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell. The project was funded in part by F.R.S.-FNRS " Ulysse" Incentive Grant for Mobility in Scientific Research.

A novel approach to gravitation from fluid theory: Titius-Bode structures, flat rotation rate of galaxies, and other predictions

NASA Astrophysics Data System (ADS)

Munera, Hector A.

Following the discovery of quantum phenomena at laboratory scale (Couder & Fort 2006), de Broglie pilot wave theory (De Broglie 1962) has been revived under a hydrodynamic guise (Bush 2015). Theoretically, it boils down to solving the transport equations for the energy and linear momentum densities of a postulated fundamental fluid in terms of classical wave equations, which inherently are Lorentz-invariant and scale-invariant. Instead of the conventional harmonic solutions, for astronomical and gravitational problems the novel solutions for the homogeneous wave equation in spherical coordinates are more suitable (Munera et al. 1995, Munera & Guzman 1997, and Munera 2000). Two groups of solutions are particularly relevant: (a) The inherently-quantized helicoidal solutions that may be applicable to describe spiral galaxies, and (b) The non-harmonic solutions with time (t) and distance (r) entangled in the single variable q = Ct/r (C is the two-way local electromagnetic speed). When these functions are plotted against 1/q they manifestly depict quantum effects in the near field, and Newtonian-like gravity in the far-field. The near-field predicts quantized effects similar to ring structures and to Titius-Bode structures, both in our own solar system and in exoplanets, the correlation between predicted and observed structures being typically larger than 99 per cent. In the far-field, some non-harmonic functions have a rate of decrement with distance slower than inverse-square thus explaining the flat rotation rate of galaxies. Additional implications for Trojan orbits, and quantized effects in photon deflection were also noted.

A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders

NASA Astrophysics Data System (ADS)

Bucha, Blažej; Janák, Juraj

2013-07-01

We present a novel graphical user interface program GrafLab (GRAvity Field LABoratory) for spherical harmonic synthesis (SHS) created in MATLAB®. This program allows to comfortably compute 38 various functionals of the geopotential up to ultra-high degrees and orders of spherical harmonic expansion. For the most difficult part of the SHS, namely the evaluation of the fully normalized associated Legendre functions (fnALFs), we used three different approaches according to required maximum degree: (i) the standard forward column method (up to maximum degree 1800, in some cases up to degree 2190); (ii) the modified forward column method combined with Horner's scheme (up to maximum degree 2700); (iii) the extended-range arithmetic (up to an arbitrary maximum degree). For the maximum degree 2190, the SHS with fnALFs evaluated using the extended-range arithmetic approach takes only approximately 2-3 times longer than its standard arithmetic counterpart, i.e. the standard forward column method. In the GrafLab, the functionals of the geopotential can be evaluated on a regular grid or point-wise, while the input coordinates can either be read from a data file or entered manually. For the computation on a regular grid we decided to apply the lumped coefficients approach due to significant time-efficiency of this method. Furthermore, if a full variance-covariances matrix of spherical harmonic coefficients is available, it is possible to compute the commission errors of the functionals. When computing on a regular grid, the output functionals or their commission errors may be depicted on a map using automatically selected cartographic projection.

Gravity is the Key Experiment to Address the Habitability of the Ocean in Jupiter's Moon Europa

NASA Astrophysics Data System (ADS)

Sessa, A. M.; Dombard, A. J.

2013-12-01

Life requires three constituents: a liquid solvent (i.e., water), a chemical system that can form large molecules to record genetic information (e.g., carbon based) as well as chemical nutrients (e.g., nitrogen, phosphorous), and a chemical disequilibrium system that can provide metabolic energy. While it is believed that there is a saline water layer located between the rock and ice layers in Jupiter's moon Europa, which would satisfy the first requirement, it is unknown if the other conditions are currently met. The likelihood that Europa is a haven for life in our Solar System skyrockets, however, if there is currently active volcanism at the rock-water interface, much the same that volcanic processes enable the chemosynthetic life that forms the basis of deep sea-vent communities at the bottom of Earth's oceans. Exploring the volcanic activity on this interface is challenging, as direct observation via a submersible or high-resolution indirect observations via a dense global seismic network on the surface is at present technically (and fiscally!) untenable. Thus, gravity studies are the best way to explore currently the structure of this all-important interface. Though mostly a silicate body with only a relatively thin (~100 km) layer of water, Europa is different from the terrestrial planets in that this rock-water interface, and not the surface, represents the largest density contrast across the moon's near-surface layers, and thus topography on this interface could conceivably dominate the gravity. Here, we calculate the potential anomalies that arise from topography on the surface, the water-ice interface (at 20 km depth), and the rock-water interface, finding that the latter dominates the free-air gravity at the longest wavelengths (spherical harmonic degrees < 10) and the Bouguer gravity at intermediate wavelengths (degrees ~10-50), and only for the shortest wavelengths (degrees > 50) does the water-ice interface (and presumably mass-density anomalies within the ice shell) dominate the Bouguer gravity. Thus, gravity can be used to explore this interface. To test whether active volcanism can be detected, we scale gravity models for the terrestrial planets down to a body the size of Europa's silicate core and with a density contrast consistent with a rock-water interface. Here, Venus and Earth serve as proxies for volcanically active bodies, while the Moon and Mars are proxies for inactive bodies. Additionally, we create gravity from synthetic topography on the base of the ice shell. Maps of the Bouguer-gravity and geoid anomalies reveal that active volcanism is characterized by small amplitudes (a few mGal and a few meters). Large-scale topography on the base of the ice shell adds larger geoid anomalies (tens of meters) but still small gravity anomalies. The absence of volcanic activity on the rock-water interface is likely characterized by larger anomalies (tens of mGal and tens of meters), plausibly because the cooler thermal structure permits the rocky lithosphere to support larger mass-density anomalies. Thus, study of the gravity may illuminate the habitability of Europa, and gravity and topography experiments on any future mission (e.g., the Europa Clipper) should be given the highest scientific priority.

High serum oxytocin is associated with metabolic syndrome in older men - The MINOS study.

PubMed

Szulc, Pawel; Amri, Ez Zoubir; Varennes, Annie; Panaia-Ferrari, Patricia; Fontas, Eric; Goudable, Joëlle; Chapurlat, Roland; Breuil, Véronique

2016-12-01

Oxytocin regulates food intake, carbohydrate and lipid metabolism, and urinary sodium excretion. We assessed the association between serum oxytocin levels and presence of metabolic syndrome (MetS) in older men. Cross-sectional study was performed in 540 volunteer men aged 50-85yrs from the MINOS cohort. Oxytocin was measured in fasting serum by radioimmunoassay (Oxytocin RIA, Phoenix Pharmaceuticals). MetS was diagnosed using the harmonized definition. Serum oxytocin was higher in 166 men with MetS vs. controls (p<0.005). After adjustment for confounders including leptin, higher oxytocin was associated with higher odds of MetS (OR=1.38 per SD, 95%CI: 1.10-1.71, p<0.005). Men with serum oxytocin >0.74pg/mL (median) had higher odds of MetS vs. men with oxytocin ⩽0.74pg/mL (OR=2.06, 95%CI: 1.33-3.18, p<0.005). Higher oxytocin levels and low testosterone levels (total or free) were significantly associated with higher odds of MetS jointly and independently of each other. Men having oxytocin >0.74pg/mL and total testosterone <300ng/dL (<10.4nmol/L) had higher odds of MetS vs. men without these characteristics (OR=3.95, 95%CI: 1.65-9.46, p<0.005). Men having 25-hydroxycholecalciferol levels <30ng/mL and oxytocin >0.74pg/mL had higher odds of MetS vs. men without these characteristics (OR=2.86, 95%CI: 1.47-5.58, p<0.01). Men having oxytocin >0.74pg/mL and osteocalcin levels <14.6ng/mL (lowest quartile) had higher odds of MetS vs. men without these characteristics (OR=4.12, 95%CI: 2.07-8.20, p<0.001). In older men, higher serum oxytocin levels are associated with higher odds of MetS regardless of potential confounders. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Information theory lateral density distribution for Earth inferred from global gravity field

NASA Technical Reports Server (NTRS)

Rubincam, D. P.

1981-01-01

Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.

Optimum data weighting and error calibration for estimation of gravitational parameters

NASA Technical Reports Server (NTRS)

Lerch, F. J.

1989-01-01

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Effects of vibration (G-jitters) on convection in micro-gravity

NASA Technical Reports Server (NTRS)

Wang, Francis C.

1994-01-01

To obtain high quality crystals, it is desirable to maintain a diffusion-limited transport process in a planar solidification surface between the solid and the melt during the crystal growth process. Due to the presence of buoyancy-driven convection, however, this situation is difficult to maintain on Earth. The microgravity environment of an orbiting space laboratory presents an alternative worth pursuing. With reduced gravity, convections very much suppressed in a space laboratory, making the environment more conducive for growing crystals with better quality. However, a space laboratory is not immune from any undesirable disturbances. Nonuniform and transient accelerations such as vibrations, g-jitters, and impulsive accelerations exist as a result of crew activities, space maneuvering, and the operations of on-board equipment. Measurements conducted on-board a U.S. Spacelab mission showed the existence of vibrations in the frequency range of 1 to 100 Hz. It was reported that a dominant mode of 17 Hz and harmonics of 54 Hz were observed and these were attributed to antenna operations. The vibration is not limited to any single plane but exists in all directions. Some data from the Russian MIR space station indicates the existence of vibration also at this frequency range.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Martian atmospheric gravity waves simulated by a high-resolution general circulation model

NASA Astrophysics Data System (ADS)

Kuroda, Takeshi; Yiǧit, Erdal; Medvedev, Alexander S.; Hartogh, Paul

2016-07-01

Gravity waves (GWs) significantly affect temperature and wind fields in the Martian middle and upper atmosphere. They are also one of the observational targets of the MAVEN mission. We report on the first simulations with a high-resolution general circulation model (GCM) and present a global distributions of small-scale GWs in the Martian atmosphere. The simulated GW-induced temperature variances are in a good agreement with available radio occultation data in the lower atmosphere between 10 and 30 km. For the northern winter solstice, the model reveals a latitudinal asymmetry with stronger wave generation in the winter hemisphere and two distinctive sources of GWs: mountainous regions and the meandering winter polar jet. Orographic GWs are filtered upon propagating upward, and the mesosphere is primarily dominated by harmonics with faster horizontal phase velocities. Wave fluxes are directed mainly against the local wind. GW dissipation in the upper mesosphere generates a body force per unit mass of tens of m s^{-1} per Martian solar day (sol^{-1}), which tends to close the simulated jets. The results represent a realistic surrogate for missing observations, which can be used for constraining GW parameterizations and validating GCMs.

Normal gravity field in relativistic geodesy

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei; Vlasov, Igor; Han, Wen-Biao

2018-02-01

Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, very long baseline interferometry, satellite laser ranging, and global navigation satellite systems have achieved an unprecedented level of accuracy in measuring 3-d coordinates of the reference points of the International Terrestrial Reference Frame and the world height system. The main geodetic reference standard to which gravimetric measurements of the of Earth's gravitational field are referred is a normal gravity field represented in the Newtonian gravity by the field of a uniformly rotating, homogeneous Maclaurin ellipsoid of which mass and quadrupole momentum are equal to the total mass and (tide-free) quadrupole moment of Earth's gravitational field. The present paper extends the concept of the normal gravity field from the Newtonian theory to the realm of general relativity. We focus our attention on the calculation of the post-Newtonian approximation of the normal field that is sufficient for current and near-future practical applications. We show that in general relativity the level surface of homogeneous and uniformly rotating fluid is no longer described by the Maclaurin ellipsoid in the most general case but represents an axisymmetric spheroid of the fourth order with respect to the geodetic Cartesian coordinates. At the same time, admitting a post-Newtonian inhomogeneity of the mass density in the form of concentric elliptical shells allows one to preserve the level surface of the fluid as an exact ellipsoid of rotation. We parametrize the mass density distribution and the level surface with two parameters which are intrinsically connected to the existence of the residual gauge freedom, and derive the post-Newtonian normal gravity field of the rotating spheroid both inside and outside of the rotating fluid body. The normal gravity field is given, similarly to the Newtonian gravity, in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce a more conventional post-Newtonian multipolar expansion of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy as it does not match the normal gravity field of the Maclaurin ellipsoid already in the Newtonian limit. We derive the post-Newtonian generalization of the Somigliana formula for the normal gravity field measured on the surface of the rotating spheroid and employed in practical work for measuring Earth's gravitational field anomalies. Finally, we discuss the possible choice of the gauge-dependent parameters of the normal gravity field model for practical applications and compare it with the existing EGM2008 model of a gravitational field.

Urine specific gravity and water hardness in relation to urolithiasis in persons with spinal cord injury.

PubMed

Chen, Y; Roseman, J M; Funkhouser, E; DeVivo, M J

2001-11-01

A matched case-control study. To clarify the influence of urine specific gravity and drinking water quality on the formation of urinary stones in persons with spinal cord injury (SCI). A rehabilitation center within a university hospital. Between 1992 and 1998, 63 stone cases (31 kidney, 27 bladder, and five both) and 289 age-duration-matched controls were recruited from a cohort of SCI patients enrolled in an on-going longitudinal study. Data on urine specific gravity and other characteristics of study participants were retrieved from the database and medical charts. Community water supply information was provided by the Alabama Department of Environmental Management. Multivariable conditional logistic regression analysis was performed to evaluate the association with stone formation. SCI individuals who had urinary stones were more likely than control subjects to use indwelling catheters and have decreased renal function. The occurrence of stones was not significantly related to gender, race, severity of injury, urinary tract infection, nor urine pH. After controlling for the potential confounding from other factors, a continuously increasing stone occurrence with increasing specific gravity was observed (P=0.05); this association was stronger for kidney (odds Ratio [OR]=1.8 per 0.010 g/cm(3)) versus bladder stones (OR=1.2) and for recurrent (OR=2.0) versus first stones (OR=1.5). Increased water hardness was not significantly associated with a decreased stone occurrence. Study results suggest that maintaining urine specific gravity below a certain level might reduce the occurrence of urinary stones. This could be easily achieved by using a dipstick for self-feedback along with appropriate fluid intake. For persons with SCI who are at an increased risk of a devastating stone disease, this prophylactic approach could be very cost-effective; however, this requires further confirmation.

Constraints on Ceres internal strcuture from the Dawn gravity and shape data

NASA Astrophysics Data System (ADS)

Ermakov, A.; Zuber, M. T.; Smith, D. E.; Fu, R. R.; Raymond, C. A.; Russell, C. T.; Park, R. S.

2015-12-01

Ceres is the largest body in the asteroid belt with a radius of approximately 470 km. It is large enough to attain a shape much closer to hydrostatic equilibrium than major asteroids. Pre-Dawn shape models of Ceres (e.g. Thomas et al., 2005; Carry et al., 2008) revealed that its shape is consistent with a hydrostatic ellipsoid. After the arrival of the Dawn spacecraft in Ceres orbit in March 2015, Framing Camera images were used to construct shape models of Ceres. Meanwhile, radio-tracking data are being used to develop gravity models. We use the Dawn-derived shape and gravity models to constrain Ceres' internal structure. These data for the first time allow estimation of the degree to which Ceres is hydrostatic. Observed non-hydrostatic effects include a 2.1 km triaxiality (difference between the two equatorial axes) as well as an 660-m center-of-mass - center-of-figure offset. The Dawn gravity data from the Survey orbit shows that Ceres has a central density concentration. Second-degree sectorial gravity coefficients are negatively correlated with topography indicating a peculiar interior structure. We compute the relative crustal thickness based on the observed Bouguer anomaly. Hydrostatic models show that Ceres appears more differentiated based on its gravity than on its shape. We expand the Ceres shape in spherical harmonics, observing that the power spectrum of topography deviates from the power law at low degrees (Fig. 1). We interpret the decrease of power at low degrees to be due to viscous relaxation. We suggest that relaxation happens on Ceres but, unlike modeled in Bland (2013), it is important only at the lowest degrees that correspond to scales of several hundreds of km. There are only a few features on Ceres of that size and at least one of them (an impact basin provisionally named Kerwan) appears relaxed. The simplest explanation is that Ceres's outer shell is not pure ice or pure rock but an ice-rock mixture that allows some relaxation at the longest wavelengths. We use the deal.ii finite-element library (Bangerth 2007) to compute relaxed topography spectra. In out future work, we plan to model viscous relaxation to constrain the viscosity profile and thermal evolution.

Millimeter-wave monolithic diode-grid frequency multiplier

NASA Technical Reports Server (NTRS)

Maserjian, Joseph (Inventor)

1990-01-01

A semiconductor diode structure useful for harmonic generation of millimeter or submillimeter wave radiation from a fundamental input wave is fabricated on a GaAs substrate. A heavily doped layer of n(sup ++) GaAs is produced on the substrate and then a layer of intrinsic GaAs on said heavily doped layer on top of which a sheet of heavy doping (++) is produced. A thin layer of intrinsic GaAs grown over the sheet is capped with two metal contacts separated by a gap to produce two diodes connected back to back through the n(sup ++) layer for multiplication of frequency by an odd multiple. If only one metal contact caps the thin layer of intrinsic GaAs, the second diode contact is produced to connect to the n(sup ++) layer for multiplication of frequency by an even number. The odd or even frequency multiple is selected by a filter. A phased array of diodes in a grid will increase the power of the higher frequency generated.

Semiclassical unified description of wobbling motion in even-even and even-odd nuclei

NASA Astrophysics Data System (ADS)

Raduta, A. A.; Poenaru, R.; Ixaru, L. Gr.

2017-11-01

A unitary description for wobbling motion in even-even and even-odd nuclei is presented. In both cases compact formulas for wobbling frequencies are derived. The accuracy of the harmonic approximation is studied for the yrast as well as for the excited bands in the even-even case. Important results for the structure of the wave function and its behavior inside the two wells of the potential energy function corresponding to the Bargmann representation are pointed out. Applications to 158Er and 163Lu reveal a very good agreement with available data. Indeed, the yrast energy levels in the even-even case and the first four triaxial superdeformed bands, TSD1, TSD2, TSD3, and TSD4, are realistically described. Also, the results agree with the data for the E 2 and M 1 intra- as well as interband transitions. Perspectives for the formalism development and an extensive application to several nuclei from various regions of the nuclides chart are presented.

Quantum dynamics of a plane pendulum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leibscher, Monika; Schmidt, Burkhard

A semianalytical approach to the quantum dynamics of a plane pendulum is developed, based on Mathieu functions which appear as stationary wave functions. The time-dependent Schroedinger equation is solved for pendular analogs of coherent and squeezed states of a harmonic oscillator, induced by instantaneous changes of the periodic potential energy function. Coherent pendular states are discussed between the harmonic limit for small displacements and the inverted pendulum limit, while squeezed pendular states are shown to interpolate between vibrational and free rotational motion. In the latter case, full and fractional revivals as well as spatiotemporal structures in the time evolution ofmore » the probability densities (quantum carpets) are quantitatively analyzed. Corresponding expressions for the mean orientation are derived in terms of Mathieu functions in time. For periodic double well potentials, different revival schemes, and different quantum carpets are found for the even and odd initial states forming the ground tunneling doublet. Time evolution of the mean alignment allows the separation of states with different parity. Implications for external (rotational) and internal (torsional) motion of molecules induced by intense laser fields are discussed.« less

The effect of sadness on global-local processing.

PubMed

von Mühlenen, Adrian; Bellaera, Lauren; Singh, Amrendra; Srinivasan, Narayanan

2018-05-04

Gable and Harmon-Jones (Psychological Science, 21(2), 211-215, 2010) reported that sadness broadens attention in a global-local letter task. This finding provided the key test for their motivational intensity account, which states that the level of spatial processing is not determined by emotional valence, but by motivational intensity. However, their finding is at odds with several other studies, showing no effect, or even a narrowing effect of sadness on attention. This paper reports two attempts to replicate the broadening effect of sadness on attention. Both experiments used a global-local letter task, but differed in terms of emotion induction: Experiment 1 used the same pictures as Gable and Harmon-Jones, taken from the IAPS dataset; Experiment 2 used a sad video underlaid with sad music. Results showed a sadness-specific global advantage in the error rates, but not in the reaction times. The same null results were also found in a South-Asian sample in both experiments, showing that effects on global/local processing were not influenced by a culturally related processing bias.

Magnetic ground state of Sr 2 IrO 4 and implications for second-harmonic generation

DOE PAGES

Di Matteo, S.; Norman, M. R.

2016-08-24

The currently accepted magnetic ground state of Sr 2IrO 4 (the -++- state) preserves inversion symmetry. This is at odds, though, with recent experiments that indicate a magnetoelectric ground state, leading to the speculation that orbital currents or more exotic magnetic multipoles might exist in this material. In this paper, we analyze various magnetic configurations and demonstrate that two of them, the magnetoelectric -+-+ state and the nonmagnetoelectric ++++ state, can explain these recent second-harmonic generation (SHG) experiments, obviating the need to invoke orbital currents. The SHG-probed magnetic order parameter has the symmetry of a parity-breaking multipole in the -+-+more » state and of a parity-preserving multipole in the ++++ state. We speculate that either might have been created by the laser pump used in the experiments. An alternative is that the observed magnetic SHG signal is a surface effect. Finally, we suggest experiments that could be performed to test these various possibilities and also address the important issue of the suppression of the RXS intensity at the L 2 edge.« less