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

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.

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.

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.

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.

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).

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.

(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.

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.

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 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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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)

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Measurement of Jupiter’s asymmetric gravity field

NASA Astrophysics Data System (ADS)

Iess, L.; Folkner, W. M.; Durante, D.; Parisi, M.; Kaspi, Y.; Galanti, E.; Guillot, T.; Hubbard, W. B.; Stevenson, D. J.; Anderson, J. D.; Buccino, D. R.; Casajus, L. Gomez; Milani, A.; Park, R.; Racioppa, P.; Serra, D.; Tortora, P.; Zannoni, M.; Cao, H.; Helled, R.; Lunine, J. I.; Miguel, Y.; Militzer, B.; Wahl, S.; Connerney, J. E. P.; Levin, S. M.; Bolton, S. J.

2018-03-01

The gravity harmonics of a fluid, rotating planet can be decomposed into static components arising from solid-body rotation and dynamic components arising from flows. In the absence of internal dynamics, the gravity field is axially and hemispherically symmetric and is dominated by even zonal gravity harmonics J2n that are approximately proportional to qn, where q is the ratio between centrifugal acceleration and gravity at the planet’s equator. Any asymmetry in the gravity field is attributed to differential rotation and deep atmospheric flows. The odd harmonics, J3, J5, J7, J9 and higher, are a measure of the depth of the winds in the different zones of the atmosphere. Here we report measurements of Jupiter’s gravity harmonics (both even and odd) through precise Doppler tracking of the Juno spacecraft in its polar orbit around Jupiter. We find a north–south asymmetry, which is a signature of atmospheric and interior flows. Analysis of the harmonics, described in two accompanying papers, provides the vertical profile of the winds and precise constraints for the depth of Jupiter’s dynamical atmosphere.

Gravity anomaly map of Mars and Moon and analysis of Venus gravity field: New analysis procedures

NASA Technical Reports Server (NTRS)

1984-01-01

The technique of harmonic splines allows direct estimation of a complete planetary gravity field (geoid, gravity, and gravity gradients) everywhere over the planet's surface. Harmonic spline results of Venus are presented as a series of maps at spacecraft and constant altitudes. Global (except for polar regions) and local relations of gravity to topography are described.

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.

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

NASA Technical Reports Server (NTRS)

Ustinov, Eugene A.; Sunseri, Richard F.

2005-01-01

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

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.

Estimating Jupiter’s Gravity Field Using Juno Measurements, Trajectory Estimation Analysis, and a Flow Model Optimization

NASA Astrophysics Data System (ADS)

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

2017-07-01

The upcoming Juno spacecraft measurements have the potential of improving our knowledge of Jupiter’s gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spatial gravity variations, but these measurements will be very accurate only over a limited latitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially regarding the Jovian flow structure and its depth, which can influence the measured gravity field. In this study we propose a new iterative method for the estimation of the Jupiter gravity field, using a simulated Juno trajectory, a trajectory estimation model, and an adjoint-based inverse model for the flow dynamics. We test this method both for zonal harmonics only and with a full gravity field including tesseral harmonics. The results show that this method can fit some of the gravitational harmonics better to the “measured” harmonics, mainly because of the added information from the dynamical model, which includes the flow structure. Thus, it is suggested that the method presented here has the potential of improving the accuracy of the expected gravity harmonics estimated from the Juno and Cassini radio science experiments.

Estimating Jupiter’s Gravity Field Using Juno Measurements, Trajectory Estimation Analysis, and a Flow Model Optimization

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

Galanti, Eli; Kaspi, Yohai; Durante, Daniele

The upcoming Juno spacecraft measurements have the potential of improving our knowledge of Jupiter’s gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spatial gravity variations, but these measurements will be very accurate only over a limited latitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially regarding the Jovian flow structure and its depth, which can influence the measured gravity field. In this study we propose a new iterative method for the estimation of the Jupiter gravity field, using a simulatedmore » Juno trajectory, a trajectory estimation model, and an adjoint-based inverse model for the flow dynamics. We test this method both for zonal harmonics only and with a full gravity field including tesseral harmonics. The results show that this method can fit some of the gravitational harmonics better to the “measured” harmonics, mainly because of the added information from the dynamical model, which includes the flow structure. Thus, it is suggested that the method presented here has the potential of improving the accuracy of the expected gravity harmonics estimated from the Juno and Cassini radio science experiments.« less

Stabilized determination of geopotential coefficients by the mixed hom-BLUP approach

NASA Technical Reports Server (NTRS)

Middel, B.; Schaffrin, B.

1989-01-01

For the determination of geopotential coefficients, data can be used from rather different sources, e.g., satellite tracking, gravimetry, or altimetry. As each data type is particularly sensitive to certain wavelengths of the spherical harmonic coefficients it is of essential importance how they are treated in a combination solution. For example the longer wavelengths are well described by the coefficients of a model derived by satellite tracking, while other observation types such as gravity anomalies, delta g, and geoid heights, N, from altimetry contain only poor information for these long wavelengths. Therefore, the lower coefficients of the satellite model should be treated as being superior in the combination. In the combination a new method is presented which turns out to be highly suitable for this purpose due to its great flexibility combined with robustness.

Identification of Correlated GRACE Monthly Harmonic Coefficients Using Pattern Recognition and Neural Networks

NASA Astrophysics Data System (ADS)

Piretzidis, D.; Sra, G.; Sideris, M. G.

2016-12-01

This study explores new methods for identifying correlation errors in harmonic coefficients derived from monthly solutions of the Gravity Recovery and Climate Experiment (GRACE) satellite mission using pattern recognition and neural network algorithms. These correlation errors are evidenced in the differences between monthly solutions and can be suppressed using a de-correlation filter. In all studies so far, the implementation of the de-correlation filter starts from a specific minimum order (i.e., 11 for RL04 and 38 for RL05) until the maximum order of the monthly solution examined. This implementation method has two disadvantages, namely, the omission of filtering correlated coefficients of order less than the minimum order and the filtering of uncorrelated coefficients of order higher than the minimum order. In the first case, the filtered solution is not completely free of correlated errors, whereas the second case results in a monthly solution that suffers from loss of geophysical signal. In the present study, a new method of implementing the de-correlation filter is suggested, by identifying and filtering only the coefficients that show indications of high correlation. Several numerical and geometric properties of the harmonic coefficient series of all orders are examined. Extreme cases of both correlated and uncorrelated coefficients are selected, and their corresponding properties are used to train a two-layer feed-forward neural network. The objective of the neural network is to identify and quantify the correlation by providing the probability of an order of coefficients to be correlated. Results show good performance of the neural network, both in the validation stage of the training procedure and in the subsequent use of the trained network to classify independent coefficients. The neural network is also capable of identifying correlated coefficients even when a small number of training samples and neurons are used (e.g.,100 and 10, respectively).

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.

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.

Identifying presence of correlated errors in GRACE monthly harmonic coefficients using machine learning algorithms

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sra, Gurveer; Karantaidis, George; Sideris, Michael G.

2017-04-01

A new method for identifying correlated errors in Gravity Recovery and Climate Experiment (GRACE) monthly harmonic coefficients has been developed and tested. Correlated errors are present in the differences between monthly GRACE solutions, and can be suppressed using a de-correlation filter. In principle, the de-correlation filter should be implemented only on coefficient series with correlated errors to avoid losing useful geophysical information. In previous studies, two main methods of implementing the de-correlation filter have been utilized. In the first one, the de-correlation filter is implemented starting from a specific minimum order until the maximum order of the monthly solution examined. In the second one, the de-correlation filter is implemented only on specific coefficient series, the selection of which is based on statistical testing. The method proposed in the present study exploits the capabilities of supervised machine learning algorithms such as neural networks and support vector machines (SVMs). The pattern of correlated errors can be described by several numerical and geometric features of the harmonic coefficient series. The features of extreme cases of both correlated and uncorrelated coefficients are extracted and used for the training of the machine learning algorithms. The trained machine learning algorithms are later used to identify correlated errors and provide the probability of a coefficient series to be correlated. Regarding SVMs algorithms, an extensive study is performed with various kernel functions in order to find the optimal training model for prediction. The selection of the optimal training model is based on the classification accuracy of the trained SVM algorithm on the same samples used for training. Results show excellent performance of all algorithms with a classification accuracy of 97% - 100% on a pre-selected set of training samples, both in the validation stage of the training procedure and in the subsequent use of the trained algorithms to classify independent coefficients. This accuracy is also confirmed by the external validation of the trained algorithms using the hydrology model GLDAS NOAH. The proposed method meet the requirement of identifying and de-correlating only coefficients with correlated errors. Also, there is no need of applying statistical testing or other techniques that require prior de-correlation of the harmonic coefficients.

CHAMP and GRACE Resonances and the Gravity Field of the Earth

NASA Astrophysics Data System (ADS)

Gooding, R. H.; Wagner, C. A.; Klokocnik, J.; Kostelecky, J.

With the far more precise orbits of CHAMP and GRACE today than was the standard 2-3 decades ago there was and is an unprecedented opportunity for determining precise and valuable values of certain lumped geopotential harmonic coefficients of selected orders independently of comprehensive gravity field models via the recently revived technique that capitalizes on the resonant variation of appropriate orbital elements the inclination in particular Here we first identify important resonances during the lifetime of CHAMP and GRACE in terms of the decaying semimajor axis these being 46 3 77 5 31 2 78 5 and 47 3 for CHAMP and 61 4 for GRACE Then we analyze state vectors for CHAMP and TLE for GRACE A from GFZ and determined the relevant lumped coefficients To increase its lifetime the CHAMP satellite orbit was raised twice in June and December 2002 so CHAMP passed through 31 2 resonance three times More accurate values for these coefficients are obtained than originally and the precision for the 62 4 overtone resonance implicit in 31 2 is striking comparable to that for 31 2 Most recently CHAMP passed throughout the 47 3 resonance yielding the opportunity to determine new lumped coefficients For GRACE we have no state vectors and have to work with the TLE only nevertheless we have lumped coefficients of 61st order from its strong 61 4 resonance In each case the resonant lumped values are compared with those derivable from various global gravity models We thereby confirm the continuing power of the resonance technique

High-frequency analysis of Earth gravity field models based on terrestrial gravity and GPS/levelling data: a case study in Greece

NASA Astrophysics Data System (ADS)

Papanikolaou, T. D.; Papadopoulos, N.

2015-06-01

The present study aims at the validation of global gravity field models through numerical investigation in gravity field functionals based on spherical harmonic synthesis of the geopotential models and the analysis of terrestrial data. We examine gravity models produced according to the latest approaches for gravity field recovery based on the principles of the Gravity field and steadystate Ocean Circulation Explorer (GOCE) and Gravity Recovery And Climate Experiment (GRACE) satellite missions. Furthermore, we evaluate the overall spectrum of the ultra-high degree combined gravity models EGM2008 and EIGEN-6C3stat. The terrestrial data consist of gravity and collocated GPS/levelling data in the overall Hellenic region. The software presented here implements the algorithm of spherical harmonic synthesis in a degree-wise cumulative sense. This approach may quantify the bandlimited performance of the individual models by monitoring the degree-wise computed functionals against the terrestrial data. The degree-wise analysis performed yields insight in the short-wavelengths of the Earth gravity field as these are expressed by the high degree harmonics.

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.

Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum

NASA Astrophysics Data System (ADS)

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

2009-04-01

This presentation 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. 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.

The Gravity field of Comet 67 P/Churyumov-Gerasimenko Expressed in Bispherical Harmonics

NASA Astrophysics Data System (ADS)

Andert, T.; Barriot, J. P.; Paetzold, M.; Sichoix, L.; Tellmann, S.; Häusler, B.

2015-12-01

On 6 August 2014, after a ten years cruise, the ESA-Rosetta spacecraft arrived at comet 67P/Churyumov-Gerasimenko. At that time the spacecraft was commanded to drift along with the comet at distances between 100 km and 50 km, the distance was then successfully lowered to 30 km in September 2014 and to 10 km in November 2014 and bound orbits could be achieved. Based on Doppler tracking data the Rosetta radio science experiment (RSI) was able to determine the mass of the nucleus and its gravity field in spherical harmonics series in order to constrain density and the internal structure of the nucleus. The shape of the comet is complex, a representation of the gravity field as belonging to one single body in either spherical or ellipsoidal harmonics series will give the shape of the body more preference than its internal structure. The observed shape of the nucleus, however, offers the opportunity to interpret it as consisting of two different bodies, namely the "head" and the "feet" sections of 67P/Churyumov-Gerasimenko, both having a nearly ellipsoidal shape. In this new approach, the bispherical harmonics expansion, the comet nucleus has been approximated by two independent lobes, each lobe represented by its own spherical harmonics expansion. As a result of the bispherical harmonics representation, it is anticipated that the gravity field will gain higher accuracy and will be less dominated by the complex shape of the comet. We have derived the analytical expressions of the gravity potential and its derivatives of a body in bispherical coordinates and applied this concept to the comet Churyumov-Gerasimenko. The paper will present the bispherical harmonics representation of the gravity field and first results derived from this new concept.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

Prediction for the Flow-induced Gravity Field of Saturn: Implications for Cassini’s Grand Finale

NASA Astrophysics Data System (ADS)

Galanti, Eli; Kaspi, Yohai

2017-07-01

The Cassini measurements of Saturn’s gravity field during its Grand Finale might shed light on a long-standing question regarding the flow on Saturn. While the cloud-level winds are well known, little is known about whether these winds are confined to the outer layers of the planet or penetrate deep into the interior. An additional complexity is added by the uncertainty in the exact rotation period of Saturn, a key factor in determining the cloud-level winds, with an effect on the north-south symmetric part of the winds. Using Saturn’s cloud-level winds we relate the flow to the gravity harmonics. We give a prediction for the odd harmonics {J}3,{J}5,{J}7,{and} {J}9 as a function of the flow depth, identifying three ranges of depths. Since the odd harmonics depend solely on the flow, and are not influenced by Saturn’s shape and static density distribution, any measured value of the odd harmonics by Cassini can be used to uniquely determine the depth of the flow. We also discuss the flow-induced even harmonics {{Δ }}{J}2,{{Δ }}{J}4,\\ldots ,{{Δ }}{J}12 that are affected by Saturn’s rotation period. While the high-degree even harmonics might also be used to determine the flow depth, the lower-degree even harmonics serve as uncertainties for analysis of the planet’s interior structure and composition. Thus, the gravity harmonics measured during the Cassini Grand Finale may be used to get a first-order estimate of the flow structure and to better constrain the planet’s density structure and composition.

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).

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.

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.

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.

The analysis of harmonic generation coefficients in the ablative Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Lu, Yan; Fan, Zhengfeng; Lu, Xinpei; Ye, Wenhua; Zou, Changlin; Zhang, Ziyun; Zhang, Wen

2017-10-01

In this research, we use the numerical simulation method to investigate the generation coefficients of the first three harmonics and the zeroth harmonic in the Ablative Rayleigh-Taylor Instability. It is shown that the interface shifts to the low temperature side during the ablation process. In consideration of the third-order perturbation theory, the first three harmonic amplitudes of the weakly nonlinear regime are calculated and then the harmonic generation coefficients are obtained by curve fitting. The simulation results show that the harmonic generation coefficients changed with time and wavelength. Using the higher-order perturbation theory, we find that more and more harmonics are generated in the later weakly nonlinear stage, which is caused by the negative feedback of the later higher harmonics. Furthermore, extending the third-order theory to the fifth-order theory, we find that the second and the third harmonics coefficients linearly depend on the wavelength, while the feedback coefficients are almost constant. Further analysis also shows that when the fifth-order theory is considered, the normalized effective amplitudes of second and third harmonics can reach about 25%-40%, which are only 15%-25% in the frame of the previous third-order theory. Therefore, the third order perturbation theory is needed to be modified by the higher-order theory when ηL reaches about 20% of the perturbation wavelength.

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.

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.

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.

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.

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.

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.

Two-harmonic complex spectral-domain optical coherence tomography using achromatic sinusoidal phase modulation

NASA Astrophysics Data System (ADS)

Lu, Sheng-Hua; Huang, Siang-Ru; Chou, Che-Chung

2018-03-01

We resolve the complex conjugate ambiguity in spectral-domain optical coherence tomography (SD-OCT) by using achromatic two-harmonic method. Unlike previous researches, the optical phase of the fiber interferometer is modulated by an achromatic phase shifter based on an optical delay line. The achromatic phase modulation leads to a wavelength-independent scaling coefficient for the two harmonics. Dividing the mean absolute value of the first harmonic by that of the second harmonic in a B-scan interferogram directly gives the scaling coefficient. It greatly simplifies the determination of the magnitude ratio between the two harmonics without the need of third harmonic and cumbersome iterative calculations. The inverse fast Fourier transform of the complex-valued interferogram constructed with the scaling coefficient, first and second harmonics yields a full-range OCT image. Experimental results confirm the effectiveness of the proposed achromatic two-harmonic technique for suppressing the mirror artifacts in SD-OCT images.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

Utilizing the Upcoming Gravity Measurements from Cassini's Proximal Orbits for Studying the Atmospheric Dynamics of Saturn - How Deep Do the Winds Penetrate?

NASA Astrophysics Data System (ADS)

Kaspi, Y.; Galanti, E.

2014-12-01

At the end of the Cassini mission, the spacecraft will descend into close-by proximal orbits around Saturn. During those proximal orbits, Cassini will obtain high precision gravity measurements of the planet. In this talk, we will discuss how this data can be used to estimate the depth of the observed flows on the planet. This can be done in several ways: 1. measurements of the high order even harmonics which beyond J10 are dominated by the dynamics; 2. measurements of odd gravity harmonics which have no contribution from a static planet, and therefore are a pure signature of dynamics; 3. upper limits on the depth can be obtained by comparing low order even harmonics from dynamical models to the difference between the measured low order even harmonics and the largest possible values of a static planet; 4. direct latitudinally varying measurements of the gravity field exerted on the spacecraft. We will discuss how these methods may be applied and show that given the expected sensitivity of Cassini the odd harmonics J3 and J5 will have the best sensitivity to deep dynamics, allowing detection of winds reaching only O(100km) deep, if those exist on Saturn. We use a hierarchy of dynamical models ranging from full 3D dynamical circulation models to simplified dynamical models where the sensitivity of the gravity field to the dynamics can be explored. In order to invert the gravity field to be measured by Cassini into the depth dependent circulation, an adjoint inverse model is constructed for the dynamical models, thus allowing backward integration of the dynamical model. This tool can be used for examination of various scenarios, including cases in which the depth of the wind depends on latitudinal position. In summary, we expect that the very end of Cassini's tour holds an opportunity for gravity measurements that may finally allow answering one of the long-lasting puzzles in planetary science regarding the depth of the zonal jets on the gas giants. In fact, as Juno will be performing similar measurements we hope to be able to build a picture of the dynamics for both Jupiter and Saturn. Answering this puzzle, will likely help explain the origin of the multiple jet streams and strong equatorial superrotation on the gas giants.

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.

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.

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.

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.

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.

The shifted harmonic approximation and asymptotic SU(2) and SU(1,1) Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Rowe, D. J.; de Guise, Hubert

2010-12-01

Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve these equations in asymptotic limits in which these eigenfunctions approach harmonic oscillator wavefunctions and thereby derive asymptotic expressions for these Clebsch-Gordan coefficients.

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%.

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

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.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less

Correction and update to 'The earth's C21 and S21 gravity coefficients and the rotation of the core'

NASA Technical Reports Server (NTRS)

Wahr, John

1990-01-01

Wahr (1987) used satellite constraints on C21 and S21 (the spherical harmonic coefficients of the earth's external gravitational potential) to infer certain properties of the core and core/mantle boundary. It is shown here, contrary to the claim by Wahr, that it is not possible to use C21 and S21 to placed bounds on the core's products of inertia. As a result, Wahr's constraints on the l = 2, m = 1 components of the core/mantle boundary topography and on the angular orientation of the inner core with respect to the earth's rotation vector are not justified. On the other hand, Wahr's conclusions about the time-averaged torque between the core and mantle and the resulting implications for the l = 2, m = 1 components of fluid pressure at the top of the core can be strengthened. Wahr's conclusions about the mean rotational flow in the core are unaltered.

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.

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.

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.

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.

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.

Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America

NASA Astrophysics Data System (ADS)

van der Wal, Wouter; Wu, Patrick; Sideris, Michael G.; Shum, C. K.

2008-10-01

Monthly geopotential spherical harmonic coefficients from the GRACE satellite mission are used to determine their usefulness and limitations for studying glacial isostatic adjustment (GIA) in North-America. Secular gravity rates are estimated by unweighted least-squares estimation using release 4 coefficients from August 2002 to August 2007 provided by the Center for Space Research (CSR), University of Texas. Smoothing is required to suppress short wavelength noise, in addition to filtering to diminish geographically correlated errors, as shown in previous studies. Optimal cut-off degrees and orders are determined for the destriping filter to maximize the signal to noise ratio. The halfwidth of the Gaussian filter is shown to significantly affect the sensitivity of the GRACE data (with respect to upper mantle viscosity and ice loading history). Therefore, the halfwidth should be selected based on the desired sensitivity. It is shown that increase in water storage in an area south west of Hudson Bay, from the summer of 2003 to the summer of 2006, contributes up to half of the maximum estimated gravity rate. Hydrology models differ in the predictions of the secular change in water storage, therefore even 4-year trend estimates are influenced by the uncertainty in water storage changes. Land ice melting in Greenland and Alaska has a non-negligible contribution, up to one-fourth of the maximum gravity rate. The estimated secular gravity rate shows two distinct peaks that can possibly be due to two domes in the former Pleistocene ice cover: west and south east of Hudson Bay. With a limited number of models, a better fit is obtained with models that use the ICE-3G model compared to the ICE-5G model. However, the uncertainty in interannual variations in hydrology models is too large to constrain the ice loading history with the current data span. For future work in which GRACE will be used to constrain ice loading history and the Earth's radial viscosity profile, it is important to include realistic uncertainty estimates for hydrology models and land ice melting in addition to the effects of lateral heterogeneity.

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.

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.

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.

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.

Orthogonality of spherical harmonic coefficients

NASA Astrophysics Data System (ADS)

McLeod, M. G.

1980-08-01

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

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.

Terrestrial gravity data analysis for interim gravity model improvement

NASA Technical Reports Server (NTRS)

1987-01-01

This is the first status report for the Interim Gravity Model research effort that was started on June 30, 1986. The basic theme of this study is to develop appropriate models and adjustment procedures for estimating potential coefficients from terrestrial gravity data. The plan is to use the latest gravity data sets to produce coefficient estimates as well as to provide normal equations to NASA for use in the TOPEX/POSEIDON gravity field modeling program.

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).

The design of a multi-harmonic step-tunable gyrotron

NASA Astrophysics Data System (ADS)

Qi, Xiang-Bo; Du, Chao-Hai; Zhu, Juan-Feng; Pan, Shi; Liu, Pu-Kun

2017-03-01

The theoretical study of a step-tunable gyrotron controlled by successive excitation of multi-harmonic modes is presented in this paper. An axis-encircling electron beam is employed to eliminate the harmonic mode competition. Physics images are depicted to elaborate the multi-harmonic interaction mechanism in determining the operating parameters at which arbitrary harmonic tuning can be realized by magnetic field sweeping to achieve controlled multiband frequencies' radiation. An important principle is revealed that a weak coupling coefficient under a high-harmonic interaction can be compensated by a high Q-factor. To some extent, the complementation between the high Q-factor and weak coupling coefficient makes the high-harmonic mode potential to achieve high efficiency. Based on a previous optimized magnetic cusp gun, the multi-harmonic step-tunable gyrotron is feasible by using harmonic tuning of first-to-fourth harmonic modes. Multimode simulation shows that the multi-harmonic gyrotron can operate on the 34 GHz first-harmonic TE11 mode, 54 GHz second-harmonic TE21 mode, 74 GHz third-harmonic TE31 mode, and 94 GHz fourth-harmonic TE41 mode, corresponding to peak efficiencies of 28.6%, 35.7%, 17.1%, and 11.4%, respectively. The multi-harmonic step-tunable gyrotron provides new possibilities in millimeter-terahertz source development especially for advanced terahertz applications.

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.

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 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.

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.

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.

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.

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

Determination of mean gravity anomalies in the Taiwan Island

NASA Technical Reports Server (NTRS)

Chang, Ruey-Gang

1989-01-01

The fitting and proper regression coefficients were made of one hundred seventeen 10 x 10' blocks with observed gravity data and corresponding elevation in the Taiwan Island. To compare five different predicted models, and the proper one for the mean gravity anomalies were determined. The predicted gravity anomalies of the non-observed gravity blocks were decided when the coefficients obtained through the model with the weighted mean method. It was suggested that the mean gravity anomalies of 10 x 10' blocks should be made when comprehensive the observed and predicted data.

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.

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.

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.

The motions of satellites and asteroids - Natural probes of Jovian gravity

NASA Technical Reports Server (NTRS)

Greenberg, R. J.

1976-01-01

Before the recent Pioneer probes, our knowledge of Jupiter's gravitational field was obtained from the motions of satellites and asteroids. The study of orbital perturbations of asteroids near the 2:1 commensurability yielded a value of the mass of the Jupiter system at least as precise as that obtained by the artificial probes. Precession of the inner satellites' orbits placed constraints on the harmonic coefficients J2 and J4. A correction to the satellite determination of J4 lowers its mean value closer to the Pioneer result. The orbital grouping among the outer satellites and the resonance among the Galilean satellites are described in detail, but the origins of these phenomena are not understood. However, recent research suggests that the explanation will be intimately associated with models of the origin and evolution of the planet itself.

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.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.

PubMed

Michael, J Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.

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.

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.

Limb and gravity-darkening coefficients for the TESS satellite at several metallicities, surface gravities, and microturbulent velocities

NASA Astrophysics Data System (ADS)

Claret, A.

2017-04-01

Aims: We present new gravity and limb-darkening coefficients for a wide range of effective temperatures, gravities, metallicities, and microturbulent velocities. These coefficients can be used in many different fields of stellar physics as synthetic light curves of eclipsing binaries and planetary transits, stellar diameters, line profiles in rotating stars, and others. Methods: The limb-darkening coefficients were computed specifically for the photometric system of the space mission tess and were performed by adopting the least-square method. In addition, the linear and bi-parametric coefficients, by adopting the flux conservation method, are also available. On the other hand, to take into account the effects of tidal and rotational distortions, we computed the passband gravity-darkening coefficients y(λ) using a general differential equation in which we consider the effects of convection and of the partial derivative (∂lnI(λ) /∂lng)Teff. Results: To generate the limb-darkening coefficients we adopt two stellar atmosphere models: atlas (plane-parallel) and phoenix (spherical, quasi-spherical, and r-method). The specific intensity distribution was fitted using five approaches: linear, quadratic, square root, logarithmic, and a more general one with four terms. These grids cover together 19 metallicities ranging from 10-5 up to 10+1 solar abundances, 0 ≤ log g ≤ 6.0 and 1500 K ≤Teff ≤ 50 000 K. The calculations of the gravity-darkening coefficients were performed for all plane-parallel ATLAS models. Tables 2-29 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/600/A30

Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies

NASA Technical Reports Server (NTRS)

Kim, Hyung Rae; von Frese, Ralph R. B.; Taylor, Patrick T.

2013-01-01

The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest

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.

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.

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.

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.

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.

Evaluation of thermograph data for California streams

USGS Publications Warehouse

Limerinos, J.T.

1978-01-01

Statistical analysis of water-temperature data from California streams indicates that, for most purposes, long-term operation of thermographs (automatic water-temperature recording instruments) does not provide a more useful record than either short-term operation of such instruments or periodic measurements. Harmonic analyses were made of thermograph records 5 to 14 years in length from 82 stations. More than 80 percent of the annual variation in water temperature is explained by the harmonic function for 77 of the 82 stations. Harmonic coefficients based on 8 years of thermograph record at 12 stations varied only slightly from coefficients computed using two equally split 4-year records. At five stations where both thermograph and periodic (10 to 23 measurements per year) data were collected concurrently, harmonic coefficients for periodic data were defined nearly as well as those for thermograph data. Results of this analysis indicate that, except where detailed surveillance of water temperatures is required or where there is a chance of temporal change, thermograph operations can be reduced substantially without affecting the usefulness of temperature records.

The moment of inertia and isostasy of Mars

NASA Technical Reports Server (NTRS)

Reasenberg, R. D.

1977-01-01

The systematic and large deviation of the gravitational equipotential surface (EPS) of Mars from a spheroid of revolution suggests a description of Mars in terms of a spheroid nearly in isostatic equilibrium with an extra mass in the Tharsis region. The displacement from Mars and the shape of the spheroid are calculated by using this description and a Mars gravity model. The EPS is represented as a contour map of its height above the spheroid. This representation provides the first clear demonstration that the Hellas depression coincides with a depression in the EPS. The disequilibrium contribution of Tharsis to the coefficient J2 of the second-degree harmonics of gravitational potential of Mars is estimated to be (126 + or - 5) times 10 to the minus 6th. The optical flattening and dynamic flattening calculated on this basis are in substantially better agreement than are those calculated in the usual way.

Earth-moon system: Dynamics and parameter estimation; numerical considerations and program documentation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1976-01-01

Major activities included coding and verifying equations of motion for the earth-moon system. Some attention was also given to numerical integration methods and parameter estimation methods. Existing analytical theories such as Brown's lunar theory, Eckhardt's theory for lunar rotation, and Newcomb's theory for the rotation of the earth were coded and verified. These theories serve as checks for the numerical integration. Laser ranging data for the period January 1969 - December 1975 was collected and stored on tape. The main goal of this research is the development of software to enable physical parameters of the earth-moon system to be estimated making use of data available from the Lunar Laser Ranging Experiment and the Very Long Base Interferometry experiment of project Apollo. A more specific goal is to develop software for the estimation of certain physical parameters of the moon such as inertia ratios, and the third and fourth harmonic gravity coefficients.

Comparison of observed and modeled seasonal crustal vertical displacements derived from multi-institution GPS and GRACE solutions

NASA Astrophysics Data System (ADS)

Gu, Yanchao; Fan, Dongming; You, Wei

2017-07-01

Eleven GPS crustal vertical displacement (CVD) solutions for 110 IGS08/IGS14 core stations provided by the International Global Navigation Satellite Systems Service Analysis Centers are compared with seven Gravity Recovery and Climate Experiment (GRACE)-modeled CVD solutions. The results of the internal comparison of the GPS solutions from multiple institutions imply large uncertainty in the GPS postprocessing. There is also evidence that GRACE solutions from both different institutions and different processing approaches (mascon and traditional spherical harmonic coefficients) show similar results, suggesting that GRACE can provide CVD results of good internal consistency. When the uncertainty of the GPS data is accounted for, the GRACE data can explain as much as 50% of the actual signals and more than 80% of the GPS annual signals. Our study strongly indicates that GRACE data have great potential to correct the nontidal loading in GPS time series.

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.

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics.

PubMed

Meziane, A; Norris, A N; Shuvalov, A L

2011-10-01

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface. © 2011 Acoustical Society of America

Periodic Heat Transfer at Small Pressure Fluctuations

NASA Technical Reports Server (NTRS)

Pfriem, H.

1943-01-01

The effect of cyclic gas pressure variations on the periodic heat transfer at a flat wall is theoretically analyzed and the differential equation describing the process and its solution for relatively. Small pressure fluctuations developed, thus explaining the periodic heat cycle between gas and wall surface. The processes for pure harmonic pressure and temperature oscillations, respectively, in the gas space are described by means of a constant heat transfer coefficient and the equally constant phase angle between the appearance of the maximum values of the pressure and heat flow most conveniently expressed mathematically in the form of a complex heat transfer coefficient. Any cyclic pressure oscillations, can be reduced by Fourier analysis to harmonic oscillations, which result in specific, mutual relationships of heat-transfer coefficients and phase angles for the different harmonics.

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.

Approximating high angular resolution apparent diffusion coefficient profiles using spherical harmonics under BiGaussian assumption

NASA Astrophysics Data System (ADS)

Cao, Ning; Liang, Xuwei; Zhuang, Qi; Zhang, Jun

2009-02-01

Magnetic Resonance Imaging (MRI) techniques have achieved much importance in providing visual and quantitative information of human body. Diffusion MRI is the only non-invasive tool to obtain information of the neural fiber networks of the human brain. The traditional Diffusion Tensor Imaging (DTI) is only capable of characterizing Gaussian diffusion. High Angular Resolution Diffusion Imaging (HARDI) extends its ability to model more complex diffusion processes. Spherical harmonic series truncated to a certain degree is used in recent studies to describe the measured non-Gaussian Apparent Diffusion Coefficient (ADC) profile. In this study, we use the sampling theorem on band-limited spherical harmonics to choose a suitable degree to truncate the spherical harmonic series in the sense of Signal-to-Noise Ratio (SNR), and use Monte Carlo integration to compute the spherical harmonic transform of human brain data obtained from icosahedral schema.

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.

Construction of SO(5)⊃SO(3) spherical harmonics and Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Caprio, M. A.; Rowe, D. J.; Welsh, T. A.

2009-07-01

The SO(5)⊃SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1,1)×SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃SO(3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients it becomes possible to compute the matrix elements of collective model observables by purely algebraic methods. Program summaryProgram title: GammaHarmonic Catalogue identifier: AECY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 346 421 No. of bytes in distributed program, including test data, etc.: 16 037 234 Distribution format: tar.gz Programming language: Mathematica 6 Computer: Any which supports Mathematica Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux Classification: 4.2 Nature of problem: Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S. Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors). Solution method: Construction of SO(5) ⊃ SO(3) spherical harmonics by orthonormalization, obtained from a generating set of functions, according to the method of Rowe, Turner, and Repka [1]. Matrix elements and Clebsch-Gordan coefficients follow by construction and integration of SO(3) scalar products. Running time: Depends strongly on the maximum SO(5) and SO(3) representation labels involved. A few minutes for the calculation in the Mathematica notebook. References: [1] D.J. Rowe, P.S. Turner, J. Repka, J. Math. Phys. 45 (2004) 2761.

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

Assessment of terrestrial water contributions to polar motion from GRACE and hydrological models

NASA Astrophysics Data System (ADS)

Jin, S. G.; Hassan, A. A.; Feng, G. P.

2012-12-01

The hydrological contribution to polar motion is a major challenge in explaining the observed geodetic residual of non-atmospheric and non-oceanic excitations since hydrological models have limited input of comprehensive global direct observations. Although global terrestrial water storage (TWS) estimated from the Gravity Recovery and Climate Experiment (GRACE) provides a new opportunity to study the hydrological excitation of polar motion, the GRACE gridded data are subject to the post-processing de-striping algorithm, spatial gridded mapping and filter smoothing effects as well as aliasing errors. In this paper, the hydrological contributions to polar motion are investigated and evaluated at seasonal and intra-seasonal time scales using the recovered degree-2 harmonic coefficients from all GRACE spherical harmonic coefficients and hydrological models data with the same filter smoothing and recovering methods, including the Global Land Data Assimilation Systems (GLDAS) model, Climate Prediction Center (CPC) model, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis products and European Center for Medium-Range Weather Forecasts (ECMWF) operational model (opECMWF). It is shown that GRACE is better in explaining the geodetic residual of non-atmospheric and non-oceanic polar motion excitations at the annual period, while the models give worse estimates with a larger phase shift or amplitude bias. At the semi-annual period, the GRACE estimates are also generally closer to the geodetic residual, but with some biases in phase or amplitude due mainly to some aliasing errors at near semi-annual period from geophysical models. For periods less than 1-year, the hydrological models and GRACE are generally worse in explaining the intraseasonal polar motion excitations.

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.

Measurement of attenuation coefficients of the fundamental and second harmonic waves in water

NASA Astrophysics Data System (ADS)

Zhang, Shuzeng; Jeong, Hyunjo; Cho, Sungjong; Li, Xiongbing

2016-02-01

Attenuation corrections in nonlinear acoustics play an important role in the study of nonlinear fluids, biomedical imaging, or solid material characterization. The measurement of attenuation coefficients in a nonlinear regime is not easy because they depend on the source pressure and requires accurate diffraction corrections. In this work, the attenuation coefficients of the fundamental and second harmonic waves which come from the absorption of water are measured in nonlinear ultrasonic experiments. Based on the quasilinear theory of the KZK equation, the nonlinear sound field equations are derived and the diffraction correction terms are extracted. The measured sound pressure amplitudes are adjusted first for diffraction corrections in order to reduce the impact on the measurement of attenuation coefficients from diffractions. The attenuation coefficients of the fundamental and second harmonics are calculated precisely from a nonlinear least squares curve-fitting process of the experiment data. The results show that attenuation coefficients in a nonlinear condition depend on both frequency and source pressure, which are much different from a linear regime. In a relatively lower drive pressure, the attenuation coefficients increase linearly with frequency. However, they present the characteristic of nonlinear growth in a high drive pressure. As the diffraction corrections are obtained based on the quasilinear theory, it is important to use an appropriate source pressure for accurate attenuation measurements.

Global Mass Flux Solutions from GRACE: A Comparison of Parameter Estimation Strategies - Mass Concentrations Versus Stokes Coefficients

NASA Technical Reports Server (NTRS)

Rowlands, D. D.; Luthcke, S. B.; McCarthy J. J.; Klosko, S. M.; Chinn, D. S.; Lemoine, F. G.; Boy, J.-P.; Sabaka, T. J.

2010-01-01

The differences between mass concentration (mas con) parameters and standard Stokes coefficient parameters in the recovery of gravity infonnation from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4deg x 4deg at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mas con solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2deg equal area mascons estimated every 10 days is presented.

The effect of Jupiter oscillations on Juno gravity measurements

NASA Astrophysics Data System (ADS)

Durante, Daniele; Guillot, Tristan; Iess, Luciano

2017-01-01

Seismology represents a unique method to probe the interiors of giant planets. Recently, Saturn's f-modes have been indirectly observed in its rings, and there is strong evidence for the detection of Jupiter global modes by means of ground-based, spatially-resolved, velocimetry measurements. We propose to exploit Juno's extremely accurate radio science data by looking at the gravity perturbations that Jupiter's acoustic modes would produce. We evaluate the perturbation to Jupiter's gravitational field using the oscillation spectrum of a polytrope with index 1 and the corresponding radial eigenfunctions. We show that Juno will be most sensitive to the fundamental mode (n = 0), unless its amplitude is smaller than 0.5 cm/s, i.e. 100 times weaker than the n ∼ 4 - 11 modes detected by spatially-resolved velocimetry. The oscillations yield contributions to Juno's measured gravitational coefficients similar to or larger than those expected from shallow zonal winds (extending to depths less than 300 km). In the case of a strong f-mode (radial velocity ∼ 30 cm/s), these contributions would become of the same order as those expected from deep zonal winds (extending to 3000 km), especially on the low degree zonal harmonics, therefore requiring a new approach to the analysis of Juno data.

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

Comparison of undulation difference accuracies using gravity anomalies and gravity disturbances. [for ocean geoid

NASA Technical Reports Server (NTRS)

Jekeli, C.

1980-01-01

Errors in the outer zone contribution to oceanic undulation differences computed from a finite set of potential coefficients based on satellite measurements of gravity anomalies and gravity disturbances are analyzed. Equations are derived for the truncation errors resulting from the lack of high-degree coefficients and the commission errors arising from errors in the available lower-degree coefficients, and it is assumed that the inner zone (spherical cap) is sufficiently covered by surface gravity measurements in conjunction with altimetry or by gravity anomaly data. Numerical computations of error for various observational conditions reveal undulation difference errors ranging from 13 to 15 cm and from 6 to 36 cm in the cases of gravity anomaly and gravity disturbance data, respectively for a cap radius of 10 deg and mean anomalies accurate to 10 mgal, with a reduction of errors in both cases to less than 10 cm as mean anomaly accuracy is increased to 1 mgal. In the absence of a spherical cap, both cases yield error estimates of 68 cm for an accuracy of 1 mgal and between 93 and 160 cm for the lesser accuracy, which can be reduced to about 110 cm by the introduction of a perfect 30-deg reference field.

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.

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

Virial Coefficients from Unified Statistical Thermodynamics of Quantum Gases Trapped under Generic Power Law Potential in d Dimension and Equivalence of Quantum Gases

NASA Astrophysics Data System (ADS)

Bahauddin, Shah Mohammad; Mehedi Faruk, Mir

2016-09-01

From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.

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.

Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

NASA Technical Reports Server (NTRS)

Gurgiolo, Chris; Vinas, Adolfo F.

2009-01-01

This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

Results from Radio Tracking the Rosetta Spacecraft: Gravity, Internal Structure and Nucleus Composition of 67P/Churyumov-Gerasimenko

NASA Astrophysics Data System (ADS)

Hahn, M.; Andert, T.; Asmar, S.; Bird, M. K.; Häusler, B.; Peter, K.; Tellmann, S.; Weissman, P. R.; Barriot, J. P.; Sierks, H.

2017-12-01

When Rosetta arrived at its target comet 67P/Churyumov-Gerasimenko it first performed a series of distant flybys (100 - 30 km). During this mission phase the mass of the comets nucleus could be determined by analyzing the RSI radio tracking data. In combination with the volume from images of the OSIRIS camera this resulted in a precise bulk density determination. That already gave first insights into the comets interior structure. The nucleus appears to be a low-density, highly porous dusty body. From bound orbits with distances below 30 km the low degree and order gravity field coefficients could be derived. The gravity field coefficients strongly depend on the nucleus irregular shape and on the interior mass distribution. The shape is very well reconstructed from of the OSIRIS camera images. Various models of the interior nucleus structure and density distributions are used to compute simulated values of the gravity field coefficients. A comparison with the observed coefficients yields the feasibility of the theoretical interior structure. Thus, the gravity field helps constraining models of the internal structure, the composition and also of the origin and formation of the comets nucleus.

An assessment of the ICE6G_C(VM5a) glacial isostatic adjustment model

NASA Astrophysics Data System (ADS)

Purcell, A.; Tregoning, P.; Dehecq, A.

2016-05-01

The recent release of the next-generation global ice history model, ICE6G_C(VM5a), is likely to be of interest to a wide range of disciplines including oceanography (sea level studies), space gravity (mass balance studies), glaciology, and, of course, geodynamics (Earth rheology studies). In this paper we make an assessment of some aspects of the ICE6G_C(VM5a) model and show that the published present-day radial uplift rates are too high along the eastern side of the Antarctic Peninsula (by ˜8.6 mm/yr) and beneath the Ross Ice Shelf (by ˜5 mm/yr). Furthermore, the published spherical harmonic coefficients—which are meant to represent the dimensionless present-day changes due to glacial isostatic adjustment (GIA)—contain excessive power for degree ≥90, do not agree with physical expectations and do not represent accurately the ICE6G_C(VM5a) model. We show that the excessive power in the high-degree terms produces erroneous uplift rates when the empirical relationship of Purcell et al. (2011) is applied, but when correct Stokes coefficients are used, the empirical relationship produces excellent agreement with the fully rigorous computation of the radial velocity field, subject to the caveats first noted by Purcell et al. (2011). Using the Australian National University (ANU) groups CALSEA software package, we recompute the present-day GIA signal for the ice thickness history and Earth rheology used by Peltier et al. (2015) and provide dimensionless Stokes coefficients that can be used to correct satellite altimetry observations for GIA over oceans and by the space gravity community to separate GIA and present-day mass balance change signals. We denote the new data sets as ICE6G_ANU.

Spheroidal models of the exterior gravitational field of Asteroids Bennu and Castalia

NASA Astrophysics Data System (ADS)

Sebera, Josef; Bezděk, Aleš; Pešek, Ivan; Henych, Tomáš

2016-07-01

Gravitational field of small bodies can be modeled e.g. with mascons, a polyhedral model or in terms of harmonic functions. If the shape of a body is close to the spheroid, it is advantageous to employ the spheroidal basis functions for expressing the gravitational field. Spheroidal harmonic models, similarly to the spherical ones, may be used in navigation and geophysical tasks. We focus on modeling the exterior gravitational field of oblate-like Asteroid (101955) Bennu and prolate-like Asteroid (4769) Castalia with spheroidal harmonics. Using the Gauss-Legendre quadrature and the spheroidal basis functions, we converted the gravitational potential of a particular polyhedral model of a constant density into the spheroidal harmonics. The results consist of (i) spheroidal harmonic coefficients of the exterior gravitational field for the Asteroids Bennu and Castalia, (ii) spherical harmonic coefficients for Bennu, and (iii) the first and second-order Cartesian derivatives in the local spheroidal South-East-Up frame for both bodies. The spheroidal harmonics offer biaxial flexibility (compared with spherical harmonics) and low computational costs that allow high-degree expansions (compared with ellipsoidal harmonics). The obtained spheroidal models for Bennu and Castalia represent the exterior gravitational field valid on and outside the Brillouin spheroid but they can be used even under this surface. For Bennu, 5 m above the surface the agreement with point-wise integration was 1% or less, while it was about 10% for Castalia due to its more irregular shape. As the shape models may produce very high frequencies, it was crucial to use higher maximum degree to reduce the aliasing. We have used the maximum degree 360 to achieve 9-10 common digits (in RMS) when reconstructing the input (the gravitational potential) from the spheroidal coefficients. The physically meaningful maximum degree may be lower (≪ 360) but its particular value depends on the distance and/or on the application (navigation, exploration, etc.).

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.

Traveling wave and soliton solutions of coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients.

PubMed

Zhong, Wei-Ping; Belić, Milivoj

2010-10-01

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

Solid harmonic wavelet scattering for predictions of molecule properties

NASA Astrophysics Data System (ADS)

Eickenberg, Michael; Exarchakis, Georgios; Hirn, Matthew; Mallat, Stéphane; Thiry, Louis

2018-06-01

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory (DFT). Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which we compute invariant "solid harmonic scattering coefficients" that account for different types of interactions at different scales. Multilinear regressions of various physical properties of molecules are computed from these invariant coefficients. Numerical experiments show that these regressions have near state-of-the-art performance, even with relatively few training examples. Predictions over small sets of scattering coefficients can reach a DFT precision while being interpretable.

Analytical Solution of Coupled Perturbation of Tesseral Harmonic Terms of Mars's Non-Spherical Gravitational Potential

NASA Astrophysics Data System (ADS)

Zhou, Chui-hong; Yu, Sheng-xian; Liu, Lin

2012-10-01

The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars' tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J2. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10-4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10-4 in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration.

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.

Co-Seismic Mass Dislocation and its Effect on Earth's Rotation and Gravity

NASA Technical Reports Server (NTRS)

Chao, B. F.; Gross, R. S.

2002-01-01

Mantle processes often involve large-scale mass transport, ranging from mantle convection, tectonic motions, glacial isostatic adjustment, to tides, atmospheric and oceanic loadings, volcanism and seismicity. On very short time scale of less than an hour, co-seismic event, apart from the shaking that is the earthquake, leaves behind permanent (step-function-like) dislocations in the crust and mantle. This redistribution of mass changes the Earth's inertia tensor (and hence Earth's rotation in both length-of-day and polar motion), and the gravity field (in terms of spherical harmonic Stokes coefficients). The question is whether these effects are large enough to be of any significance. In this paper we report updated calculation results based on Chao & Gross (1987). The calculation uses the normal mode summation scheme, applied to nearly twenty thousand major earthquakes that occurred during 1976-2002, according to source mechanism solutions given by the Harvard Central Moment Tensor catalog. Compared to the truly large ones earlier in the century, the earthquakes we study are individually all too small to have left any discernible signature in geodetic records of Earth rotation or global gravity field. However, their collective effects continue to exhibit an extremely strong statistical tendencies. For example, earthquakes conspire to decrease J2 and J22 while shortening LOD, resulting in a rounder and more compact Earth. Strong tendency is also seen in the earthquakes trying to nudge the Earth rotation pole towards approximately 140 degrees E, roughly opposite to the observed polar drift direction. The geophysical significance and implications will be further studied.

Co-Seismic Mass Dislocation and Its Effect on Earth's Rotation and Gravity

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.

1999-01-01

Mantle processes often involve large-scale mass transport, ranging from mantle convection, tectonic motions, glacial isostatic adjustment, to tides, atmospheric and oceanic loadings, volcanism and seismicity. On very short time scale of less than an hour, co-seismic event, apart from the "shaking" that is the earthquake, leaves behind permanent (step-function-like) dislocations in the crust and mantle. This redistribution of mass changes the Earth's inertia tensor (and hence Earth's rotation in both length-of-day and polar motion), and the gravity field (in terms of spherical harmonic Stokes coefficients). The question is whether these effects are large enough to be of any significance. In this paper we report updated calculation results. The calculation uses the normal mode summation scheme, applied to 15,814 major earthquakes that occurred during 1976-1998, according to source mechanism solutions given by the Harvard Central Moment Tensor catalog. Compared to the truly large ones earlier in the century, the earthquakes we study are individually all too small to have left any discernible signature in geodetic records of Earth rotation or global gravity field. However, their collective effects continue to exhibit an extremely strong statistical tendencies. For example, earthquakes conspire to decrease J(sub 2) and J(sub 22) while shortening LOD, resulting in a rounder and more compact Earth. Strong tendency is also seen in the earthquakes trying to "nudge" the Earth rotation pole towards about 140 degree E, roughly opposite to the observed polar drift direction. The geophysical significance and implications will be further studied.

GRACE AOD1B Product Release 06: Long-Term Consistency and the Treatment of Atmospheric Tides

NASA Astrophysics Data System (ADS)

Dobslaw, Henryk; Bergmann-Wolf, Inga; Dill, Robert; Poropat, Lea; Flechtner, Frank

2017-04-01

The GRACE satellites orbiting the Earth at very low altitudes are affected by rapid changes in the Earth's gravity field caused by mass redistribution in atmosphere and oceans. To avoid temporal aliasing of such high-frequency variability into the final monthly-mean gravity fields, those effects are typically modelled during the numerical orbit integration by appling the 6-hourly GRACE Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) a priori model. In preparation of the next GRACE gravity field re-processing currently performed by the GRACE Science Data System, a new version of AOD1B has been calculated. The data-set is based on 3-hourly surface pressure anomalies from ECMWF that have been mapped to a common reference orography by means of ECMWF's mean sea-level pressure diagnostic. Atmospheric tides as well as the corresponding oceanic response at the S1, S2, S3, and L2 frequencies and its annual modulations have been fitted and removed in order to retain the non-tidal variability only. The data-set is expanded into spherical harmonics complete up to degree and order 180. In this contribution, we will demonstrate that AOD1B RL06 is now free from spurious jumps in the time-series related to occasional changes in ECMWF's operational numerical weather prediction system. We will also highlight the rationale for separating tidal signals from the AOD1B coefficients, and will finally discuss the current quality of the AOD1B forecasts that have been introduced very recently for GRACE quicklook or near-realtime applications.

Determination of the natural convection coefficient in low-gravity

NASA Technical Reports Server (NTRS)

Goldmeer, J.; Motevalli, V.; Haghdoust, M.; Jumper, G.

1992-01-01

Fire safety is an important issue in the current space program; ignition in low-g needs to be studied. The reduction in the gravitational acceleration causes changes in the ignition process. This paper examines the effect of gravity on natural convection, which is one of the important parameters in the ignition process. The NASA-Lewis 2.2 Second Drop Tower provided the low-gravity environment for the experiments. A series of experiments was conducted to measure the temperature of a small copper plate which was heated by a high intensity lamp. These experiments verified that in low-gravity the plate temperature increased faster than in the corresponding 1-g cases, and that the natural convection coefficient rapidly decreased in the low-gravity environment.

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.

Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky's truncation coefficients

NASA Astrophysics Data System (ADS)

Bucha, Blažej; Hirt, Christian; Kuhn, Michael

2018-04-01

Spectral gravity forward modelling is a technique that converts a band-limited topography into its implied gravitational field. This conversion implicitly relies on global integration of topographic masses. In this paper, a modification of the spectral technique is presented that provides gravity effects induced only by the masses located inside or outside a spherical cap centred at the evaluation point. This is achieved by altitude-dependent Molodensky's truncation coefficients, for which we provide infinite series expansions and recurrence relations with a fixed number of terms. Both representations are generalized for an arbitrary integer power of the topography and arbitrary radial derivative. Because of the altitude-dependency of the truncation coefficients, a straightforward synthesis of the near- and far-zone gravity effects at dense grids on irregular surfaces (e.g. the Earth's topography) is computationally extremely demanding. However, we show that this task can be efficiently performed using an analytical continuation based on the gradient approach, provided that formulae for radial derivatives of the truncation coefficients are available. To demonstrate the new cap-modified spectral technique, we forward model the Earth's degree-360 topography, obtaining near- and far-zone effects on gravity disturbances expanded up to degree 3600. The computation is carried out on the Earth's surface and the results are validated against an independent spatial-domain Newtonian integration (1 μGal RMS agreement). The new technique is expected to assist in mitigating the spectral filter problem of residual terrain modelling and in the efficient construction of full-scale global gravity maps of highest spatial resolution.

Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series

NASA Astrophysics Data System (ADS)

Chanard, Kristel; Fleitout, Luce; Calais, Eric; Rebischung, Paul; Avouac, Jean-Philippe

2018-04-01

We model surface displacements induced by variations in continental water, atmospheric pressure, and nontidal oceanic loading, derived from the Gravity Recovery and Climate Experiment (GRACE) for spherical harmonic degrees two and higher. As they are not observable by GRACE, we use at first the degree-1 spherical harmonic coefficients from Swenson et al. (2008, https://doi.org/10.1029/2007JB005338). We compare the predicted displacements with the position time series of 689 globally distributed continuous Global Navigation Satellite System (GNSS) stations. While GNSS vertical displacements are well explained by the model at a global scale, horizontal displacements are systematically underpredicted and out of phase with GNSS station position time series. We then reestimate the degree 1 deformation field from a comparison between our GRACE-derived model, with no a priori degree 1 loads, and the GNSS observations. We show that this approach reconciles GRACE-derived loading displacements and GNSS station position time series at a global scale, particularly in the horizontal components. Assuming that they reflect surface loading deformation only, our degree-1 estimates can be translated into geocenter motion time series. We also address and assess the impact of systematic errors in GNSS station position time series at the Global Positioning System (GPS) draconitic period and its harmonics on the comparison between GNSS and GRACE-derived annual displacements. Our results confirm that surface mass redistributions observed by GRACE, combined with an elastic spherical and layered Earth model, can be used to provide first-order corrections for loading deformation observed in both horizontal and vertical components of GNSS station position time series.

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!

Simplified aeroelastic modeling of horizontal axis wind turbines

NASA Technical Reports Server (NTRS)

Wendell, J. H.

1982-01-01

Certain aspects of the aeroelastic modeling and behavior of the horizontal axis wind turbine (HAWT) are examined. Two simple three degree of freedom models are described in this report, and tools are developed which allow other simple models to be derived. The first simple model developed is an equivalent hinge model to study the flap-lag-torsion aeroelastic stability of an isolated rotor blade. The model includes nonlinear effects, preconing, and noncoincident elastic axis, center of gravity, and aerodynamic center. A stability study is presented which examines the influence of key parameters on aeroelastic stability. Next, two general tools are developed to study the aeroelastic stability and response of a teetering rotor coupled to a flexible tower. The first of these tools is an aeroelastic model of a two-bladed rotor on a general flexible support. The second general tool is a harmonic balance solution method for the resulting second order system with periodic coefficients. The second simple model developed is a rotor-tower model which serves to demonstrate the general tools. This model includes nacelle yawing, nacelle pitching, and rotor teetering. Transient response time histories are calculated and compared to a similar model in the literature. Agreement between the two is very good, especially considering how few harmonics are used. Finally, a stability study is presented which examines the effects of support stiffness and damping, inflow angle, and preconing.

Stream-temperature characteristics in Georgia

USGS Publications Warehouse

Dyar, T.R.; Alhadeff, S. Jack

1997-01-01

Stream-temperature measurements for 198 periodic and 22 daily record stations were analyzed using a harmonic curve-fitting procedure. Statistics of data from 78 selected stations were used to compute a statewide stream-temperature harmonic equation, derived using latitude, drainage area, and altitude for natural streams having drainage areas greater than about 40 square miles. Based on the 1955-84 reference period, the equation may be used to compute long-term natural harmonic stream-temperature coefficients to within an on average of about 0.4? C. Basin-by-basin summaries of observed long-term stream-temperature characteristics are included for selected stations and river reaches, particularly along Georgia's mainstem streams. Changes in the stream- temperature regimen caused by the effects of development, principally impoundments and thermal power plants, are shown by comparing harmonic curves and coefficients from the estimated natural values to the observed modified-condition values.

Third-harmonic generation of a laser-driven quantum dot with impurity

NASA Astrophysics Data System (ADS)

Sakiroglu, S.; Kilic, D. Gul; Yesilgul, U.; Ungan, F.; Kasapoglu, E.; Sari, H.; Sokmen, I.

2018-06-01

The third-harmonic generation (THG) coefficient for a laser-driven quantum dot with an on-center Gaussian impurity under static magnetic field is theoretically investigated. Laser field effect is treated within the high-frequency Floquet approach and the analytical expression of the THG coefficient is deduced from the compact density-matrix approach. The numerical results demonstrate that the application of intense laser field causes substantial changes on the behavior of THG. In addition the position and magnitude of the resonant peak of THG coefficient is significantly affected by the magnetic field, quantum dot size and the characteristic parameters of the impurity potential.

A study of isotropic-nematic transition of quadrupolar Gay-Berne fluid using density-functional theory approach

NASA Astrophysics Data System (ADS)

Singh, Ram Chandra; Ram, Jokhan

2011-11-01

The effects of quadrupole moments on the isotropic-nematic (IN) phase transitions are studied using the density-functional theory (DFT) for a Gay-Berne (GB) fluid for a range of length-to-breadth parameters ? in the reduced temperature range ? . The pair-correlation functions of the isotropic phase, which enter into the DFT as input parameters are found by solving the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 are considered. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent function. As the length-to-breadth ratio of quadrupolar GB molecules is increased, the IN transition is seen to move to lower density (and pressure) at a given temperature. It has been observed that the DFT is good to study the IN transitions in such fluids. The theoretical results have also been compared with the computer simulation results wherever they are available.

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.

Photospheric magnetic fields in six magnetographs

NASA Astrophysics Data System (ADS)

Virtanen, Ilpo; Mursula, Kalevi

2016-10-01

Photospheric magnetic field has been routinely observed since 1950s, but calibrated digital data exist only since 1970s. The longest uniform data set is measured at the Wilcox Solar Observatory (WSO), covering 40 years from 1976 onwards. However, the WSO instrument operates in very low spatial resolution and suffers from saturation of strong fields. Other, higher resolution instruments like those at NSO Kitt Peak (KP) offer a more detailed view of the solar magnetic field, but several instrument updates make the data less uniform. While the different observatories show a similar large scale structure of the photospheric field, the measured magnetic field intensities differ significantly between the observatories. In this work we study the photospheric magnetic fields and, especially, the scaling of the magnetic field intensity between six independent data sets. We use synoptic maps constructed from the measurements of the photospheric magnetic field at Wilcox Solar Observatory, Mount Wilson Observatory (MWO), Kitt Peak (KP), SOLIS, SOHO/MDI and SDO/HMI. We calculate the harmonic expansion of the magnetic field from all six data sets and investigate the scaling of harmonic coefficients between the observations. We investigate how scaling depends on latitude and field strength, as well as on the solar cycle phase, and what is the effect of polar field filling in KP, SOLIS and MDI. We find that scaling factors based on harmonic coefficients are in general smaller than scaling factors based on pixel-by-pixel comparison or histogram techniques. This indicates that a significant amount of total flux is contained in the high harmonics of the higher resolution observations that are beyond the resolution of WSO. We note that only scaling factors based on harmonic coefficients should be used when using the PFSS-model, since the other methods tend to lead to overestimated values of the magnetic flux. The scaling of the low order harmonic coefficients is typically different than for higher terms. The most problematic harmonic is the axial quadrupole term, which is known to be noisy and to suffer from observational limitations (e.g., the vantage point effect). We did not find significant solar cycle variation in the scaling factors.

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.

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.

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2017-08-01

In order to move the polar singularity of arbitrary spherical harmonic expansion to a point on the equator, we rotate the expansion around the y-axis by 90° such that the x-axis becomes a new pole. The expansion coefficients are transformed by multiplying a special value of Wigner D-matrix and a normalization factor. The transformation matrix is unchanged whether the coefficients are 4 π fully normalized or Schmidt quasi-normalized. The matrix is recursively computed by the so-called X-number formulation (Fukushima in J Geodesy 86: 271-285, 2012a). As an example, we obtained 2190× 2190 coefficients of the rectangular rotated spherical harmonic expansion of EGM2008. A proper combination of the original and the rotated expansions will be useful in (i) integrating the polar orbits of artificial satellites precisely and (ii) synthesizing/analyzing the gravitational/geomagnetic potentials and their derivatives accurately in the high latitude regions including the arctic and antarctic area.

A comprehensive study of Mercury and MESSENGER orbit determination

NASA Astrophysics Data System (ADS)

Genova, Antonio; Mazarico, Erwan; Goossens, Sander; Lemoine, Frank G.; Neumann, Gregory A.; Nicholas, Joseph B.; Rowlands, David D.; Smith, David E.; Zuber, Maria; Solomon, Sean C.

2016-10-01

The MErcury, Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft orbited the planet Mercury for more than 4 years. The probe started its science mission in orbit around Mercury on 18 March 2011. The Mercury Laser Altimeter (MLA) and radio science system were the instruments dedicated to geodetic observations of the topography, gravity field, orientation, and tides of Mercury. X-band radio-tracking range-rate data collected by the NASA Deep Space Network (DSN) allowed the determination of Mercury's gravity field to spherical harmonic degree and order 100, the planet's obliquity, and the Love number k2.The extensive range data acquired in orbit around Mercury during the science mission (from April 2011 to April 2015), and during the three flybys of the planet in 2008 and 2009, provide a powerful dataset for the investigation of Mercury's ephemeris. The proximity of Mercury's orbit to the Sun leads to a significant perihelion precession attributable to the gravitational flattening of the Sun (J2) and the Parameterized Post-Newtonian (PPN) coefficients γ and β, which describe the space curvature produced by a unit rest mass and the nonlinearity in superposition of gravity, respectively. Therefore, the estimation of Mercury's ephemeris can provide crucial information on the interior structure of the Sun and Einstein's general theory of relativity. However, the high correlation among J2, γ, and β complicates the combined recovery of these parameters, so additional assumptions are required, such as the Nordtvedt relationship η = 4β - γ - 3.We have modified our orbit determination software, GEODYN II, to enable the simultaneous integration of the spacecraft and central body trajectories. The combined estimation of the MESSENGER and Mercury orbits allowed us to determine a more accurate gravity field, orientation, and tides of Mercury, and the values of GM and J2 for the Sun, where G is the gravitational constant and M is the solar mass. Several test cases illuminate results on the estimation of PPN parameters.

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.

The 5'×5' global geoid model GGM2016

NASA Astrophysics Data System (ADS)

Shen, WenBin; Han, Jiancheng

2016-04-01

We provide an updated 5'×5' global geoid model GGM2016, which is determined based on the shallow layer method (Shen 2006). We choose an inner surface S below the EGM2008 geoid, and the layer bounded by the inner surface S and the Earth's geographical surface E is referred to as the shallow layer. The Earth's geographical surface E is determined by the digital topographic model DTM2006.0 combining with the DNSC2008 mean sea surface. We determine the 3D shallow layer model (SLM) using the refined crust density model CRUST1.0-5min, which is an improved 5'×5' density model of the CRUST1.0 with taking into account the corrections of the areas covered by ice sheets and the land-ocean crossing regions. Based on the SLM and the gravity field EGM2008 defined outside the Earth's geographical surface E, we determine the gravity field EGM2008S defined in the region outside the inner surface S, extending the gravity field's definition domain from the domain outside E to the domain outside S. Based on the geodetic equation W(P)=W0, where W0 is the geopotential constant on the geoid, we determine a 5'×5' global geoid model GGM2016, which provides both the 5'×5' grid values and spherical harmonic coefficient expressions. Comparisons show that the GGM2016 fits the globally available GPS/leveling points better than the EGM2008 geoid. This study is supported by National 973 Project China (grant Nos. 2013CB733301 and 2013CB733305), NSFC (grant Nos. 41174011, 41210006, 41429401, 41128003, 41021061).

Tests of local Lorentz invariance violation of gravity in the standard model extension with pulsars.

PubMed

Shao, Lijing

2014-03-21

The standard model extension is an effective field theory introducing all possible Lorentz-violating (LV) operators to the standard model and general relativity (GR). In the pure-gravity sector of minimal standard model extension, nine coefficients describe dominant observable deviations from GR. We systematically implemented 27 tests from 13 pulsar systems to tightly constrain eight linear combinations of these coefficients with extensive Monte Carlo simulations. It constitutes the first detailed and systematic test of the pure-gravity sector of minimal standard model extension with the state-of-the-art pulsar observations. No deviation from GR was detected. The limits of LV coefficients are expressed in the canonical Sun-centered celestial-equatorial frame for the convenience of further studies. They are all improved by significant factors of tens to hundreds with existing ones. As a consequence, Einstein's equivalence principle is verified substantially further by pulsar experiments in terms of local Lorentz invariance in gravity.

Determination of Enceladus' gravity field from Cassini radio science data

NASA Astrophysics Data System (ADS)

Parisi, Marzia; Iess, Luciano; Ducci, Marco

2014-05-01

In May 2012 the Cassini spacecraft completed its last gravity flyby of Saturn's moon Enceladus (identified as E19 in the sequence), following E9 in April 2010 and E12 in November 2010. The multiarc analysis of the gravity data collected during these low-altitude encounters has produced a stable solution for the gravity field of Enceladus, leading to compelling inferences and implications on the interior structure, but also raising new questions on the evolution of this small but yet fascinating icy body. The gravitational signature of the satellite was detected by means of precise Doppler tracking of the Cassini spacecraft around closest approach (±3h) of the three flybys. Cassini tracking system exploits both X/X and X/Ka links, with accuracies that range between 0.02 - 0.09 mm/s at 60 s integration time. Range-rate measurements were processed into a multi-arc least square filter so as to attain a solution for the quadrupole field of Enceladus and its degree-3 zonal harmonic J3, the most important indication of hemispherical asymmetries. In addition to these crucial parameters, corrections to the estimated orbits of Cassini and Enceladus were applied. The inclusion in the dynamical model of the neutral particle drag exerted by Enceladus south polar plumes (1) is essential for a satisfactory orbital fit. The results of the analysis show that Enceladus is indeed characterized by a predominant quadrupole term, with its J2/C22 ratio being that of a body not in hydrostatic equilibrium. The estimate of tesseral degree-2 coefficients (C21, S21 and C22), being statistically close to 0 (at a 3-σ level), imply that the adopted rotational model for the satellite is consistent with the observed gravity field. Furthermore, the estimated value for J3 turned out to be statistically significant (although only about 1/50 of J2) and pointing at a significant hemispherical asymmetry that is consistent with the presence of a regional sea at depth. References (1) C.C. Porco et al., Science 311, 1393 (2006).

Tests and comparisons of gravity models.

NASA Technical Reports Server (NTRS)

Marsh, J. G.; Douglas, B. C.

1971-01-01

Optical observations of the GEOS satellites were used to obtain orbital solutions with different sets of geopotential coefficients. The solutions were compared before and after modification to high order terms (necessary because of resonance) and were then analyzed by comparing subsequent observations with predicted trajectories. The most important source of error in orbit determination and prediction for the GEOS satellites is the effect of resonance found in most published sets of geopotential coefficients. Modifications to the sets yield greatly improved orbits in most cases. The results of these comparisons suggest that with the best optical tracking systems and gravity models, satellite position error due to gravity model uncertainty can reach 50-100 m during a heavily observed 5-6 day orbital arc. If resonant coefficients are estimated, the uncertainty is reduced considerably.

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.

The earth's C21 and S21 gravity coefficients and the rotation of the core

NASA Technical Reports Server (NTRS)

Wahr, John M.

1987-01-01

Observational results for the earth's C21 and S21 gravity coefficients can be used to constrain the mean equatorial rotation of the core with respect to the mantle. Current satellite gravity solutions suggest the equatorial rotation rate is no larger than 1 x 10 to the -7th times the earth's diurnal spin rate, a limit more than one order of magnitude smaller than the polar rotation rate inferred from the westward drift of the earth's magnetic field. The next generation gravity solutions should improve this constraint by more than one order of magnitude. Implications for the fluid pressure at the core-mantle boundary and for the shape of that boundary are discussed.

Evaluating Descent and Ascent Trajectories Near Non-Spherical Bodies

NASA Technical Reports Server (NTRS)

Werner, Robert A.

2010-01-01

Spacecraft landing on small bodies pass through regions where conventional gravitation formulations using exterior spherical harmonics are inaccurate. An investigation shows that a formulation using interior solid spherical harmonics might be satisfactory. Interior spherical harmonic expansions are usable inside an imaginary, empty sphere. For this application, such a sphere could be positioned in empty space above the intended landing site and rotating with the body. When the spacecraft is inside this sphere, the interior harmonic expansion would be used instead of the conventional, exterior harmonic expansion. Coefficients can be determined by a least-squares fit to gravitation measurements synthesized from conventional formulations. Due to their unfamiliarity, recurrences for interior, as well as exterior, expansions are derived. Hotine's technique for partial derivatives of exterior spherical harmonics is extended to interior harmonics.

An improved model for the Earth's gravity field

NASA Technical Reports Server (NTRS)

Tapley, B. D.; Shum, C. K.; Yuan, D. N.; Ries, J. C.; Schutz, B. E.

1989-01-01

An improved model for the Earth's gravity field, TEG-1, was determined using data sets from fourteen satellites, spanning the inclination ranges from 15 to 115 deg, and global surface gravity anomaly data. The satellite measurements include laser ranging data, Doppler range-rate data, and satellite-to-ocean radar altimeter data measurements, which include the direct height measurement and the differenced measurements at ground track crossings (crossover measurements). Also determined was another gravity field model, TEG-1S, which included all the data sets in TEG-1 with the exception of direct altimeter data. The effort has included an intense scrutiny of the gravity field solution methodology. The estimated parameters included geopotential coefficients complete to degree and order 50 with selected higher order coefficients, ocean and solid Earth tide parameters, Doppler tracking station coordinates and the quasi-stationary sea surface topography. Extensive error analysis and calibration of the formal covariance matrix indicate that the gravity field model is a significant improvement over previous models and can be used for general applications in geodesy.

Enriching and Separating Primary Copper Impurity from Pb-3 Mass Pct Cu Melt by Super-Gravity Technology

NASA Astrophysics Data System (ADS)

Yang, Yuhou; Song, Bo; Song, Gaoyang; Yang, Zhanbing; Xin, Wenbin

2016-10-01

In this study, super-gravity technology was introduced in the lead bullion-refining process to investigate the enriching and separating laws of copper impurity from Pb-3 mass pct Cu melt. With the gravity coefficient G = 700 at the cooling rate of ν = 5 K min-1, the entire copper phase gathers at the upper area of the sample, and it is hard to find any copper particles at the bottom area of the sample. The floatation movement of copper phase was greatly intensified by super gravity and the mass pct of copper in tailing lead is up to 8.631 pct, while that in the refined lead is only 0.113 pct. The refining rate of lead bullion reached up to 94.27 pct. Copper-phase impurity can be separated effectively from Pb-3 mass pct Cu melt by filtration method in super-gravity field, and the separation efficiency increased with the increasing gravity coefficient in the range of G ≥ 10. After filtration at 613 K (340 °C) with gravity coefficient G = 100 for 10 minutes, the refined lead, with just 0.157 mass pct copper impurity, was separated to the bottom of the crucible, and the copper dross containing only 23.56 mass pct residual lead was intercepted by the carbon fiber felt, leading to the separation efficiency up to 96.18 pct (meaning a great reduction in metal loss).

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.

Constraining the interior density profile of a Jovian planet from precision gravity field data

NASA Astrophysics Data System (ADS)

Movshovitz, Naor; Fortney, Jonathan J.; Helled, Ravit; Hubbard, William B.; Thorngren, Daniel; Mankovich, Chris; Wahl, Sean; Militzer, Burkhard; Durante, Daniele

2017-10-01

The external gravity field of a planetary body is determined by the distribution of mass in its interior. Therefore, a measurement of the external field, properly interpreted, tells us about the interior density profile, ρ(r), which in turn can be used to constrain the composition in the interior and thereby learn about the formation mechanism of the planet. Planetary gravity fields are usually described by the coefficients in an expansion of the gravitational potential. Recently, high precision measurements of these coefficients for Jupiter and Saturn have been made by the radio science instruments on the Juno and Cassini spacecraft, respectively.The resulting coefficients come with an associated uncertainty. And while the task of matching a given density profile with a given set of gravity coefficients is relatively straightforward, the question of how best to account for the uncertainty is not. In essentially all prior work on matching models to gravity field data, inferences about planetary structure have rested on imperfect knowledge of the H/He equation of state and on the assumption of an adiabatic interior. Here we wish to vastly expand the phase space of such calculations. We present a framework for describing all the possible interior density structures of a Jovian planet, constrained only by a given set of gravity coefficients and their associated uncertainties. Our approach is statistical. We produce a random sample of ρ(a) curves drawn from the underlying (and unknown) probability distribution of all curves, where ρ is the density on an interior level surface with equatorial radius a. Since the resulting set of density curves is a random sample, that is, curves appear with frequency proportional to the likelihood of their being consistent with the measured gravity, we can compute probability distributions for any quantity that is a function of ρ, such as central pressure, oblateness, core mass and radius, etc. Our approach is also bayesian, in that it can utilize any prior assumptions about the planet's interior, as necessary, without being overly constrained by them.We demonstrate this approach with a sample of Jupiter interior models based on recent Juno data and discuss prospects for Saturn.

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.

Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods

NASA Technical Reports Server (NTRS)

Chau, Jessica Furrer; Or, Dani; Sukop, Michael C.; Steinberg, S. L. (Principal Investigator)

2005-01-01

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.

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

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.

The influence of the atmosphere on geoid and potential coefficient determinations from gravity data

NASA Technical Reports Server (NTRS)

Rummel, R.; Rapp, R. H.

1976-01-01

For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moritz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correction term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30 deg, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055 millionths at n = 2, m = 2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.

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.

Spherical harmonics coefficients for ligand-based virtual screening of cyclooxygenase inhibitors.

PubMed

Wang, Quan; Birod, Kerstin; Angioni, Carlo; Grösch, Sabine; Geppert, Tim; Schneider, Petra; Rupp, Matthias; Schneider, Gisbert

2011-01-01

Molecular descriptors are essential for many applications in computational chemistry, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure and properties. We investigate a spherical harmonics descriptor for shape-based virtual screening. We introduce and validate a partially rotation-invariant three-dimensional molecular shape descriptor based on the norm of spherical harmonics expansion coefficients. Using this molecular representation, we parameterize molecular surfaces, i.e., isosurfaces of spatial molecular property distributions. We validate the shape descriptor in a comprehensive retrospective virtual screening experiment. In a prospective study, we virtually screen a large compound library for cyclooxygenase inhibitors, using a self-organizing map as a pre-filter and the shape descriptor for candidate prioritization. 12 compounds were tested in vitro for direct enzyme inhibition and in a whole blood assay. Active compounds containing a triazole scaffold were identified as direct cyclooxygenase-1 inhibitors. This outcome corroborates the usefulness of spherical harmonics for representation of molecular shape in virtual screening of large compound collections. The combination of pharmacophore and shape-based filtering of screening candidates proved to be a straightforward approach to finding novel bioactive chemotypes with minimal experimental effort.

Lorentz violation and gravity

NASA Astrophysics Data System (ADS)

Bailey, Quentin G.

2007-08-01

This work explores the theoretical and experimental aspects of Lorentz violation in gravity. A set of modified Einstein field equations is derived from the general Lorentz-violating Standard-Model Extension (SME). Some general theoretical implications of these results are discussed. The experimental consequences for weak-field gravitating systems are explored in the Earth- laboratory setting, the solar system, and beyond. The role of spontaneous Lorentz-symmetry breaking is discussed in the context of the pure-gravity sector of the SME. To establish the low-energy effective Einstein field equations, it is necessary to take into account the dynamics of 20 coefficients for Lorentz violation. As an example, the results are compared with bumblebee models, which are general theories of vector fields with spontaneous Lorentz violation. The field equations are evaluated in the post- newtonian limit using a perfect fluid description of matter. The post-newtonian metric of the SME is derived and compared with some standard test models of gravity. The possible signals for Lorentz violation due to gravity-sector coefficients are studied. Several new effects are identified that have experimental implications for current and future tests. Among the unconventional effects are a new type of spin precession for a gyroscope in orbit and a modification to the local gravitational acceleration on the Earth's surface. These and other tests are expected to yield interesting sensitivities to dimensionless gravity- sector coefficients.

Comment on "An Assessment of the ICE-6G_C (VM5a) Glacial Isostatic Adjustment Model" by Purcell et al.

NASA Astrophysics Data System (ADS)

Richard Peltier, W.; Argus, Donald F.; Drummond, Rosemarie

2018-02-01

The most recently published model of the glacial isostatic adjustment process in the ICE-NG (VMX) sequence from the University of Toronto, denoted ICE-6G_C (VM5a), was originally developed to degree and order 256 in spherical harmonics and has been shown to provide accurate fits to a voluminous database of GPS observations from North America, Eurasia, and Antarctica, to time dependent gravity data being provided by the GRACE satellites, and to radiocarbon-dated relative sea level histories through the Holocene epoch. The authors of the Purcell et al. (2016, https://doi.org/10.1002/2015JB012742) paper have suggested this model to be flawed. We have produced a further version of our model, denoted ICE-6G_D (VM5a), by employing the same BEDMAP2 bathymetry for the Southern Ocean as employed in their analysis which has somewhat reduced the differences between our results. However, significant physically important differences remain, including the magnitude of present-day vertical crustal motion in the embayments and in the spectrum of Stokes coefficients for present-day geoid height time dependence which continues to "flatten" at high spherical harmonic degree. We explore the reasons for these differences and trace them to the use by Purcell et al. of a loading history for the embayments that differs significantly from that tabulated for both the original and modified versions of our model.

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.

Analysis of higher harmonics on bidirectional heat pulse propagation experiment in helical and tokamak plasmas

NASA Astrophysics Data System (ADS)

Kobayashi, T.; Ida, K.; Inagaki, S.; Tsuchiya, H.; Tamura, N.; Choe, G. H.; Yun, G. S.; Park, H. K.; Ko, W. H.; Evans, T. E.; Austin, M. E.; Shafer, M. W.; Ono, M.; López-bruna, D.; Ochando, M. A.; Estrada, T.; Hidalgo, C.; Moon, C.; Igami, H.; Yoshimura, Y.; Tsujimura, T. Ii.; Itoh, S.-I.; Itoh, K.

2017-07-01

In this contribution we analyze modulation electron cyclotron resonance heating (MECH) experiment and discuss higher harmonic frequency dependence of transport coefficients. We use the bidirectional heat pulse propagation method, in which both inward propagating heat pulse and outward propagating heat pulse are analyzed at a radial range, in order to distinguish frequency dependence of transport coefficients due to hysteresis from that due to other reasons, such as radially dependent transport coefficients, a finite damping term, or boundary effects. The method is applied to MECH experiments performed in various helical and tokamak devices, i.e. Large Helical Device (LHD), TJ-II, Korea Superconducting Tokamak Advanced Research (KSTAR), and Doublet III-D (DIII-D) with different plasma conditions. The frequency dependence of transport coefficients are clearly observed, showing a possibility of existence of transport hysteresis in flux-gradient relation.

Improved power control using optimal adjustable coefficients for three-phase photovoltaic inverter under unbalanced grid voltage.

PubMed

Wang, Qianggang; Zhou, Niancheng; Lou, Xiaoxuan; Chen, Xu

2014-01-01

Unbalanced grid faults will lead to several drawbacks in the output power quality of photovoltaic generation (PV) converters, such as power fluctuation, current amplitude swell, and a large quantity of harmonics. The aim of this paper is to propose a flexible AC current generation method by selecting coefficients to overcome these problems in an optimal way. Three coefficients are brought in to tune the output current reference within the required limits of the power quality (the current harmonic distortion, the AC current peak, the power fluctuation, and the DC voltage fluctuation). Through the optimization algorithm, the coefficients can be determined aiming to generate the minimum integrated amplitudes of the active and reactive power references with the constraints of the inverter current and DC voltage fluctuation. Dead-beat controller is utilized to track the optimal current reference in a short period. The method has been verified in PSCAD/EMTDC software.

Improved Power Control Using Optimal Adjustable Coefficients for Three-Phase Photovoltaic Inverter under Unbalanced Grid Voltage

PubMed Central

Wang, Qianggang; Zhou, Niancheng; Lou, Xiaoxuan; Chen, Xu

2014-01-01

Unbalanced grid faults will lead to several drawbacks in the output power quality of photovoltaic generation (PV) converters, such as power fluctuation, current amplitude swell, and a large quantity of harmonics. The aim of this paper is to propose a flexible AC current generation method by selecting coefficients to overcome these problems in an optimal way. Three coefficients are brought in to tune the output current reference within the required limits of the power quality (the current harmonic distortion, the AC current peak, the power fluctuation, and the DC voltage fluctuation). Through the optimization algorithm, the coefficients can be determined aiming to generate the minimum integrated amplitudes of the active and reactive power references with the constraints of the inverter current and DC voltage fluctuation. Dead-beat controller is utilized to track the optimal current reference in a short period. The method has been verified in PSCAD/EMTDC software. PMID:25243215

Combination of GRACE monthly gravity field solutions from different processing strategies

NASA Astrophysics Data System (ADS)

Jean, Yoomin; Meyer, Ulrich; Jäggi, Adrian

2018-02-01

We combine the publicly available GRACE monthly gravity field time series to produce gravity fields with reduced systematic errors. We first compare the monthly gravity fields in the spatial domain in terms of signal and noise. Then, we combine the individual gravity fields with comparable signal content, but diverse noise characteristics. We test five different weighting schemes: equal weights, non-iterative coefficient-wise, order-wise, or field-wise weights, and iterative field-wise weights applying variance component estimation (VCE). The combined solutions are evaluated in terms of signal and noise in the spectral and spatial domains. Compared to the individual contributions, they in general show lower noise. In case the noise characteristics of the individual solutions differ significantly, the weighted means are less noisy, compared to the arithmetic mean: The non-seasonal variability over the oceans is reduced by up to 7.7% and the root mean square (RMS) of the residuals of mass change estimates within Antarctic drainage basins is reduced by 18.1% on average. The field-wise weighting schemes in general show better performance, compared to the order- or coefficient-wise weighting schemes. The combination of the full set of considered time series results in lower noise levels, compared to the combination of a subset consisting of the official GRACE Science Data System gravity fields only: The RMS of coefficient-wise anomalies is smaller by up to 22.4% and the non-seasonal variability over the oceans by 25.4%. This study was performed in the frame of the European Gravity Service for Improved Emergency Management (EGSIEM; http://www.egsiem.eu) project. The gravity fields provided by the EGSIEM scientific combination service (ftp://ftp.aiub.unibe.ch/EGSIEM/) are combined, based on the weights derived by VCE as described in this article.

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.

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.

Using Radial Basis Functions in Airborne Gravimetry for Local Geoid Improvement

NASA Astrophysics Data System (ADS)

Li, Xiaopeng

2017-04-01

Radial basis functions (RBF, Schmidt et al 2007, Klees and Wittwer 2007, Klees et al 2008) have been extensively used in satellite geodetic applications (Eicker 2008, Wittwer 2009, Naeimi 2013, among others). However, to date, to the author's knowledge, their roles in processing and modeling airborne gravity data have not been fully advocated or extensively investigated in detail, though compared with satellite missions, the airborne data is more suitable for this kind of localized basis functions especially considering the following facts: (1) Unlike the satellite missions that can provide global or near global data coverage, airborne gravity data is usually geographically limited. (2) It is also band limited in the frequency domain, considering that various filter banks and/or de-noising techniques (Li 2007) have to be applied to overcome the low signal-to-noise ratio problem that is present in airborne gravimetric systems. This is mainly due to the mechanical and mathematical limitations in computing the accelerations (both the kinematic and dynamic accelerations, Jekeli 2000). (3) It is much easier to formulate the RBF observation equations from an airborne gravimetric system (either a scalar one (Forsberg and Olesen 2010) or a vector one (Kwon and Jekeli 2001)) than from any satellite mission, especially compared with Gravity Recovery and Climate Experiment satellites (GRACE, Tapley et al. 2004) where many accurate background environmental models have to be used in order to separate out the gravity related functionals. As a result, in this study, a set of band-limited RBF is developed to model and downward continue the airborne gravity data for local geoid improvement. First, the algorithm is tested with synthesized data from global coefficient models such as EIGEN6c4 (Försteet al. 2014), during which the RBF not only successfully recovers a harmonic field but also presents filtering properties due to its particular design in the frequency domain. Then, the software is tested for the GSVS14 (Geoid Slope Validation Survey 2014) area as well as for the area around Puerto Rico and the U.S. Virgin Islands by using the real airborne gravity data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D, Smith 2007) project. The newly acquired cm-level accurate GPS/Leveling bench marks prove the RBF airborne enhanced geoid models are not inferior to other models computed by conventional approaches. By fully utilizing the three dimensional correlation information among the flight tracks, the RBF can also be used as a data editing tool for airborne data adjustment and cleaning.

Constraining Saturn's interior density profile from precision gravity field measurement obtained during Grand Finale

NASA Astrophysics Data System (ADS)

Movshovitz, N.; Fortney, J. J.; Helled, R.; Hubbard, W. B.; Mankovich, C.; Thorngren, D.; Wahl, S. M.; Militzer, B.; Durante, D.

2017-12-01

The external gravity field of a planetary body is determined by the distribution of mass in its interior. Therefore, a measurement of the external field, properlyinterpreted, tells us about the interior density profile, ρ(r), which in turn can be used to constrain the composition in the interior and thereby learn about theformation mechanism of the planet. Recently, very high precision measurements of the gravity coefficients for Saturn have been made by the radio science instrument on the Cassini spacecraft during its Grand Finale orbits. The resulting coefficients come with an associated uncertainty. The task of matching a given density profile to a given set of gravity coefficients is relatively straightforward, but the question of how to best account for the uncertainty is not. In essentially all prior work on matching models to gravity field data inferences about planetary structure have rested on assumptions regarding the imperfectly known H/He equation of state and the assumption of an adiabatic interior. Here we wish to vastly expand the phase space of such calculations. We present a framework for describing all the possible interior density structures of a Jovian planet constrained by a given set of gravity coefficients and their associated uncertainties. Our approach is statistical. We produce a random sample of ρ(a) curves drawn from the underlying (and unknown) probability distribution of all curves, where ρ is the density on an interior level surface with equatorial radius a. Since the resulting set of density curves is a random sample, that is, curves appear with frequency proportional to the likelihood of their being consistent with the measured gravity, we can compute probability distributions for any quantity that is a function of ρ, such as central pressure, oblateness, core mass and radius, etc. Our approach is also Bayesian, in that it can utilize any prior assumptions about the planet's interior, as necessary, without being overly constrained by them. We apply this approach to produce a sample of Saturn interior models based on gravity data from Grand Finale orbits and discuss their implications.

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.

A technique for the determination of center of gravity and rolling resistance for tilt-seat wheelchairs.

PubMed

Lemaire, E D; Lamontagne, M; Barclay, H W; John, T; Martel, G

1991-01-01

A balance platform setup was defined for use in the determination of the center of gravity in the sagittal plane for a wheelchair and patient. Using the center of gravity information, measurements from the wheelchair and patient (weight, tire coefficients of friction), and various assumptions (constant speed, level-concrete surface, patient-wheelchair system is a rigid body), a method for estimating the rolling resistance for a wheelchair was outlined. The center of gravity and rolling resistance techniques were validated against criterion values (center of gravity error = 1 percent, rolling resistance root mean square error = 0.33 N, rolling resistance Pearson correlation coefficient = 0.995). Consistent results were also obtained from a test dummy and five subjects. Once the center of gravity is known, it is possible to evaluate the stability of a wheelchair (in terms of tipping over) and the interaction between the level of stability and rolling resistance. These quantitative measures are expected to be of use in the setup of wheelchairs with a variable seat angle and variable wheelbase length or when making comparisons between different wheelchairs.

Decoupling Identification for Serial Two-Link Two-Inertia System

NASA Astrophysics Data System (ADS)

Oaki, Junji; Adachi, Shuichi

The purpose of our study is to develop a precise model by applying the technique of system identification for the model-based control of a nonlinear robot arm, under taking joint-elasticity into consideration. We previously proposed a systematic identification method, called “decoupling identification,” for a “SCARA-type” planar two-link robot arm with elastic joints caused by the Harmonic-drive® reduction gears. The proposed method serves as an extension of the conventional rigid-joint-model-based identification. The robot arm is treated as a serial two-link two-inertia system with nonlinearity. The decoupling identification method using link-accelerometer signals enables the serial two-link two-inertia system to be divided into two linear one-link two-inertia systems. The MATLAB®'s commands for state-space model estimation are utilized in the proposed method. Physical parameters such as motor inertias, link inertias, joint-friction coefficients, and joint-spring coefficients are estimated through the identified one-link two-inertia systems using a gray-box approach. This paper describes accuracy evaluations using the two-link arm for the decoupling identification method under introducing closed-loop-controlled elements and varying amplitude-setup of identification-input. Experimental results show that the identification method also works with closed-loop-controlled elements. Therefore, the identification method is applicable to a “PUMA-type” vertical robot arm under gravity.

Soliton tunneling in the nonlinear Schrödinger equation with variable coefficients and an external harmonic potential.

PubMed

Zhong, Wei-Ping; Belić, Milivoj R

2010-05-01

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such solutions occurring under special conditions; specifically when the spatial solitons pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity coefficients. Our results show that the solitons display tunneling effects not only when passing through the nonlinear potential barriers or wells but also when passing through the diffractive barriers or wells. During tunneling the solitons may also undergo a controllable compression.

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.

Investigation of a geodesy coexperiment to the Gravity Probe B relativity gyroscope program

NASA Technical Reports Server (NTRS)

Everitt, C. W. F.; Parkinson, Bradford W.; Tapley, Mark

1993-01-01

Geodesy is the science of measuring the gravitational field of and positions on the Earth. Estimation of the gravitational field via gravitation gradiometry, the measurement of variations in the direction and magnitude of gravitation with respect to position, is this dissertation's focus. Gravity Probe B (GP-B) is a Stanford satellite experiment in gravitational physics. GP-B will measure the precession the rotating Earth causes on the space time around it by observing the precessions of four gyroscopes in a circular, polar, drag-free orbit at 650 km altitude. The gyroscopes are nearly perfect niobium-coated spheres of quartz, operating at 1.8 K to permit observations with extremely low thermal noise. The permissible gyroscope drift rate is miniscule, so the torques on the gyros must be tiny. A drag-free control system, by canceling accelerations caused by nongravitational forces, minimizes the support forces and hence torques. The GP-B system offers two main possibilities for geodesy. One is as a drag-free satellite to be used in trajectory-based estimates of the Earth's gravity field. We described calculations involving that approach in our previous reports, including comparison of laser only, GPS only, and combined tracking and a preliminary estimate of the possibility of estimating relativistic effects on the orbit. The second possibility is gradiometry. This technique has received a more cursory examination in previous reports, so we concentrate on it here. We explore the feasibility of using the residual suspension forces centering the GP-B gyros as gradiometer signals for geodesy. The objective of this work is a statistical prediction of the formal uncertainty in an estimate of the Earth's gravitation field using data from GP-B. We perform an instrument analysis and apply two mathematical techniques to predict uncertainty. One is an analytical approach using a flat-Earth approximation to predict geopotential information quality as a function of spatial wavelength. The second estimates the covariance matrix arising in a least-squares estimate of a spherical harmonic representation of the geopotential using GP-B gradiometer data. The results show that the GP-B data set can be used to create a consistent estimate of the geopotential up to spherical harmonic degree and order 60. The formal uncertainty of all coefficients between degrees 5 and 50 is reduced by factors of up to 30 over current satellite-only estimates and up to 7 over estimates which include surface data. The primary conclusion resulting from this study is that the gravitation gradiometer geodesy coexperiment to GP-B is both feasible and attractive.

A New Unified Approach to Determine Geocenter Motion Using Space Geodesy and GRACE Gravity Data

NASA Astrophysics Data System (ADS)

Wu, X.; Kusche, J.; Landerer, F. W.

2016-12-01

Spherical harmonic expansions of Earth's surface mass variations start from three degree-1 terms. These longest-wavelength terms induce geocenter motion between the center-of-mass of the total Earth system (CM) and the center-of-figure of the solid Earth surface (CF), and a degree-1 surface deformation field. For complete spectral coverage and robust assessment of geographic mass budget using GRACE data, very accurate knowledge of geocenter motion between CM and CF is required with precision goals of 0.2 mm in annual amplitude and 0.2 mm/yr leading to equivalent degree-1 coefficients. However, GRACE's K-band ranging data system is not sensitive to these variation modes. Although satellite laser ranging (SLR) system is thought to have the most reliable sensitivity to CM, its surface network is very sparse and can only deliver motion between CM and the center of a changing network (CN) of roughly 20 unevenly distributed stations. Recently, the network has been extended to include 82 stations with their geocentric displacements derived by transferring SLR's CM sensitivity to other technique networks through local tie and co-motion constraints. The CM-CN motion of this network has a better agreement with the geocenter motion result from a global inversion of relative GPS, GRACE, and the ECCO ocean bottom pressure (OBP) model. Still, there is no guarantee that such a CM-CN motion is the same as the CM-CF motion. Also, the global inversion result is subject to the impact of unknown errors in the OBP model. To improve reliability of geocenter motion determination, we use a new unified approach to geocenter motion determination by combining geocentric displacements of ground stations with GRACE gravity data. Both translational and deformational signatures will be exploited for retrieval of the degree-1 surface mass variation coefficients. Higher degree terms are estimated simultaneously using GRACE gravity data, which further improves CF knowledge and reduces aliasing effects. Such a data combination also uses full covariance matrices of all data types to facilitate a reliable variance component estimation. High-precision results for non-linear geocenter motion have been achieved and will be reported. We will also discuss challenges and strategies for improving geocenter velocity determination.

Harmonic regression of Landsat time series for modeling attributes from national forest inventory data

NASA Astrophysics Data System (ADS)

Wilson, Barry T.; Knight, Joseph F.; McRoberts, Ronald E.

2018-03-01

Imagery from the Landsat Program has been used frequently as a source of auxiliary data for modeling land cover, as well as a variety of attributes associated with tree cover. With ready access to all scenes in the archive since 2008 due to the USGS Landsat Data Policy, new approaches to deriving such auxiliary data from dense Landsat time series are required. Several methods have previously been developed for use with finer temporal resolution imagery (e.g. AVHRR and MODIS), including image compositing and harmonic regression using Fourier series. The manuscript presents a study, using Minnesota, USA during the years 2009-2013 as the study area and timeframe. The study examined the relative predictive power of land cover models, in particular those related to tree cover, using predictor variables based solely on composite imagery versus those using estimated harmonic regression coefficients. The study used two common non-parametric modeling approaches (i.e. k-nearest neighbors and random forests) for fitting classification and regression models of multiple attributes measured on USFS Forest Inventory and Analysis plots using all available Landsat imagery for the study area and timeframe. The estimated Fourier coefficients developed by harmonic regression of tasseled cap transformation time series data were shown to be correlated with land cover, including tree cover. Regression models using estimated Fourier coefficients as predictor variables showed a two- to threefold increase in explained variance for a small set of continuous response variables, relative to comparable models using monthly image composites. Similarly, the overall accuracies of classification models using the estimated Fourier coefficients were approximately 10-20 percentage points higher than the models using the image composites, with corresponding individual class accuracies between six and 45 percentage points higher.

Rotationally invariant clustering of diffusion MRI data using spherical harmonics

NASA Astrophysics Data System (ADS)

Liptrot, Matthew; Lauze, François

2016-03-01

We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation. After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.1 The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice.

Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

NASA Astrophysics Data System (ADS)

Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

2018-05-01

Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

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.

Spherical Harmonics Analysis of the ECMWF Global Wind Fields at the 10-Meter Height Level During 1985: A Collection of Figures Illustrating Results

NASA Technical Reports Server (NTRS)

Sanchez, Braulio V.; Nishihama, Masahiro

1997-01-01

Half-daily global wind speeds in the east-west (u) and north-south (v) directions at the 10-meter height level were obtained from the European Centre for Medium Range Weather Forecasts (ECMWF) data set of global analyses. The data set covered the period 1985 January to 1995 January. A spherical harmonic expansion to degree and order 50 was used to perform harmonic analysis of the east-west (u) and north-south (v) velocity field components. The resulting wind field is displayed, as well as the residual of the fit, at a particular time. The contribution of particular coefficients is shown. The time variability of the coefficients up to degree and order 3 is presented. Corresponding power spectrum plots are given. Time series analyses were applied also to the power associated with degrees 0-10; the results are included.

Modification of LAMPF's magnet-mapping code for offsets of center coordinates

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

Hurd, J.W.; Gomulka, S.; Merrill, F.

1991-01-01

One of the magnet measurements performed at LAMPF is the determination of the cylindrical harmonics of a quadrupole magnet using a rotating coil. The data are analyzed with the code HARMAL to derive the amplitudes of the harmonics. Initially, the origin of the polar coordinate system is the axis of the rotating coil. A new coordinate system is found by a simple translation of the old system such that the dipole moment in the new system is zero. The origin of this translated system is referred to as the magnetic center. Given this translation, the code calculates the coefficients ofmore » the cylindrical harmonics in the new system. The code has been modified to use an analytical calculation to determine these new coefficients. The method of calculation is described and some implications of this formulation are presented. 8 refs., 2 figs.« less

Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging.

PubMed

Weavers, Paul T; Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Tryggestad, Erik J; Gunter, Jeffrey L; McGee, Kiaran P; Litwiller, Daniel V; Hwang, Ken-Pin; Bernstein, Matt A

2017-05-01

Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs. 5th) spherical harmonic coefficients for better spatial accuracy in MRI. A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems. A decrease in the root-mean-square error (RMSE) over a 50cm diameter spherical volume from 1.80mm to 0.77mm is reported here in the case of replacing the vendor's standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner. The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor standard corrections. Copyright © 2016 Elsevier Inc. All rights reserved.

Second harmonic generation: Effects of the multiple reflections of the fundamental and the second harmonic waves on the Maker fringes

NASA Astrophysics Data System (ADS)

Tellier, Gildas; Boisrobert, Christian

2007-11-01

The Maker fringes technique is commonly used for the determination of nonlinear optical coefficients. In this article, we present a new formulation of Maker fringes in parallel-surface samples, using boundary conditions taking into account the anisotropy of the crystal, the refractive-index dispersion, and the reflections of the fundamental and the second harmonic waves inside the material. Complete expressions for the generated second harmonic intensity are given for birefringent crystals for the case of no pump depletion. A comparison between theory and experimental results is made, showing the accuracy of our theoretical expressions.

Sensitivity of selected geomagnetic properties to truncation level of spherical harmonic expansions

NASA Technical Reports Server (NTRS)

Benton, E. R.; Estes, R. H.; Langel, R. A.; Muth, L. A.

1982-01-01

The model dependence of Gauss coefficients associated with a lack of spherical harmonic orthogonality on a nonuniform Magsat data grid is shown to be minor, where the fitting level exceeds the harmonic order by a value of approximately four. The shape of the magnetic energy spectrum outside the core, and the sensitivity to truncation level of magnetic contour location and the number of their intersections on the core-mantle boundary, suggest that spherical harmonic expansions of the main geomagnetic field should be truncated at a truncation level value of not more than eight if they are to be extrapolated to the core.

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.

Geoid Recovery Using Geophysical Inverse Theory Applied to Satellite to Satellite Tracking Data

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

2000-01-01

This report describes a new method for determination of the geopotential, or the equivalent geoid. It is based on Satellite-to-Satellite Tracking (SST) of two co-orbiting low earth satellites separated by a few hundred kilometers. The analysis is aimed at the GRACE Mission, though it is generally applicable to any SST data. It is proposed that the SST be viewed as a mapping mission. That is, the result will be maps of the geoid or gravity, as contrasted with determination of spherical harmonics or Fourier coefficients. A method has been developed, based on Geophysical Inverse Theory (GIT), that can provide maps at a prescribed (desired) resolution and the corresponding error map from the SST data. This computation can be done area by area avoiding simultaneous recovery of all the geopotential information. The necessary elements of potential theory, celestial mechanics, and Geophysical Inverse Theory are described, a computation architecture is described, and the results of several simulations presented. Centimeter accuracy geoids with 50 to 100 km resolution can be recovered with a 30 to 60 day mission.

SELENE mission: mathematical model for SST Doppler measurements

NASA Astrophysics Data System (ADS)

Ping, J.; Kono, Y.; Kawano, N.; Hanada, H.; Matsumoto, K.

2001-09-01

Japanese lunar exploration mission, SELENE, has been planned to be launched into space by using H II-a rocket in the Summer of 2004. This mission is composed of 3 subsatellites, a main lunar orbiter, a relay satellite and a free flying VLBI radio source. One of its main scientific objectives is the estimation of high order and degree spherical harmonic coefficients for the lunar gravity field. Different tracking methods will be employed in SELENE. The key tracking method is 4 way Satellite-to-Satellite Tracking (SST) technique. By this way, the tracking data can be obtained through the relay when the low altitude main orbiter is flying at the far-side of the Moon and can not be "seen" from the Earth. To success the historical tracking data, a complete coverage of Doppler tracking from an orbiter at sufficiently low altitude with high tracking accuracy can be obtained. The 4 way SST has various configurations. For SELENE, the SST tracking mode is introduced here, the mathematical relation between range rate and 4 way Doppler count number is established, and a data processing stream frame by using GEODYN II is suggested.

Oceanic tide maps and spherical harmonic coefficients from Geosat altimetry

NASA Technical Reports Server (NTRS)

Cartwright, D. E.; Ray, R. D.; Sanchez, B. V.

1991-01-01

Maps and tables for the global ocean tides, 69 degree N to 68 degree S, derived from two years of Geosat altimetry are presented. Global maps of local and Greenwich admittance of the (altimetric) ocean tide, and maps of amplitude and Greenwich phase lag of the ocean tide are shown for M(sub 2), S(sub 2), N(sub 2), O(sub 1), and K(sub 1). Larger scale maps of amplitude and phases are also shown for regional areas of special interest. Spherical harmonic coefficients of the ocean tide through degree and order 8 are tabulated for the six major constituents.

On the frequency spectra of the core magnetic field Gauss coefficients

NASA Astrophysics Data System (ADS)

Lesur, Vincent; Wardinski, Ingo; Baerenzung, Julien; Holschneider, Matthias

2018-03-01

From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k-2 slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.

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.

Is the Non-Dipole Magnetic Field Random?

NASA Technical Reports Server (NTRS)

Walker, Andrew D.; Backus, George E.

1996-01-01

Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.

Large amplitude Fourier transformed ac voltammetry at a rotating disc electrode: a versatile technique for covering Levich and flow rate insensitive regimes in a single experiment.

PubMed

Bano, Kiran; Kennedy, Gareth F; Zhang, Jie; Bond, Alan M

2012-04-14

The theory for large amplitude Fourier transformed ac voltammetry at a rotating disc electrode is described. Resolution of time domain data into dc and ac harmonic components reveals that the mass transport for the dc component is controlled by convective-diffusion, while the background free higher order harmonic components are flow rate insensitive and mainly governed by linear diffusion. Thus, remarkable versatility is available; Levich behaviour of the dc component limiting current provides diffusion coefficient values and access to higher harmonics allows fast electrode kinetics to be probed. Two series of experiments (dc and ac voltammetry) have been required to extract these parameters; here large amplitude ac voltammetry with RDE methodology is used to demonstrate that kinetics and diffusion coefficient information can be extracted from a single experiment. To demonstrate the power of this approach, theoretical and experimental comparisons of data obtained for the reversible [Ru(NH(3))(6)](3+/2+) and quasi-reversible [Fe(CN)(6)](3-/4-) electron transfer processes are presented over a wide range of electrode rotation rates and with different concentrations and electrode materials. Excellent agreement of experimental and simulated data is achieved, which allows parameters such as electron transfer rate, diffusion coefficient, uncompensated resistance and others to be determined using a strategically applied approach that takes into account the different levels of sensitivity of each parameter to the dc or the ac harmonic.

Estimating Geocenter Motion and Changes in the Earth's Dynamic Oblateness from a Statistically Optimal Combination of GRACE Data and Geophysical Models

NASA Astrophysics Data System (ADS)

Sun, Y.; Ditmar, P.; Riva, R.

2016-12-01

Time-varying gravity field solutions of the GRACE satellite mission enable an observation of Earth's mass transport on a monthly basis since 2002. One of the remaining challenges is how to complement these solutions with sufficiently accurate estimates of very low-degree spherical harmonic coefficients, particularly degree-1 coefficients and C20. An absence or inaccurate estimation of these coefficients may result in strong biases in mass transports estimates. Variations in degree-1 coefficients reflect geocenter motion and variations in the C20coefficients describe changes in the Earth's dynamic oblateness (ΔJ2). In this study, we developed a novel methodology to estimate monthly variations in degree-1 and C20coefficients by combing GRACE data with oceanic mass anomalies (combination approach). Unlike the method by Swenson et al. (2008), the proposed approach exploits noise covariance information of both input datasets and thus produces stochastically optimal solutions. A numerical simulation study is carried out to verify the correctness and performance of the proposed approach. We demonstrate that solutions obtained with the proposed approach have a significantly higher quality, as compared to the method by Swenson et al. Finally, we apply the proposed approach to real monthly GRACE solutions. To evaluate the obtained results, we calculate mass transport time-series over selected regions where minimal mass anomalies are expected. A clear reduction in the RMS of the mass transport time-series (more than 50 %) is observed there when the degree-1 and C20 coefficients obtained with the proposed approach are used. In particular, the seasonal pattern in the mass transport time-series disappears almost entirely. The traditional approach (degree-1 coefficients based on Swenson et al. (2008) and C20 based on SLR data), in contrast, does not reduce that RMS or even makes it larger (e.g., over the Sahara desert). We further show that the degree-1 variations play a major role in the observed improvement. At the same time, the usage of the C20 solutions obtained with the combination approach yields a similar accuracy of mass anomaly estimates, as compared to the results based on SLR analysis. The computed degree-1 and C20 coefficients will be made publicly available.

A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

NASA Astrophysics Data System (ADS)

Krzyścin, Janusz

1990-01-01

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. Using Gent and Taylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.

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.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

NASA Astrophysics Data System (ADS)

Bansal, Dipanshu; Aref, Amjad; Dargush, Gary; Delaire, Olivier

2016-09-01

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound \\text{FeSi} over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.

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…

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).

A problem in representing the core magnetic field of the earth using spherical harmonics

NASA Technical Reports Server (NTRS)

Carle, H. M.; Harrison, C. G. A.

1982-01-01

Although there are computational advantages to the representation of the earth's magnetic field by spherical harmonic coefficients of the magnetic potential, up to the thirteenth degree and order, the following disadvantages emerge: (1) the use of spherical harmonics of up to a certain degree does not remove wavelengths greater than a certain value from the surface fields, and (2) the total field magnitudes represented by spherical harmonics up to a certain degree have minimum wavelengths equal to the circumference of the earth divided by twice the maximum degree of the harmonic used. The implications of the ways in which surface fields are separated into core and crustal components are discussed, and it is concluded that since field signals are generated in the core, the representation of the core field by spherical harmonics of potential does not adequately represent all core field components.

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.

Circular current loops, magnetic dipoles and spherical harmonic analysis.

USGS Publications Warehouse

Alldredge, L.R.

1980-01-01

Spherical harmonic analysis (SHA) is the most used method of describing the Earth's magnetic field, even though spherical harmonic coefficients (SHC) almost completely defy interpretation in terms of real sources. Some moderately successful efforts have been made to represent the field in terms of dipoles placed in the core in an effort to have the model come closer to representing real sources. Dipole sources are only a first approximation to the real sources which are thought to be a very complicated network of electrical currents in the core of the Earth. -Author

Using Tikhonov Regularization for Spatial Projections from CSR Regularized Spherical Harmonic GRACE Solutions

NASA Astrophysics Data System (ADS)

Save, H.; Bettadpur, S. V.

2013-12-01

It has been demonstrated before that using Tikhonov regularization produces spherical harmonic solutions from GRACE that have very little residual stripes while capturing all the signal observed by GRACE within the noise level. This paper demonstrates a two-step process and uses Tikhonov regularization to remove the residual stripes in the CSR regularized spherical harmonic coefficients when computing the spatial projections. We discuss methods to produce mass anomaly grids that have no stripe features while satisfying the necessary condition of capturing all observed signal within the GRACE noise level.

Effects of electromagnetic fields on the nonlinear optical properties of asymmetric double quantum well under intense laser field

NASA Astrophysics Data System (ADS)

Yesilgul, U.; Sari, H.; Ungan, F.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.; Sökmen, I.

2017-03-01

In this study, the effects of electric and magnetic fields on the optical rectification and second and third harmonic generation in asymmetric double quantum well under the intense non-resonant laser field is theoretically investigated. We calculate the optical rectification and second and third harmonic generation within the compact density-matrix approach. The theoretical findings show that the influence of electric, magnetic, and intense laser fields leads to significant changes in the coefficients of nonlinear optical rectification, second and third harmonic generation.

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.

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).

A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and other tracking data

NASA Technical Reports Server (NTRS)

Lemonie, Frank G. R.; Smith, David E.; Zuber, Maria T.; Neumann, Gregory A.

1997-01-01

A spherical harmonic model of the lunar gravity field complete to degree and order 70 has been developed from S band Doppler tracking data from the Clementine mission, as well as historical tracking data from Lunar Orbiters 1-5 and the Apollo 15 and 16 subsatellites. The model combines 361,000 Doppler observations from Clementine with 347,000 historical observations. The historical data consist of mostly 60-s Doppler with a noise of 0.25 to several mm/s. The Clementine data consist of mostly 10-s Doppler data, with a data noise of 0.25 mm/s for the observations from the Deep Space Network, and 2.5 mm/s for the data from a naval tracking station at Pomonkey, Maryland. Observations provided Clementine, provide the strongest satellite constraint on the Moon's low-degree field. In contrast the historical data, collected by spacecraft that had lower periapsis altitudes, provide distributed regions of high-resolution coverage within +/- 29 deg of the nearside lunar equator. To obtain the solution for a high-degree field in the absence of a uniform distribution of observations, we applied an a priori power law constraint of the form 15 x 10(exp -5)/sq l which had the effect of limiting the gravitational power and noise at short wavelengths. Coefficients through degree and order 18 are not significantly affected by the constraint, and so the model permits geophysical analysis of effects of the major basins at degrees 10-12. The GLGM-2 model confirms major features of the lunar gravity field shown in previous gravitational field models but also reveals significantly more detail, particularly at intermediate wavelengths (10(exp 3) km). Free-air gravity anomaly maps derived from the new model show the nearside and farside highlands to be gravitationally smooth, reflecting a state of isostatic compensation. Mascon basins (including Imbrium, Serenitatis, Crisium, Smythii, and Humorum) are denoted by gravity highs first recognized from Lunar Orbiter tracking. All of the major mascons are bounded by annuli of negative anomalies representing significant subsurface mass deficiencies. Mare Orientale appears as a minor mascon surrounded by a horseshoe-shaped gravity low centered on the Inner and Outer Rook rings that is evidence of significant subsurface structural heterogeneity. Although direct tracking is not available over a significant part of the lunar farside, GLGM-2 resolves negative anomalies that correlate with many farside basins, including South Pole-Aitken, Hertzsprung, Korolev, Moscoviense, Tsiolkovsky, and Freundlich-Sharonov.

Spherical Cap Harmonic Modelling of 400 Years of Secular Variation in the South-west Pacific

NASA Astrophysics Data System (ADS)

Ingham, M.; Alfheid, M.; Ingham, E. M.; Turner, G. M.

2014-12-01

Historical magnetic data recorded in ship's logs on voyages of exploration and trade in the south-west Pacific have been used as a basis for constructing a model of secular variation in the region using spherical cap harmonic (SCH) analysis. The spherical cap used is centred on colatitude 115° and longitude 160° and has a radius of 50°, thus covering New Zealand, Australia and parts of Antarctica. Gaps in the observational data have been filled by an iterative procedure started by using IGRF field values to obtain SCH models for 2000, 1950 and 1900 and assuming that the spherical cap coefficients have a linear variation in time over the 400 year time period of the model, as is observed to a first approximation for Gauss coefficients calculated from a global spherical harmonic analysis. The resulting field models have generally smooth spatial and temporal variations in declination, inclination and intensity which show some differences from the variations calculated using the global spherical harmonic model gufm1. The technique clearly shows promise for producing more refined models of secular variation in the south-west Pacific when the historical data are supplemented by archeomagnetic and paleomagnetic data.

Periodically poled potassium niobate for second-harmonic generation at 463 nm.

PubMed

Meyn, J P; Klein, M E; Woll, D; Wallenstein, R; Rytz, D

1999-08-15

We report on the fabrication and characterization of quasi-phase-matched potassium niobate crystals for second-harmonic generation. Periodic 30-mum -pitch antiparallel ferroelectric domains are fabricated by means of poling in an electrical field. Both birefrigence and periodic phase shift of the generated second harmonic contribute to phase matching when the d(31) nonlinear optical tensor element is used. 3.8 mW of second-harmonic radiation at 463 nm is generated by frequency doubling of the output of master-oscillator power-amplifier diode laser in a 5-mm-long crystal. The measured effective nonlinear coefficient is 3.7pm/V. The measured spectral acceptance bandwidth of 0.25 nm corresponds to the theoretical value.

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.

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.

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.;

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

NASA Technical Reports Server (NTRS)

Tripathi, A. K.; Singhal, R. P.; Khazanov, G. V.; Avanov, L. A.

2016-01-01

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave-Particle Interactions

NASA Technical Reports Server (NTRS)

Tripathi, A. K.; Singhal, R. P.; Khazanov, G. V.; Avanov, L. A.

2016-01-01

Electron pitch angle (D(sub (alpha alpha))) and momentum (D(sub pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L=4.6 and 6.8 for electron energies less than or equal to 10 keV. Landau (n=0) resonance and cyclotron harmonic resonances n= +/- 1, +/-2, ... +/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n=+1 and n=+2. A major contribution to momentum diffusion coefficients appears from n=+2. However, the banded structures in D(sub alpha alpha) and D(sub pp) coefficients appear only in the profile of diffusion coefficients for n=+2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D(sub pp) diffusion coefficient for ECH waves is one to two orders smaller than D(sub alpha alpha) coefficients. For chorus waves, D(sub pp) coefficients are about an order of magnitude smaller than D(sub alpha alpha) coefficients for the case n does not equal 0. In case of Landau resonance, the values of D(sub pp) coefficient are generally larger than the values of D(sub alpha alpha) coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n= +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies 1 greater than or equal to keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L=4.6 and above 200 eV for L=6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

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.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

DOE PAGES

Bansal, Dipanshu; Aref, Amjad; Dargush, Gary; ...

2016-07-20

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. In this study, we illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Our results agreemore » well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.« less

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

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

Bansal, Dipanshu; Aref, Amjad; Dargush, Gary

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally-derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. In this study, we illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Our results agreemore » well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.« less

Quasi-phase-matching of high-order harmonics in plasma plumes: theory and experiment.

PubMed

Strelkov, V V; Ganeev, R A

2017-09-04

We theoretically analyze the phase-matching of high-order harmonic generation (HHG) in multi-jet plasmas and find the harmonic orders for which the quasi-phase-matching (QPM) is achieved depending on the parameters of the plasma and the generating beam. HHG by single- and two-color generating fields is analyzed. The QMP is studied experimentally for silver, indium and manganese plasmas using near IR and mid-IR laser fields. The theory is validated by comparison with our experimental observations, as well as published experimental data. In particular, the plasma densities and the harmonic phase coefficients reconstructed from the observed harmonic spectra using our theory agree with the corresponding parameters found using other methods. Our theory allows defining the plasma jet and the generating field properties, which can maximize the HHG efficiency due to QPM.

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.

One dimensional blood flow in a planetocentric orbit

NASA Astrophysics Data System (ADS)

Haranas, Ioannis; Gkigkitzis, Ioannis

2012-05-01

All life on earth is accustomed to the presence of gravity. When gravity is altered, biological processes can go awry. It is of great importance to ensure safety during a spaceflight. Long term exposure to microgravity can trigger detrimental physiological responses in the human body. Fluid redistribution coupled with fluid loss is one of the effects. In particular, in microgravity blood volume is shifted towards the thorax and head. Sympathetic nervous system-induced vasoconstriction is needed to maintain arterial pressure, while venoconstriction limits venous pooling of blood prevents further reductions in venous return of blood to the heart. In this paper, we modify an existing one dimensional blood flow model with the inclusion of the hydrostatic pressure gradient that further depends on the gravitational field modified by the oblateness and rotation of the Earth. We find that the velocity of the blood flow VB is inversely proportional to the blood specific volume d, also proportional to the oblateness harmonic coefficient J2, the angular velocity of the Earth ωE, and finally proportional to an arbitrary constant c. For c = -0.39073 and ξH = -0.5 mmHg, all orbits result to less blood flow velocities than that calculated on the surface of the Earth. From all considered orbits, elliptical polar orbit of eccentricity e = 0.2 exhibit the largest flow velocity VB = 1.031 m/s, followed by the orbits of inclination i = 45°and 0°. The Earth's oblateness and its rotation contribute a 0.7% difference to the blood flow velocity.

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.

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.

Commercial Production of Heavy Metal Fluoride Glass Fiber in Space

NASA Technical Reports Server (NTRS)

Tucker, Dennis S.; Workman, Gary L.; Smith, Guy A.

1998-01-01

International Space Station Alpha (ISSA) will provide a platform not only for materials research but also a possible means to produce products in space which cannot be easily produced on the ground. Some products may even be superior to those now produced in unit gravity due to the lack of gravity induced convection effects. Our research with ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN glass) has shown that gravity does indeed play a major role in the crystallization behavior of this material. At the present time ZBLAN is being produced on earth in fiber optic form for use in surgical lasers and fiber optic lasers among other applications. High attenuation coefficients, however, have kept this material from being used in other applications such as long haul data transmission links. The high attenuation coefficients are due to impurities which can be removed through improved processing techniques and crystals which can only be removed or prevented from forming by processing in a reduced gravity environment.

Testing quantum gravity through dumb holes

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

Pourhassan, Behnam, E-mail: b.pourhassan@du.ac.ir; Faizal, Mir, E-mail: f2mir@uwaterloo.ca; Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, BC V1V 1V7

We propose a method to test the effects of quantum fluctuations on black holes by analyzing the effects of thermal fluctuations on dumb holes, the analogs for black holes. The proposal is based on the Jacobson formalism, where the Einstein field equations are viewed as thermodynamical relations, and so the quantum fluctuations are generated from the thermal fluctuations. It is well known that all approaches to quantum gravity generate logarithmic corrections to the entropy of a black hole and the coefficient of this term varies according to the different approaches to the quantum gravity. It is possible to demonstrate thatmore » such logarithmic terms are also generated from thermal fluctuations in dumb holes. In this paper, we claim that it is possible to experimentally test such corrections for dumb holes, and also obtain the correct coefficient for them. This fact can then be used to predict the effects of quantum fluctuations on realistic black holes, and so it can also be used, in principle, to experimentally test the different approaches to quantum gravity.« less

Marine Geoid Undulation Assessment Over South China Sea Using Global Geopotential Models and Airborne Gravity Data

NASA Astrophysics Data System (ADS)

Yazid, N. M.; Din, A. H. M.; Omar, K. M.; Som, Z. A. M.; Omar, A. H.; Yahaya, N. A. Z.; Tugi, A.

2016-09-01

Global geopotential models (GGMs) are vital in computing global geoid undulations heights. Based on the ellipsoidal height by Global Navigation Satellite System (GNSS) observations, the accurate orthometric height can be calculated by adding precise and accurate geoid undulations model information. However, GGMs also provide data from the satellite gravity missions such as GRACE, GOCE and CHAMP. Thus, this will assist to enhance the global geoid undulations data. A statistical assessment has been made between geoid undulations derived from 4 GGMs and the airborne gravity data provided by Department of Survey and Mapping Malaysia (DSMM). The goal of this study is the selection of the best possible GGM that best matches statistically with the geoid undulations of airborne gravity data under the Marine Geodetic Infrastructures in Malaysian Waters (MAGIC) Project over marine areas in Sabah. The correlation coefficients and the RMS value for the geoid undulations of GGM and airborne gravity data were computed. The correlation coefficients between EGM 2008 and airborne gravity data is 1 while RMS value is 0.1499.In this study, the RMS value of EGM 2008 is the lowest among the others. Regarding to the statistical analysis, it clearly represents that EGM 2008 is the best fit for marine geoid undulations throughout South China Sea.

Lifshitz black branes and DC transport coefficients in massive Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Kuang, Xiao-Mei; Papantonopoulos, Eleftherios; Wu, Jian-Pin; Zhou, Zhenhua

2018-03-01

We construct analytical Lifshitz massive black brane solutions in massive Einstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of these black brane solutions and obtain the thermodynamical stability conditions. On the dual nonrelativistic boundary field theory with Lifshitz symmetry, we analytically compute the DC transport coefficients, including the electric conductivity, thermoelectric conductivity, and thermal conductivity. The novel property of our model is that the massive term supports the Lifshitz black brane solutions with z ≠1 in such a way that the DC transport coefficients in the dual field theory are finite. We also find that the Wiedemann-Franz law in this dual boundary field theory is violated, which indicates that it may involve strong interactions.

On the theory of 3-phase squirrel-cage induction motors including space harmonics and mutual slotting

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

Papp, G.C.

1991-03-01

In this paper general equations for the asynchronous squirrel-cage motor which contain the influence of space harmonics and the mutual slotting are derived by using among others the power-invariant symmetrical component transformation and a time-dependent transformation with which, under certain circumstances, the rotor-position angle can be removed from the coefficient matrix. The developed models implemented in a machine-independent computer program form powerful tools, with which the influence of space harmonics in relation to the geometric data of specific motors can be analyzed for steady-state and transient performances.

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.

Beating motion of a circular cylinder in vortex-induced vibrations

NASA Astrophysics Data System (ADS)

Shen, Linwei; Chan, Eng-Soon; Wei, Yan

2018-04-01

In this paper, beating phenomenon of a circular cylinder in vortex-induced vibration is studied by numerical simulations in a systematic manner. The cylinder mass coefficients of 2 and 10 are considered, and the Reynolds number is 150. Two distinctive frequencies, namely cylinder oscillation and vortex shedding frequencies, are obtained from the harmonic analysis of the cylinder displacement. The result is consistent with that observed in laboratory experiments. It is found that the cylinder oscillation frequency changes with the natural frequency of the cylinder while the reduced velocity is varied. The added-mass coefficient of the cylinder in beating motion is therefore estimated. Meanwhile, the vortex shedding frequency does not change dramatically in the beating situations. In fact, it is very close to 0.2. Accordingly, the lift force coefficient has two main components associated with these two frequencies. Besides, higher harmonics of the cylinder oscillation frequency appear in the spectrum of the lift coefficient. Moreover, the vortex shedding timing is studied in the beating motion by examining the instantaneous flow fields in the wake, and two scenarios of the vortex formation are observed.

Permutation-symmetric three-particle hyper-spherical harmonics based on the S3 ⊗ SO(3)rot ⊂ O(2)⊗SO(3)rot ⊂ U(3)⋊S2 ⊂ O(6) subgroup chain

NASA Astrophysics Data System (ADS)

Salom, Igor; Dmitrašinović, V.

2017-07-01

We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3 ⊗ SO(3)rot ⊂ O (2) ⊗ SO(3)rot ⊂ U (3) ⋊S2 ⊂ O (6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O (2) is the ;democracy transformation;, or ;kinematic rotation; group for three particles; SO(3)rot is the 3D rotation group, and U (3) , O (6) are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3)rot ⊂ SU (3) degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K ≤ 6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ , ρ) with coefficients given as algebraic numbers unless the ;operator method; is chosen for the lifting of the SO(3)rot ⊂ SU (3) multiplicity and the dimension of the degenerate subspace is greater than four - in which case one must resort to numerical diagonalization; the latter condition is not met by any K ≤ 15 harmonic, or by any L ≤ 7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics) in two ways: 1) by explicit evaluation of integrals and 2) by reduction to known SU (3) Clebsch-Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.

Approximation method for determining the static stability of a monoplane glider

NASA Technical Reports Server (NTRS)

Lippisch, A

1927-01-01

The calculations in this paper afford an approximate solution of the static stability. A derivation of the formulas for moment coefficient of a wing, moment coefficient of elevator, and the total moment of the combined wing and elevator and the moment coefficient with reference to the center of gravity are provided.

Improvement of the Earth's gravity field from terrestrial and satellite data

NASA Technical Reports Server (NTRS)

Rapp, Richard H.

1992-01-01

The determination of the Earth's gravitational potential can be done through the analysis of satellite perturbations, the analysis of surface gravity data, or both. The combination of the two data types yields a solution that combines the strength of each method: the longer wavelength strength in the satellite analysis with the better high frequency information from surface gravity data. Since 1972, Ohio State has carried out activities that have provided surface gravity data to a number of organizations who have developed combination potential coefficient models that describe the Earth's gravitational potential.

Expected precision of Europa Clipper gravity measurements

NASA Astrophysics Data System (ADS)

Verma, Ashok K.; Margot, Jean-Luc

2018-11-01

The primary gravity science objective of NASA's Clipper mission to Europa is to confirm the presence or absence of a global subsurface ocean beneath Europa's Icy crust. Gravity field measurements obtained with a radio science investigation can reveal much about Europa's interior structure. Here, we conduct extensive simulations of the radio science measurements with the anticipated spacecraft trajectory and attitude (17F12v2) and assets on the spacecraft and the ground, including antenna orientations and beam patterns, transmitter characteristics, and receiver noise figures. In addition to two-way Doppler measurements, we also include radar altimeter crossover range measurements. We concentrate on ± 2 h intervals centered on the closest approach of each of the 46 flybys. Our covariance analyses reveal the precision with which the tidal Love number k2, second-degree gravity coefficients Cbar20 and Cbar22 , and higher-order gravity coefficients can be determined. The results depend on the Deep Space Network (DSN) assets that are deployed to track the spacecraft. We find that some DSN allocations are sufficient to conclusively confirm the presence or absence of a global ocean. Given adequate crossover range performance, it is also possible to evaluate whether the ice shell is hydrostatic.

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.

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 interior structure of Enceladus from Cassini gravity measurements

NASA Astrophysics Data System (ADS)

Iess, Luciano

2015-04-01

The Cassini spacecraft flew by the small Saturnian moon Enceladus in three close flybys (April 28, 2010, November 30, 2010 and May 2, 2012, to carry out measurements of the satellite's gravity field [1]. One of the main motivations was the search for a hemispherical asymmetry in the gravity field, the gravitational counterpart of the striking North-South asymmetry shown by optical imaging and other Cassini instruments in the geological features of the moon. The estimation of Enceladus' gravity field by Cassini was especially complex because of the small surface gravity (0.11 m/s2), the short duration of the gravitational interaction (only a few minutes) and the small, nearly impulsive, neutral particles drag occurring when the spacecraft crossed the south polar plume during the first and the third flyby. Including the non-gravitational acceleration due to the plume in the dynamical model was crucial to obtain a reliable solution for the gravity field. In order to maximize the sensitivity to the hemispherical asymmetry, controlled by the spherical harmonic coefficient J3, the closest approaches occurred at the low altitudes (respectively 100, 48 and 70 km), and at high latitudes in both hemispheres (89°S, 62°N, and 72°S). Enceladus' gravity field is dominated by large quadrupole terms not far from those expected for a body in a relaxed shape. Although the deviations from the hydrostaticity are weak (J2/C22=3.55±0.05), the straightforward application of the Radau-Darwin approximation yields a value of the moment of inertia factor (MOIF=C/MR2) that is incompatible (0.34) with the differentiated interior structure suggested by cryovolcanism and the large heat flow. The other remarkable feature of the gravity field is the small but still statistically significant value of J3 (106 x J3 = -115.3±22.9). A differentiated interior structure (corresponding to a smaller MOIF) may be reconciled with the gravity measurement by assuming that the rocky core has retained some memory of a faster rotation rate (about 10% above current). J3, whose value is uncontaminated by tides and rotation, provides a way to separate the non-hydrostatic contribution to J2 and C22, from which we infer a MOIF of about 0.336, now compatible with a differentiated structure. Similar conclusions are obtained from the analysis of the admittance. The interpretation of J3 and the associated, negative gravity anomaly (about 2.5 mGal) is non-unique. In a proposed explanation, the anomaly originates in the core and is not directly related to the presence of liquid masses beneath the surface. Our interpretation seeks the source of the anomaly in the observed 1 km depression in the southern polar region. This mass deficiency generates indeed a negative anomaly, but its magnitude is far smaller (about 20%) than expected from an uncompensated topography. An obvious source of compensation is a reservoir of liquid water at depth, in contact with the rocky core. This interpretation is consistent with the observed cryovolcanism and the presence of silicate grains in the plumes. The estimated gravity field is more consistent with a reservoir that extends in latitude about halfway to the equator, but our data cannot rule out a thin, global ocean.

Jupiter's atmospheric jet streams extend thousands of kilometres deep.

PubMed

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

2018-03-07

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 J 3 , J 5 , J 7 and J 9 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 J 8 and J 10 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.

Banded structures in electron pitch angle diffusion coefficients from resonant wave-particle interactions

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

Tripathi, A. K., E-mail: aktrip2001@yahoo.co.in; Singhal, R. P., E-mail: rpsiitbhu@yahoo.com; Khazanov, G. V., E-mail: George.V.Khazanov@nasa.gov

2016-04-15

Electron pitch angle (D{sub αα}) and momentum (D{sub pp}) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies ≤10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = ±1, ±2, … ±5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (α) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusionmore » coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D{sub αα} and D{sub pp} coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D{sub pp} diffusion coefficient for ECH waves is one to two orders smaller than D{sub αα} coefficients. For chorus waves, D{sub pp} coefficients are about an order of magnitude smaller than D{sub αα} coefficients for the case n ≠ 0. In case of Landau resonance, the values of D{sub pp} coefficient are generally larger than the values of D{sub αα} coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89° and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10° and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies ≥1 keV, and for whistler mode chorus waves, structures appear for energies >2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.« less

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.

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.

On the origins of Earth rotation anomalies: New insights on the basis of both “paleogeodetic” data and Gravity Recovery and Climate Experiment (GRACE) data

NASA Astrophysics Data System (ADS)

Peltier, W. R.; Luthcke, Scott B.

2009-11-01

The theory previously developed to predict the impact on Earth's rotational state of the late Pleistocene glaciation cycle is extended. In particular, we examine the extent to which a departure of the infinite time asymptote of the viscoelastic tidal Love number of degree 2, "k2T," from the observed "fluid" Love number, "kf," impacts the theory. A number of tests of the influence of the difference in these Love numbers on theoretical predictions of the model of the glacial isostatic adjustment (GIA) process are explored. Relative sea level history predictions are shown not to be sensitive to the difference even though they are highly sensitive to the influence of the changing rotational state itself. We also explore in detail the accuracy with which the Gravity Recovery and Climate Experiment (GRACE) satellite system is able to observe the global GIA process including the time-dependent amplitude of the degree 2 and order 1 spherical harmonic components of the gravitational field, the only components that are significantly influenced by rotational effects. It is explicitly shown that the GRACE observation of these properties of the time-varying gravitational field is sufficiently accurate to rule out the values predicted by the ICE-5G (VM2) model of Peltier (2004). However, we also note that this model is constrained only by data from an epoch during which modern greenhouse gas induced melting of both the great polar ice-sheets and small ice sheets and glaciers was not occurring. Such modern loss of grounded continental ice strongly influences the evolving rotational state of the planet and thus the values of the degree 2 and order 1 Stokes coefficients as they are currently being measured by the GRACE satellite system. A series of sensitivity tests are employed to demonstrate this fact. We suggest that the accuracy of scenarios for modern land ice melting may be tested by ensuring that such scenarios conform to the GRACE observations of these crucial time-dependent Stokes coefficients.

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.

Global Assessment of New GRACE Mascons Solutions for Hydrologic Applications

NASA Astrophysics Data System (ADS)

Save, H.; Zhang, Z.; Scanlon, B. R.; Wiese, D. N.; Landerer, F. W.; Long, D.; Longuevergne, L.; Chen, J.

2016-12-01

Advances in GRACE (Gravity Recovery and Climate Experiment) satellite data processing using new mass concentration (mascon) solutions have greatly increased the spatial localization and amplitude of recovered total Terrestrial Water Storage (TWS) signals; however, limited testing has been conduct on land hydrologic applications. In this study we compared TWS anomalies from (1) Center for Space Research mascons (CSR-M) solution with (2) NASA JPL mascon (JPL-M) solution, and with (3) a CSR gridded spherical harmonic rescaled (sf) solution from Tellus (CSRT-GSH.sf) in 176 river basins covering 80% of the global land area. There is good correspondence in TWS anomalies from mascons (CSR-M and JPL-M) and SH solutions based on high correlations between time series (rank correlation coefficients mostly >0.9). The long-term trends in basin TWS anomalies represent a relatively small signal (up to ±20 mm/yr) with differences among GRACE solutions and inter-basin variability increasing with decreasing basin size. Long-term TWS declines are greatest in (semi)arid and irrigated basins. Annual and semiannual signals have much larger amplitudes (up to ±250 mm). There is generally good agreement among GRACE solutions, increasing confidence in seasonal fluctuations from GRACE data. Rescaling spherical harmonics to restore lost signal increases agreement with mascons solutions for long-term trends and seasonal fluctuations. There are many advantages to using GRACE mascons solutions relative to SH solutions, such as reduced leakage from land to ocean increasing signal amplitude, and constraining results by applying geophysical data during processing with little or no post-processing requirements, making mascons more user friendly for non-geodetic users. This inter-comparison of various GRACE solutions should allow hydrologists to better select suitable GRACE products for hydrologic applications.

Towards the inversion of GRACE gravity fields for present-day ice-mass changes and glacial-isostatic adjustment in North America and Greenland

NASA Astrophysics Data System (ADS)

Sasgen, Ingo; Klemann, Volker; Martinec, Zdeněk

2012-09-01

We perform an inversion of gravity fields from the Gravity Recovery and Climate Experiment (GRACE) (August 2002 to August 2009) of four processing centres for glacial-isostatic adjustment (GIA) over North America and present-day ice-mass change in Alaska and Greenland. We apply a statistical filtering approach to reduce noise in the GRACE data by confining our investigations to GRACE coefficients containing a statistically significant linear trend. Selecting the subset of reliable coefficients in all GRACE time series (GFZ RL04, ITG 2010, JPL RL04 and CSR RL04) results in a non-isotropic smoothing of the GRACE gravity fields, which is effective in reducing the north-south oriented striping associated with correlated errors in GRACE coefficients. In a next step, forward models of GIA induced by the glacial history NAWI (Zweck and Huybrechts, 2005), as well as present-day ice mass changes in Greenland from ICESat (Sørensen et al., 2011) and Alaska from airborne laser altimetry (Arendt et al., 2002) are simultaneously adjusted in scale to minimize the misfit to the filtered GRACE trends. From the adjusted models, we derive the recent sea-level contributions for Greenland and Alaska (August 2002 to August 2009), and, interpret the residual misfit over the GIA-dominated region around the Hudson Bay, Canada, in terms of mantle viscosities beneath North America.

The measurement of solute diffusion coefficients in dilute liquid alloys: the influence of unit gravity and g-jitter on buoyancy convection.

PubMed

Smith, R W; Yang, B J; Huang, W D

2004-11-01

Liquid diffusion experiments conducted on the MIR space station using the Canadian Space Agency QUELD II processing facility and the microgravity isolation mount (MIM) showed that g-jitter significantly increased the measured solute diffusion coefficients. In some experiments, milli-g forced vibration was superimposed on the sample when isolated from the ambient g-jitter; this resulted in markedly increased solute transport. To further explore the effects arising in these long capillary diffusion couples from the absence of unit-gravity and the presence of the forced g-jitter, the effects of a 1 milli-g forcing vibration on the mass transport in a 1.5 mm diameter long capillary diffusion couple have been simulated. In addition, to increase understanding of the role of unit gravity in determining the extent to which gravity can influence measured diffusion coefficient values, comparative experiments involving gold, silver, and antimony diffusing in liquid lead have been carried out using a similar QUELD II facility to that employed in the QUELD II/MIM/MIR campaign but under terrestrial conditions. It was found that buoyancy-driven convection may still persist in the liquid even when conditions are arranged for a continuously decreasing density gradient up the axis of a vertical long capillary diffusion couple due to the presence of small radial temperature gradients.

Methods of harmonic synthesis for global geopotential models and their first-, second- and third-order gradients

NASA Astrophysics Data System (ADS)

Fantino, E.; Casotto, S.

2009-07-01

Four widely used algorithms for the computation of the Earth’s gravitational potential and its first-, second- and third-order gradients are examined: the traditional increasing degree recursion in associated Legendre functions and its variant based on the Clenshaw summation, plus the methods of Pines and Cunningham-Metris, which are free from the singularities that distinguish the first two methods at the geographic poles. All four methods are reorganized with the lumped coefficients approach, which in the cases of Pines and Cunningham-Metris requires a complete revision of the algorithms. The characteristics of the four methods are studied and described, and numerical tests are performed to assess and compare their precision, accuracy, and efficiency. In general the performance levels of all four codes exhibit large improvements over previously published versions. From the point of view of numerical precision, away from the geographic poles Clenshaw and Legendre offer an overall better quality. Furthermore, Pines and Cunningham-Metris are affected by an intrinsic loss of precision at the equator and suffer from additional deterioration when the gravity gradients components are rotated into the East-North-Up topocentric reference system.

Viscoelastic responses of a hard transition zone - Effects on postglacial uplifts and rotational signatures

NASA Technical Reports Server (NTRS)

Spada, Giorgio; Sabadini, Roberto; Yuen, David A.

1991-01-01

A five-layer viscoelastic spherical model is used to calculate the transient displacements of postglacial rebound, the induced polar motions, and the temporal variations of the geopotential up to degree 8 of the zonal coefficients. Two models - one with two viscoelastic layers separated at 670 km, and the other with three layers in which a hard garnet layer lies between the upper and lower mantle - are compared. Forward modeling shows that it may be possible to discern the presence of a hard garnet layer with a viscosity of at least ten times greater than the upper mantle, on the basis of uplift data near the center of the former Laurentide ice-sheet and from polar wander and j2 data. Temporal variations of higher gravity harmonics, such as j6 and j8, can potentially place even tighter constraints on the rheological properties of the hard transition zone. A lower mantle viscosity between 2 and 4 x 10 to the 22nd Pa is generally preferred in models with a garnet layer which may be as large as 50 times more viscous than the upper mantle.

Dynamics of gas-thrust bearings

NASA Technical Reports Server (NTRS)

Stiffler, A. K.; Tapia, R. R.

1978-01-01

Computer program calculates load coefficients, up to third harmonic, for hydrostatic gas thrust bearings. Program is useful in identification of industrial situations where gas-thrust bearings have potential applications.

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.

Correlation techniques and measurements of wave-height statistics

NASA Technical Reports Server (NTRS)

Guthart, H.; Taylor, W. C.; Graf, K. A.; Douglas, D. G.

1972-01-01

Statistical measurements of wave height fluctuations have been made in a wind wave tank. The power spectral density function of temporal wave height fluctuations evidenced second-harmonic components and an f to the minus 5th power law decay beyond the second harmonic. The observations of second harmonic effects agreed very well with a theoretical prediction. From the wave statistics, surface drift currents were inferred and compared to experimental measurements with satisfactory agreement. Measurements were made of the two dimensional correlation coefficient at 15 deg increments in angle with respect to the wind vector. An estimate of the two-dimensional spatial power spectral density function was also made.

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.

Quantum gravity boundary terms from the spectral action of noncommutative space.

PubMed

Chamseddine, Ali H; Connes, Alain

2007-08-17

We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.

Three Least-Squares Minimization Approaches to Interpret Gravity Data Due to Dipping Faults

NASA Astrophysics Data System (ADS)

Abdelrahman, E. M.; Essa, K. S.

2015-02-01

We have developed three different least-squares minimization approaches to determine, successively, the depth, dip angle, and amplitude coefficient related to the thickness and density contrast of a buried dipping fault from first moving average residual gravity anomalies. By defining the zero-anomaly distance and the anomaly value at the origin of the moving average residual profile, the problem of depth determination is transformed into a constrained nonlinear gravity inversion. After estimating the depth of the fault, the dip angle is estimated by solving a nonlinear inverse problem. Finally, after estimating the depth and dip angle, the amplitude coefficient is determined using a linear equation. This method can be applied to residuals as well as to measured gravity data because it uses the moving average residual gravity anomalies to estimate the model parameters of the faulted structure. The proposed method was tested on noise-corrupted synthetic and real gravity data. In the case of the synthetic data, good results are obtained when errors are given in the zero-anomaly distance and the anomaly value at the origin, and even when the origin is determined approximately. In the case of practical data (Bouguer anomaly over Gazal fault, south Aswan, Egypt), the fault parameters obtained are in good agreement with the actual ones and with those given in the published literature.

An approach for spherical harmonic analysis of non-smooth data

NASA Astrophysics Data System (ADS)

Wang, Hansheng; Wu, Patrick; Wang, Zhiyong

2006-12-01

A method is proposed to evaluate the spherical harmonic coefficients of a global or regional, non-smooth, observable dataset sampled on an equiangular grid. The method is based on an integration strategy using new recursion relations. Because a bilinear function is used to interpolate points within the grid cells, this method is suitable for non-smooth data; the slope of the data may be piecewise continuous, with extreme changes at the boundaries. In order to validate the method, the coefficients of an axisymmetric model are computed, and compared with the derived analytical expressions. Numerical results show that this method is indeed reasonable for non-smooth models, and that the maximum degree for spherical harmonic analysis should be empirically determined by several factors including the model resolution and the degree of non-smoothness in the dataset, and it can be several times larger than the total number of latitudinal grid points. It is also shown that this method is appropriate for the approximate analysis of a smooth dataset. Moreover, this paper provides the program flowchart and an internet address where the FORTRAN code with program specifications are made available.

Second-harmonic generation from a thin spherical layer and No-generation conditions

NASA Astrophysics Data System (ADS)

Kapshai, V. N.; Shamyna, A. A.

2017-09-01

In the Rayleigh-Gans-Debye approximation, we solve the problem of second-harmonic generation by an elliptically polarized electromagnetic wave incident on the surface of a spherical particle that is coated by an optically nonlinear layer and is placed in a dielectric. The formulas obtained characterize the spatial distribution of the electric field of the second harmonic in the far-field zone. The most general form of the second-order dielectric susceptibility tensor is considered, which contains four independent components, with three of them being nonchiral and one, chiral. Consistency and inconsistencies between the obtained solution and formulas from works of other authors are found. We analyze the directivity patterns that characterize the spatial distribution of the generated radiation for the nonchiral layer and their dependences on the anisotropy and ellipticity coefficients of the incident wave. It is found that, with increasing radius of the nonlinear layer, the generated radiation becomes more directional. Combinations of parameters for which no radiation is generated are revealed. Based on this, we propose methods for experimental determination of the anisotropy coefficients.

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.

Laterally azo-bridged h-shaped ferroelectric dimesogens for second-order nonlinear optics: ferroelectricity and second harmonic generation.

PubMed

Zhang, Yongqiang; Martinez-Perdiguero, Josu; Baumeister, Ute; Walker, Christopher; Etxebarria, Jesus; Prehm, Marko; Ortega, Josu; Tschierske, Carsten; O'Callaghan, Michael J; Harant, Adam; Handschy, Mark

2009-12-30

Two classes of laterally azo-bridged H-shaped ferroelectric liquid crystals (FLCs), incorporating azobenzene and disperse red 1 (DR-1) chromophores along the FLC polar axes, were synthesized and characterized by polarized light microscopy, differential scanning calorimetry, 2D X-ray diffraction analysis, and electro-optical investigations. They represent the first H-shaped FLC materials exhibiting the ground-state, thermodynamically stable enantiotropic SmC* phase, i.e., ground-state ferroelectricity. Second harmonic generation measurements of one compound incorporating a DR-1 chromophore at the incident wavelength of 1064 nm give a nonlinear coefficient of d(22) = 17 pm/V, the largest nonlinear optics coefficient reported to date for calamitic FLCs. This value enables viable applications of FLCs in nonlinear optics.

Analytic expressions for perturbations and partial derivatives of range and range rate of a spacecraft with respect to the coefficient of the second harmonic

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1973-01-01

Closed-form analytic expressions for the time variations of instantaneous orbital parameters and of the topocentric range and range rate of a spacecraft moving in the gravitational field of an oblate large body are derived using a first-order variation of parameters technique. In addition, the closed-form analytic expressions for the partial derivatives of the topocentric range and range rate are obtained, with respect to the coefficient of the second harmonic of the potential of the central body (J sub 2). The results are applied to the motion of a point-mass spacecraft moving in the orbit around the equatorially elliptic, oblate sun, with J sub 2 approximately equal to .000027.

Geomagnetic temporal change: 1903-1982 - A spline representation

NASA Technical Reports Server (NTRS)

Langel, R. A.; Kerridge, D. J.; Barraclough, D. R.; Malin, S. R. C.

1986-01-01

The secular variation of the earth's magnetic field is itself subject to temporal variations. These are investigated with the aid of the coefficients of a series of spherical harmonic models of secular variation deduced from data for the interval 1903-1982 from the worldwide network of magnetic observatories. For some studies it is convenient to approximate the time variation of the spherical harmonic coefficients with a smooth, continuous, function; for this a spline fitting is used. The phenomena that are investigated include periodicities, discontinuities, and correlation with the length of day. The numerical data presented will be of use for further investigations and for the synthesis of secular variation at any place and at any time within the interval of the data - they are not appropriate for temporal extrapolations.

Atlas of wide-field-of-view outgoing longwave radiation derived from Nimbus 6 Earth radiation budget data set, July 1975 to June 1978

NASA Technical Reports Server (NTRS)

Bess, T. Dale; Smith, G. Louis

1987-01-01

An atlas of monthly mean outgoing longwave radiation global contour maps and associated spherical harmonic coefficients is presented. The atlas contains 36 months of continuous data from July 1975 to June 1978. The data were derived from the first Earth radiation budget experiment, which was flown on the Nimbus-6 Sun-synchronous satellite in 1975. Only the wide-field-of-view longwave measurements are cataloged in this atlas. The contour maps along with the associated sets of spherical harmonic coefficients form a valuable data set for studying different aspects of our changing climate over monthly, annual, and interannual scales in the time domain, and over regional, zonal, and global scales in the spatial domain.

Fluid-gravity model for the chiral magnetic effect.

PubMed

Kalaydzhyan, Tigran; Kirsch, Ingo

2011-05-27

We consider the STU model as a gravity dual of a strongly coupled plasma with multiple anomalous U(1) currents. In the bulk we add additional background gauge fields to include the effects of external electric and magnetic fields on the plasma. Reducing the number of chemical potentials in the STU model to two and interpreting them as quark and chiral chemical potential, we obtain a holographic description of the chiral magnetic and chiral vortical effects (CME and CVE) in relativistic heavy-ion collisions. These effects formally appear as first-order transport coefficients in the electromagnetic current. We compute these coefficients from our model using fluid-gravity duality. We also find analogous effects in the axial-vector current. Finally, we briefly discuss a variant of our model, in which the CME/CVE is realized in the late-time dynamics of an expanding plasma. © 2011 American Physical Society

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

Relaxation of structural parameters and potential coefficients of nonrigid molecules. General symmetry properties and application to ab initio study of 1,2-difluoroethane

NASA Astrophysics Data System (ADS)

Ha, T.-K.; Günthard, H. H.

1989-07-01

Structural parameters like bond length, bond angles, etc. and harmonic and anharmonic potential coefficients of molecules with internal rotation, inversion or puckering modes are generally assumed to vary with the large amplitude internal coordinates in a concerted manner (relaxation). Taking the coordinate vectors of the nuclear configuration of semirigid molecules with relaxation (SRMRs) as functions of relaxing structural parameters and finite amplitude internal coordinate, the isometric group of SRMRs is discussed and the irreducible representations of the latter are shown to classify into engendered and nonengendered ones. On this basis a concept of equivalent sets of nuclei SRMRs is introduced and an analytical expression is derived which defines the most general functional form of relaxation increments of all common types of structural parameters compatible with isometric symmetry. This formula is shown to be a close analog of an analytical expression defining the transformations induced by the isometric group of infinitesimal internal coordinates associated with typical structural parameters. Furthermore analogous formulae are given for the most general form of the relaxation of harmonic potential coefficients as a function of finite internal coordinates. The general relations are illustrated by ab initio calculations for 1,2-difluoroethane at the MP4/DZP//HF/4-31G* level for twelve values of the dihedral angle including complete structure optimization. The potential to internal rotation is found to be in essential agreement with experimentally derived data. For a complete set of ab initio structural parameters the associated relaxation increments are represented as Fourier series, which are shown to confirm the form predicted by the general formula and the isometric group of 1,2-difluoroethane. Depending on type of the structural parameters (bond length, bond angles, etc.), the associated relaxation increments appear to follow some simple rules. Similarly a complete set of harmonic potential coefficients derived from the ab initio calculations will be analyzed in terms of Fourier series and shown to conform to the symmetry requirements of the symmetry group. Relaxation of potential coefficients is found to amount to up to ≈5% for some types of diagonal and nondiagonal terms and to reflect certain "topological" rules similar to regularities of harmonic potential constants of quasi-rigid molecules found in empirical determinations of valence force fields.

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.

Theoretical gravity and limb-darkening coefficients for the MOST satellite photometric system

NASA Astrophysics Data System (ADS)

Claret, A.; Dragomir, D.; Matthews, J. M.

2014-07-01

Aims: We present new calculations of limb and gravity-darkening coefficients to be used as input in many fields of stellar physics such as synthetic light curves of double-lined eclipsing binaries and planetary transits, studies of stellar diameters or line profiles in rotating stars. Methods: We compute the limb-darkening coefficients specifically for the photometric system of the satellite MOST (Microvariability and Oscillations in STars). All computations were performed by adopting the least-square method, but for completeness we also performed calculations for the linear and bi-parametric approaches by adopting the flux conservation method. The passband gravity-darkening coefficients y(λ) were computed by adopting a more general differential equation, which also takes the effects of convection into account. Results: We used two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX (spherical and quasi-spherical). We adopted six laws to describe the specific intensity distribution: linear, quadratic, square root, logarithmic, exponential, and a more general one with four terms. The covered ranges of Teff, log g, metallicities, and microturbulent velocities are (1500-50 000 K, 0-5.5, -5.0-+1.0, 0-8 km s-1), respectively. Tables 2-23 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/567/A3

Local gravity field modeling using spherical radial basis functions and a genetic algorithm

NASA Astrophysics Data System (ADS)

Mahbuby, Hany; Safari, Abdolreza; Foroughi, Ismael

2017-05-01

Spherical Radial Basis Functions (SRBFs) can express the local gravity field model of the Earth if they are parameterized optimally on or below the Bjerhammar sphere. This parameterization is generally defined as the shape of the base functions, their number, center locations, bandwidths, and scale coefficients. The number/location and bandwidths of the base functions are the most important parameters for accurately representing the gravity field; once they are determined, the scale coefficients can then be computed accordingly. In this study, the point-mass kernel, as the simplest shape of SRBFs, is chosen to evaluate the synthesized free-air gravity anomalies over the rough area in Auvergne and GNSS/Leveling points (synthetic height anomalies) are used to validate the results. A two-step automatic approach is proposed to determine the optimum distribution of the base functions. First, the location of the base functions and their bandwidths are found using the genetic algorithm; second, the conjugate gradient least squares method is employed to estimate the scale coefficients. The proposed methodology shows promising results. On the one hand, when using the genetic algorithm, the base functions do not need to be set to a regular grid and they can move according to the roughness of topography. In this way, the models meet the desired accuracy with a low number of base functions. On the other hand, the conjugate gradient method removes the bias between derived quasigeoid heights from the model and from the GNSS/leveling points; this means there is no need for a corrector surface. The numerical test on the area of interest revealed an RMS of 0.48 mGal for the differences between predicted and observed gravity anomalies, and a corresponding 9 cm for the differences in GNSS/leveling points.

Evaluation of GOCE-based Global Geoid Models in Finnish Territory

NASA Astrophysics Data System (ADS)

Saari, Timo; Bilker-Koivula, Mirjam

2015-04-01

The gravity satellite mission GOCE made its final observations in the fall of 2013. By then it had exceeded its expected lifespan of one year with more than three additional years. Thus, the mission collected more data from the Earth's gravitational field than expected, and more comprehensive global geoid models have been derived ever since. The GOCE High-level Processing Facility (HPF) by ESA has published GOCE global gravity field models annually. We compared all of the 12 HPF-models as well as 3 additional GOCE, 11 GRACE and 6 combined GOCE+GRACE models with GPS-levelling data and gravity observations in Finland. The most accurate models were compared against high resolution global geoid models EGM96 and EGM2008. The models were evaluated up to three different degrees and order: 150 (the common maximum for the GRACE models), 240 (the common maximum for the GOCE models) and maximum. When coefficients up to degree and order 150 are used, the results of the GOCE models are comparable with the results of the latest GRACE models. Generally, all of the latest GOCE and GOCE+GRACE models give standard deviations of the height anomaly differences of around 15 cm and of gravity anomaly differences of around 10 mgal over Finland. The best solutions were not always achieved with the highest maximum degree and order of the satellite gravity field models, since the highest coefficients (above 240) may be less accurately determined. Over Finland, the latest GOCE and GOCE+GRACE models give similar results as the high resolution models EGM96 and EGM2008 when coefficients up to degree and order 240 are used. This is mainly due to the high resolution terrestrial data available in the area of Finland, which was used in the high resolution models.

The formation and analysis of a 5 deg equal area block terrestrial gravity field

NASA Technical Reports Server (NTRS)

Rapp, R. H.

1972-01-01

A set of 23,355 1 degree x 1 degree mean free air anomalies were used to predict a set of 5 degree equal area anomalies and their standard errors. Using the 1 degree data incorporating geophysically predicted values of ACIC, 1283 5 degree blocks were computed. Excluding the geophysically predicted anomalies 1249 blocks were computed. The 1 degree data were also used to compute covariance functions and the equatorial gravity and flattening implied by this data. The predicted anomalies were supplemented by model anomalies to form a complete 1654 global anomaly field. These data were used in a weighted least squares to determine potential coefficients to degree 15, and in a summation type formulation to determine potential coefficients to degree 25. These potential coefficients sets are compared to recent satellite determinations.

International trade network: fractal properties and globalization puzzle.

PubMed

Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata

2014-12-12

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

International Trade Network: Fractal Properties and Globalization Puzzle

NASA Astrophysics Data System (ADS)

Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata

2014-12-01

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

Research Studies on Photons and Biphotons

DTIC Science & Technology

2013-10-01

harmonic transmit through the crystal . Scattered photons are detected by a YAP:Ce scintillation detector with energy resolution of 30. We choose to phase...counts as a function of photon energy is shown in Fig. 2a at full intensity (no filter before the diamond crystal ) and at the peak of the phase matching...are generated in the crystal or due to elastic scattering from the residual harmonic content in the incident beam. The absorption coefficients for Al

How transfer flights shape the structure of the airline network.

PubMed

Ryczkowski, Tomasz; Fronczak, Agata; Fronczak, Piotr

2017-07-17

In this paper, we analyse the gravity model in the global passenger air-transport network. We show that in the standard form, the model is inadequate for correctly describing the relationship between passenger flows and typical geo-economic variables that characterize connected countries. We propose a model for transfer flights that allows exploitation of these discrepancies in order to discover hidden subflows in the network. We illustrate its usefulness by retrieving the distance coefficient in the gravity model, which is one of the determinants of the globalization process. Finally, we discuss the correctness of the presented approach by comparing the distance coefficient to several well-known economic events.

Combined analysis of magnetic and gravity anomalies using normalized source strength (NSS)

NASA Astrophysics Data System (ADS)

Li, L.; Wu, Y.

2017-12-01

Gravity field and magnetic field belong to potential fields which lead inherent multi-solution. Combined analysis of magnetic and gravity anomalies based on Poisson's relation is used to determinate homology gravity and magnetic anomalies and decrease the ambiguity. The traditional combined analysis uses the linear regression of the reduction to pole (RTP) magnetic anomaly to the first order vertical derivative of the gravity anomaly, and provides the quantitative or semi-quantitative interpretation by calculating the correlation coefficient, slope and intercept. In the calculation process, due to the effect of remanent magnetization, the RTP anomaly still contains the effect of oblique magnetization. In this case the homology gravity and magnetic anomalies display irrelevant results in the linear regression calculation. The normalized source strength (NSS) can be transformed from the magnetic tensor matrix, which is insensitive to the remanence. Here we present a new combined analysis using NSS. Based on the Poisson's relation, the gravity tensor matrix can be transformed into the pseudomagnetic tensor matrix of the direction of geomagnetic field magnetization under the homologous condition. The NSS of pseudomagnetic tensor matrix and original magnetic tensor matrix are calculated and linear regression analysis is carried out. The calculated correlation coefficient, slope and intercept indicate the homology level, Poisson's ratio and the distribution of remanent respectively. We test the approach using synthetic model under complex magnetization, the results show that it can still distinguish the same source under the condition of strong remanence, and establish the Poisson's ratio. Finally, this approach is applied in China. The results demonstrated that our approach is feasible.

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.

The Impact of Complex Forcing on the Viscous Torsional Vibration Damper's Work in the Crankshaft of the Rotating Combustion Engine

NASA Astrophysics Data System (ADS)

Jagiełowicz-Ryznar, C.

2016-12-01

The numerical calculations results of torsional vibration of the multi-cylinder crankshaft in the serial combustion engine (MC), including a viscous damper (VD), at complex forcing, were shown. In fact, in the MC case the crankshaft rotation forcings spectrum is the sum of harmonic forcing whose amplitude can be compared with the amplitude of the 1st harmonic. A significant impact, in the engine operational velocity, on the vibration damping process of MC, may be the amplitude of the 2nd harmonic of a forcing moment. The calculations results of MC vibration, depending on the amplitude of the 2nd harmonic of the forcing moment, for the first form of the torsional vibration, were shown. Higher forms of torsional vibrations have no practical significance. The calculations assume the optimum damping coefficient VD, when the simple harmonic forcing is equal to the base critical velocity of the MC crankshaft.

Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation

NASA Astrophysics Data System (ADS)

Celebrano, Michele; Wu, Xiaofei; Baselli, Milena; Großmann, Swen; Biagioni, Paolo; Locatelli, Andrea; de Angelis, Costantino; Cerullo, Giulio; Osellame, Roberto; Hecht, Bert; Duò, Lamberto; Ciccacci, Franco; Finazzi, Marco

2015-05-01

Boosting nonlinear frequency conversion in extremely confined volumes remains a challenge in nano-optics research, but can enable applications in nanomedicine, photocatalysis and background-free biosensing. To obtain brighter nonlinear nanoscale sources, approaches that enhance the electromagnetic field intensity and counter the lack of phase matching in nanoplasmonic systems are often employed. However, the high degree of symmetry in the crystalline structure of plasmonic materials (metals in particular) and in nanoantenna designs strongly quenches second harmonic generation. Here, we describe doubly-resonant single-crystalline gold nanostructures with no axial symmetry displaying spatial mode overlap at both the excitation and second harmonic wavelengths. The combination of these features allows the attainment of a nonlinear coefficient for second harmonic generation of ˜5 × 10-10 W-1, enabling a second harmonic photon yield higher than 3 × 106 photons per second. Theoretical estimations point toward the use of our nonlinear plasmonic nanoantennas as efficient platforms for label-free molecular sensing.

Assessment of a solid-phase reagent for urinary specific gravity determination.

PubMed

Chu, S Y; Sparks, D

1984-02-01

We have compared the specific gravity (S.G.) determined by the N-Multistix method with that obtained from the Total Solids (TS) meter. Overall, 88.7% of the specific gravity results obtained with the reagent strip method were within 0.005 of those obtained with the TS meter. There was a good correlation between the methods and there was no bias for the group means obtained by either method. A good correlation was also found between the S.G. on the strip and osmolality (correlation coefficient of 0.955). The results obtained with the reagent strip for urinary specific gravity therefore appear acceptable for routine laboratory purposes.

Geopotential coefficient determination and the gravimetric boundary value problem: A new approach

NASA Technical Reports Server (NTRS)

Sjoeberg, Lars E.

1989-01-01

New integral formulas to determine geopotential coefficients from terrestrial gravity and satellite altimetry data are given. The formulas are based on the integration of data over the non-spherical surface of the Earth. The effect of the topography to low degrees and orders of coefficients is estimated numerically. Formulas for the solution of the gravimetric boundary value problem are derived.

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.

Fixed Packed Bed Reactors in Reduced Gravity

NASA Technical Reports Server (NTRS)

Motil, Brian J.; Balakotaiah, Vemuri; Kamotani, Yasuhiro; McCready, Mark J.

2004-01-01

We present experimental data on flow pattern transitions, pressure drop and flow characteristics for cocurrent gas-liquid flow through packed columns in microgravity. The flow pattern transition data indicates that the pulse flow regime exists over a wider range of gas and liquid flow rates under microgravity conditions compared to 1-g and the widely used Talmor map in 1-g is not applicable for predicting the transition boundaries. A new transition criterion between bubble and pulse flow in microgravity is proposed and tested using the data. Since there is no static head in microgravity, the pressure drop measured is the true frictional pressure drop. The pressure drop data, which has much smaller scatter than most reported 1-g data clearly shows that capillary effects can enhance the pressure drop (especially in the bubble flow regime) as much as 200% compared to that predicted by the single phase Ergun equation. The pressure drop data are correlated in terms of a two-phase friction factor and its dependence on the gas and liquid Reynolds numbers and the Suratman number. The influence of gravity on the pulse amplitude and frequency is also discussed and compared to that under normal gravity conditions. Experimental work is planned to determine the gas-liquid and liquid-solid mass transfer coefficients. Because of enhanced interfacial effects, we expect the gas-liquid transfer coefficients kLa and kGa (where a is the gas-liquid interfacial area) to be higher in microgravity than in normal gravity at the same flow conditions. This will be verified by gas absorption experiments, with and without reaction in the liquid phase, using oxygen, carbon dioxide, water and dilute aqueous amine solutions. The liquid-solid mass transfer coefficient will also be determined in the bubble as well as the pulse flow regimes using solid benzoic acid particles in the packing and measuring their rate of dissolution. The mass transfer coefficients in microgravity will be compared to those in normal gravity cocurrent flow to determine the mass transfer enhancement and propose new mass transfer correlations for two-phase gas-liquid flows through packed beds in microgravity.

Numerical modeling of marine Gravity data for tsunami hazard zone mapping

NASA Astrophysics Data System (ADS)

Porwal, Nipun

2012-07-01

Tsunami is a series of ocean wave with very high wavelengths ranges from 10 to 500 km. Therefore tsunamis act as shallow water waves and hard to predict from various methods. Bottom Pressure Recorders of Poseidon class considered as a preeminent method to detect tsunami waves but Acoustic Modem in Ocean Bottom Pressure (OBP) sensors placed in the vicinity of trenches having depth of more than 6000m fails to propel OBP data to Surface Buoys. Therefore this paper is developed for numerical modeling of Gravity field coefficients from Bureau Gravimetric International (BGI) which do not play a central role in the study of geodesy, satellite orbit computation, & geophysics but by mathematical transformation of gravity field coefficients using Normalized Legendre Polynomial high resolution ocean bottom pressure (OBP) data is generated. Real time sea level monitored OBP data of 0.3° by 1° spatial resolution using Kalman filter (kf080) for past 10 years by Estimating the Circulation and Climate of the Ocean (ECCO) has been correlated with OBP data from gravity field coefficients which attribute a feasible study on future tsunami detection system from space and in identification of most suitable sites to place OBP sensors near deep trenches. The Levitus Climatological temperature and salinity are assimilated into the version of the MITGCM using the ad-joint method to obtain the sea height segment. Then TOPEX/Poseidon satellite altimeter, surface momentum, heat, and freshwater fluxes from NCEP reanalysis product and the dynamic ocean topography DOT_DNSCMSS08_EGM08 is used to interpret sea-bottom elevation. Then all datasets are associated under raster calculator in ArcGIS 9.3 using Boolean Intersection Algebra Method and proximal analysis tools with high resolution sea floor topographic map. Afterward tsunami prone area and suitable sites for set up of BPR as analyzed in this research is authenticated by using Passive microwave radiometry system for Tsunami Hazard Zone Mapping by network of seismometers. Thus using such methodology for early Tsunami Hazard Zone Mapping also increase accuracy and reduce time period for tsunami predictions. KEYWORDS:, Tsunami, Gravity Field Coefficients, Ocean Bottom Pressure, ECCO, BGI, Sea Bottom Temperature, Sea Floor Topography.

Fixed Packed Bed Reactors in Reduced Gravity

NASA Technical Reports Server (NTRS)

Motil, Brian J.; Balakotaiah, Vemuri; Kamotani, Yasuhiro; McCready, Mark J.

2004-01-01

We present experimental data on flow pattern transitions, pressure drop and flow characteristics for cocurrent gas-liquid flow through packed columns in microgravity. The flow pattern transition data indicates that the pulse flow regime exists over a wider range of gas and liquid flow rates under microgravity conditions compared to 1-g and the widely used Talmor map in 1-g is not applicable for predicting the transition boundaries. A new transition criterion between bubble and pulse flow in microgravity is proposed and tested using the data. Since there is no static head in microgravity, the pressure drop measured is the true frictional pressure drop. The pressure drop data, which has much smaller scatter than most reported 1-g data clearly shows that capillary effects can enhance the pressure drop (especially in the bubble flow regime) as much as 200% compared to that predicted by the single phase Ergun equation. The pressure drop data are correlated in terms of a two-phase friction factor and its dependence on the gas and liquid Reynolds numbers and the Suratman number. The influence of gravity on the pulse amplitude and frequency is also discussed and compared to that under normal gravity conditions. Experimental work is planned to determine the gas-liquid mass transfer coefficients. Because of enhanced interfacial effects, we expect the gas-liquid transfer coefficients k(L)a and k(G)a (where a is the gas-liquid interfacial area) to be higher in microgravity than in normal gravity at the same flow conditions. This will be verified by gas absorption experiments, with and without reaction in the liquid phase, using oxygen, carbon dioxide, water and dilute aqueous amine solutions. The liquid-solid mass transfer coefficient will also be determined in the bubble as well as the pulse flow regimes using solid benzoic acid particles in the packing and measuring their rate of dissolution. The mass transfer coefficients in microgravity will be compared to those in normal gravity cocurrent flow to determine the mass transfer enhancement and propose new mass transfer correlations for two-phase gas-liquid flows through packed beds in microgravity.

Deconvolution and analysis of wide-angle longwave radiation data from Nimbus 6 Earth radiation budget experiment for the first year

NASA Technical Reports Server (NTRS)

Bess, T. D.; Green, R. N.; Smith, G. L.

1980-01-01

One year of longwave radiation data from July 1975 through June 1976 from the Nimbus 6 satellite Earth radiation budget experiment is analyzed by representing the radiation field by a spherical harmonic expansion. The data are from the wide field of view instrument. Contour maps of the longwave radiation field and spherical harmonic coefficients to degree 12 and order 12 are presented for a 12 month data period.

Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

DOE PAGES

Rubinstein, Robert; Kurien, Susan; Cambon, Claude

2015-06-22

The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.

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.

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.

Imprints of fluctuating proton shapes on flow in proton-lead collisions at the LHC

NASA Astrophysics Data System (ADS)

Mäntysaari, Heikki; Schenke, Björn; Shen, Chun; Tribedy, Prithwish

2017-09-01

Results for particle production in √{ s} = 5.02TeV p + Pb collisions at the Large Hadron Collider within a combined classical Yang-Mills and relativistic viscous hydrodynamic calculation are presented. We emphasize the importance of sub-nucleon scale fluctuations in the proton projectile to describe the experimentally observed azimuthal harmonic coefficients vn, demonstrating their sensitivity to the proton shape. We stress that the proton shape and its fluctuations are not free parameters in our calculations. Instead, they have been constrained using experimental data from HERA on exclusive vector meson production. Including temperature dependent shear and bulk viscosities, as well as UrQMD for the low temperature regime, we present results for mean transverse momenta, harmonic flow coefficients for charged hadrons and identified particles, as well as Hanbury-Brown-Twiss radii.

Dynamic analysis of a magnetic bearing system with flux control

NASA Technical Reports Server (NTRS)

Knight, Josiah; Walsh, Thomas; Virgin, Lawrence

1994-01-01

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

A Test of General Relativity with MESSENGER Mission Data

NASA Astrophysics Data System (ADS)

Genova, A.; Mazarico, E.; Goossens, S. J.; Lemoine, F. G.; Neumann, G. A.; Nicholas, J. B.; Rowlands, D. D.; Smith, D. E.; Zuber, M. T.; Solomon, S. C.

2016-12-01

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft initiated collection of scientific data from the innermost planet during its first flyby of Mercury in January 2008. After two additional Mercury flybys, MESSENGER was inserted into orbit around Mercury on 18 March 2011 and operated for more than four Earth years through 30 April 2015. Data acquired during the flyby and orbital phases have provided crucial information on the formation and evolution of Mercury. The Mercury Laser Altimeter (MLA) and the radio science system, for example, obtained geodetic observations of the topography, gravity field, orientation, and tides of Mercury, which helped constrain its surface and deep interior structure. X-band radio tracking data collected by the NASA Deep Space Network (DSN) allowed the determination of Mercury's gravity field to spherical harmonic degree and order 100, as well as refinement of the planet's obliquity and estimation of the tidal Love number k2. These geophysical parameters are derived from the range-rate observables that measure precisely the motion of the spacecraft in orbit around the planet. However, the DSN stations acquired two other kinds of radio tracking data, range and delta-differential one-way ranging, which also provided precise measurements of Mercury's ephemeris. The proximity of Mercury's orbit to the Sun leads to a significant perihelion precession, which was used by Einstein as confirmation of general relativity (GR) because of its inconsistency with the effects predicted from classical Newtonian theory. MESSENGER data allow the estimation of the GR parameterized post-Newtonian (PPN) coefficients γ and β. Furthermore, determination of Mercury's orbit also allows estimation of the gravitational parameter (GM) and the flattening (J2) of the Sun. We modified our orbit determination software, NASA GSFC's GEODYN II, to enable simultaneous orbit integration of both MESSENGER and the planet Mercury. The combined estimation of both orbits leads to a more accurate estimation of Mercury's gravity field, orientation, and tides. Results for these geophysical parameters, GM and J2 for the Sun, and the PPN parameters constitute updates for all of these quantities.

Modeling of Mercury tides for recovery of gravity field and interior properties

NASA Astrophysics Data System (ADS)

Padovan, S.; Margot, J.; Hauck, S. A.; Lemoine, F. G.; Mazarico, E.; Peale, S. J.; Solomon, S. C.

2011-12-01

The radio science experiment on the MESSENGER mission allows the determination of the gravitational field of Mercury. In order to secure the best possible gravity-field recovery, it is important to model all the forces acting on the spacecraft. Here we study the perturbations induced on the spacecraft by the tides raised on Mercury by the Sun. The manner by which the tides affect the orbit of MESSENGER depends on the response of the planet to the tide-raising potential. This response is directly connected to the interior properties of Mercury, and its study can help improve our understanding of the physical and chemical properties of the planet. The standard approach of modeling the strongest tidal effect on the gravitational field is by introducing a time-varying component in the degree-two harmonic coefficients of the gravity field. The amplitude of these variations depends on known quantities (mass of the Sun and Mercury, radius of Mercury and its position and relative orientation with respect to the Sun) and on the Love number k2. The value of this parameter is sensitive (among other things) to the state of the core and to the rigidity of the mantle (which in turn depends on its chemical composition). An accurate value of k2 determined from orbit perturbations can be compared to values obtained with forward modeling of the interior of Mercury. The orbital geometry and physical environment of MESSENGER make the identification of the tidal perturbation difficult. Nevertheless, recent work has shown that in the case of Mars, careful study of the effect of tides on the spacecraft trajectory can help identify which orbital and observational geometries exhibit stronger tidal signatures and are apt to provide the best possible determination of k2. Our long-term goal is to evaluate k2 for a suite of interior models and to evaluate the sensitivity of k2 to key interior properties. We will describe the orbital geometry and the tidal perturbations acting on the spacecraft trajectory with both numerical and analytical approaches, and we will report on the status of the interior modeling efforts.

Analytical solution of perturbed relative motion: an application of satellite formations to geodesy

NASA Astrophysics Data System (ADS)

Wnuk, Edwin

In the upcoming years, several space missions will be operated using a number of spacecraft flying in formation. Clusters of spacecraft with a carefully designed orbits and optimal formation geometry enable a wide variety of applications ranging from remote sensing to astronomy, geodesy and basic physics. Many of the applications require precise relative navigation and autonomous orbit control of satellites moving in a formation. For many missions a centimeter level of orbit control accuracy is required. The GRACE mission, since its launch in 2002, has been improving the Earth's gravity field model to a very high level of accuracy. This mission is a formation flying one consisting of two satellites moving in coplanar orbits and provides range and range-rate measurements between the satellites in the along-track direction. Future geodetic missions probably will employ alternative architectures using additional satellites and/or performing out-of-plane motion, e.g cartwheel orbits. The paper presents an analytical model of a satellite formation motion that enables propagation of the relative spacecraft motion. The model is based on the analytical theory of satellite relative motion that was presented in the previous our papers (Wnuk and Golebiewska, 2005, 2006). This theory takes into account the influence of the following gravitational perturbation effects: 1) zonal and tesseral harmonic geopotential coefficients up to arbitrary degree and order, 2) Lunar gravity, 3) Sun gravity. Formulas for differential perturbations were derived with any restriction concerning a plane of satellite orbits. They can be applied in both: in plane and out of plane cases. Using this propagator we calculated relative orbits and future relative satellite positions for different types of formations: in plane, out of plane, cartwheel and others. We analyzed the influence of particular parts of perturbation effects and estimated the accuracy of predicted relative spacecrafts positions. References 1,Wnuk E., Golebiewska J.,2005, ,,The relative motion of Earth's orbiting satellites", Celestial Mechanics, 91, 373-389. 2.Wnuk E., Golebiewska J.,2006, "Differential Perturbations and Semimajor Axis Estimation for Satellite Formation Orbits", American Institute of Aeronautics and Astronautics, Electronic Library, 2006, 6018.

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.

Positivity of Curvature-Squared Corrections in Gravity

NASA Astrophysics Data System (ADS)

Cheung, Clifford; Remmen, Grant N.

2017-02-01

We study the Gauss-Bonnet (GB) term as the leading higher-curvature correction to pure Einstein gravity. Assuming a tree-level ultraviolet completion free of ghosts or tachyons, we prove that the GB term has a nonnegative coefficient in dimensions greater than 4. Our result follows from unitarity of the spectral representation for a general ultraviolet completion of the GB term.

Estimating the Earth's geometry, rotation and gravity field using a multi-satellite SLR solution

NASA Astrophysics Data System (ADS)

Stefka, V.; Blossfeld, M.; Mueller, H.; Gerstl, M.; Panafidina, N.

2012-12-01

Satellite Laser Ranging (SLR) is the unique technique to determine station coordinates, Earth Orientation Parameter (EOP) and Stokes coefficients of the Earth's gravity field in one common adjustment. These parameters form the so called "three pillars" (Plag & Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as official analysis center of the International Laser Ranging Service (ILRS), DGFI is developing and maintaining software to process SLR observations called "DGFI Orbit and Geodetic parameter estimation Software" (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. To take benefit of different orbit performances (e.g. inclination and altitude), a solution using ten different spherical satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES, BLITS) covering the period of 12 years of observations is computed. The satellites are relatively weighted using a variance component estimation (VCE). The obtained weights are analyzed w.r.t. the potential of the satellite to monitor changes in the Earths geometry, rotation and gravity field. The estimated parameters (station coordinates and EOP) are validated w.r.t. official time series of the IERS. The Stokes coefficients are compared to recent gravity field solutions.

Estimating the Earth's gravity field using a multi-satellite SLR solution

NASA Astrophysics Data System (ADS)

Bloßfeld, Mathis; Stefka, Vojtech; Müller, Horst; Gerstl, Michael

2013-04-01

Satellite Laser Ranging (SLR) is the unique technique to determine station coordinates, Earth Orientation Parameter (EOP) and Stokes coefficients of the Earth's gravity field in one common adjustment. These parameters form the so called "three pillars" (Plag & Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as official analysis center of the International Laser Ranging Service (ILRS), DGFI is developing and maintaining software to process SLR observations called "DGFI Orbit and Geodetic parameter estimation Software" (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. To take benefit of different orbit performances (e.g. inclination and altitude), a solution using ten different spherical satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES, BLITS) covering 12 years of observations is computed. The satellites are relatively weighted using a variance component estimation (VCE). The obtained weights are analyzed w.r.t. the potential of the satellite to monitor changes in the Earths geometry, rotation and gravity field. The estimated parameters (station coordinates and EOP) are validated w.r.t. official time series of the IERS. The obtained Stokes coefficients are compared to recent gravity field solutions and discussed in detail.

Direct recovery of mean gravity anomalies from satellite to satellite tracking

NASA Technical Reports Server (NTRS)

Hajela, D. P.

1974-01-01

The direct recovery was investigated of mean gravity anomalies from summed range rate observations, the signal path being ground station to a geosynchronous relay satellite to a close satellite significantly perturbed by the short wave features of the earth's gravitational field. To ensure realistic observations, these were simulated with the nominal orbital elements for the relay satellite corresponding to ATS-6, and for two different close satellites (one at about 250 km height, and the other at about 900 km height) corresponding to the nominal values for GEOS-C. The earth's gravitational field was represented by a reference set of potential coefficients up to degree and order 12, considered as known values, and by residual gravity anomalies obtained by subtracting the anomalies, implied by the potential coefficients, from their terrestrial estimates. It was found that gravity anomalies could be recovered from strong signal without using any a-priori terrestrial information, i.e. considering their initial values as zero and also assigning them a zero weight matrix. While recovering them from weak signal, it was necessary to use the a-priori estimate of the standard deviation of the anomalies to form their a-priori diagonal weight matrix.

Evanescent effects can alter ultraviolet divergences in quantum gravity without physical consequences

DOE PAGES

Bern, Zvi; Cheung, Clifford; Chi, Huan -Hang; ...

2015-11-17

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D = 4 dimensions. Similarly, evanescent fields do not propagate in D = 4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R 3 counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual inmore » D = 4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly—the coefficient of the Gauss-Bonnet operator—changes under p-form duality transformations. In addition, we concur and also find that the leading R 3 divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.« less

Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences.

PubMed

Bern, Zvi; Cheung, Clifford; Chi, Huan-Hang; Davies, Scott; Dixon, Lance; Nohle, Josh

2015-11-20

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R^{3} counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D=4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly-the coefficient of the Gauss-Bonnet operator-changes under p-form duality transformations. We concur and also find that the leading R^{3} divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.

Effect of the improved accelerometer calibration method on AIUB's GRACE monthly gravity field solution

NASA Astrophysics Data System (ADS)

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

2017-04-01

The monthly global gravity field solutions derived using the measurements from the GRACE (Gravity Recovery and Climate Experiment) satellites have been continuously improved by the processing centers. One of the improvements in the processing method is a more detailed calibration of the on-board accelerometers in the GRACE satellites. The accelerometer data calibration is usually restricted to the scale factors and biases. It has been assumed that the three different axes are perfectly orthogonal in the GRACE science reference frame. Recently, it was shown by Klinger and Mayer-Gürr (2016) that a fully-populated scale matrix considering the non-orthogonality of the axes and the misalignment of the GRACE science reference frame and the GRACE accelerometer frame improves the quality of the C20 coefficient in the GRACE monthly gravity field solutions. We investigate the effect of the more detailed calibration of the GRACE accelerometer data on the C20 coefficient in the case of the AIUB (Astronomical Institute of the University of Bern) processing method using the Celestial Mechanics Approach. We also investigate the effect of the new calibration parameters on the stochastic parameters in the Celestial Mechanics Approach.

Near Real-Time Closed-Loop Optimal Control Feedback for Spacecraft Attitude Maneuvers

DTIC Science & Technology

2009-03-01

60 3.8 Positive ωi Static Thrust Fan Characterization Polynomial Coefficients . . 62 3.9 Negative ωi Static Thrust Fan...Characterization Polynomial Coefficients . 62 4.1 Coefficients for SimSAT II’s Air Drag Polynomial Function . . . . . . . . . . . 78 5.1 OLOC Simulation...maneuver. Researchers using OCT identified that naturally occurring aerodynamic drag and gravity forces could be exploited in such a way that the CMGs

Effects of organic and inorganic nitrate on aortic and carotid haemodynamics in heart failure with preserved ejection fraction.

PubMed

Chirinos, Julio A; Londono-Hoyos, Francisco; Zamani, Payman; Beraun, Melissa; Haines, Philip; Vasim, Izzah; Varakantam, Swapna; Phan, Timothy S; Cappola, Thomas P; Margulies, Kenneth B; Townsend, Raymond R; Segers, Patrick

2017-11-01

To assess the haemodynamic effects of organic vs. inorganic nitrate administration among patients with heart failure with preserved ejection fraction (HFpEF). We assessed carotid and aortic pressure-flow relations non-invasively before and after the administration of 0.4 mg of sublingual nitroglycerin (n = 26), and in a separate sub-study, in response to 12.9 mmoL of inorganic nitrate (n = 16). Nitroglycerin did not consistently reduce wave reflections arriving at the proximal aorta (change in real part of reflection coefficient, 1st harmonic: -0.09; P = 0.01; 2nd harmonic: -0.045, P = 0.16; 3rd harmonic: +0.087; P = 0.05), but produced profound vasodilatation in the carotid territory, with a significant reduction in systolic blood pressure (133.6 vs. 120.5 mmHg; P = 0.011) and a marked reduction in carotid bed vascular resistance (19 580 vs. 13 078 dynes · s/cm 5 ; P = 0.001) and carotid characteristic impedance (3440 vs. 1923 dynes · s/cm 5 ; P = 0.002). Inorganic nitrate, in contrast, consistently reduced wave reflections across the first three harmonics (change in real part of reflection coefficient, 1st harmonic: -0.12; P = 0.03; 2nd harmonic: -0.11, P = 0.01; 3rd harmonic: -0.087; P = 0.09) and did not reduce blood pressure, carotid bed vascular resistance, or carotid characteristic impedance (P = NS). Nitroglycerin produces marked vasodilatation in the carotid circulation, with a pronounced reduction in blood pressure and inconsistent effects on central wave reflections. Inorganic nitrate, in contrast, produces consistent reductions in wave reflections, and unlike nitroglycerin, it does so without significant hypotension or cerebrovascular dilatation. These haemodynamic differences may underlie the different effects on exercise capacity and side effect profile of inorganic vs. organic nitrate in HFpEF. © 2017 The Authors. European Journal of Heart Failure © 2017 European Society of Cardiology.

O1, P1, N2 models of the global ocean tide on an elastic earth plus surface potential and spherical harmonic decompositions for M2, S2, and K1

NASA Technical Reports Server (NTRS)

Parke, M. E.

1982-01-01

The models of M2, S2, and K1 presented in Parke and Hendershott (1980) are supplemented with models of O1, P1, and N2. The models satisfy specified elevation boundary conditions and are generated by fighting a small number of test functions to island data. Maps are presented of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each new component. Maps of the tidal potential seen by an observer fixed to the surface of the solid earth are also presented for all six constituents. Spherical harmonic coefficients up to order four and the rms magnitude of the coefficients to order fifteen are presented for each constituent. The rms magnitudes of the P1 and K1 coefficients normalized by their respective equilibrium amplitudes are compared to determine the effect of the diurnal core resonance.

Visual analysis of flow boiling at different gravity levels in 4.0 mm tube

NASA Astrophysics Data System (ADS)

Valencia-Castillo, C. M.; Celata, G. P.; Saraceno, L.; Zummo, G.

2014-11-01

The aim of the present paper is to describe the results of flow boiling heat transfer at low gravity and compare them with those obtained at earth gravity, evaluating possible differences. The experimental campaigns at low gravity have been performed during the parabolic flight campaign of October-November 2013. The paper will show the analysis of differences between the heat transfer coefficients and vapour bubble parameters at normal and at zero gravity. The results of 4.0 mm tube are presented and discussed. With respect to terrestrial gravity, heat transfer is systematically lower at microgravity in the range of the experimental conditions. Heat transfer differences for the two gravity conditions are related to the different bubble size in each of them. The size of a bubble in flow boiling is affected by the gravity level, being larger at low gravity, unless inertial forces are largely predominant over buoyancy and other forces acting on the bubble itself when detaching from a heated wall. Vapour bubble parameters (bubble diameter, bubble length, width, and nose velocity) have been measured.

Gravitational waves in ghost free bimetric gravity

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

Mohseni, Morteza, E-mail: m-mohseni@pnu.ac.ir

2012-11-01

We obtain a set of exact gravitational wave solutions for the ghost free bimetric theory of gravity. With a flat reference metric, the theory admits the vacuum Brinkmann plane wave solution for suitable choices of the coefficients of different terms in the interaction potential. An exact gravitational wave solution corresponding to a massive scalar mode is also admitted for arbitrary choice of the coefficients with the reference metric being proportional to the spacetime metric. The proportionality factor and the speed of the wave are calculated in terms of the parameters of the theory. We also show that a F(R) extensionmore » of the theory admits similar solutions but in general is plagued with ghost instabilities.« less

Inclined gravity currents filling basins: The influence of Reynolds number on entrainment into gravity currents

NASA Astrophysics Data System (ADS)

Hogg, Charlie A. R.; Dalziel, Stuart B.; Huppert, Herbert E.; Imberger, Jörg

2015-09-01

In many important natural and industrial systems, gravity currents of dense fluid feed basins. Examples include lakes fed by dense rivers and auditoria supplied with cooled air by ventilation systems. As we will show, the entrainment into such buoyancy driven currents can be influenced by viscous forces. Little work, however, has examined this viscous influence and how entrainment varies with the Reynolds number, Re. Using the idea of an entrainment coefficient, E, we derive a mathematical expression for the rise of the front at the top of the dense fluid ponding in a basin, where the horizontal cross-sectional area of the basin varies linearly with depth. We compare this expression to experiments on gravity currents with source Reynolds numbers, Res, covering the broad range 100 < Res < 1500. The form of the observed frontal rises was well approximated by our theory. By fitting the observed frontal rises to the theoretical form with E as the free parameter, we find a linear trend for E(Res) over the range 350 < Res < 1100, which is in the transition to turbulent flow. In the experiments, the entrainment coefficient, E, varied from 4 × 10-5 to 7 × 10-2. These observations show that viscous damping can be a dominant influence on gravity current entrainment in the laboratory and in geophysical flows in this transitional regime.

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.

A Compact Band-Pass Filter with High Selectivity and Second Harmonic Suppression

PubMed Central

Hadarig, Ramona Cosmina; de Cos Gomez, Maria Elena; Las-Heras, Fernando

2013-01-01

The design of a novel band-pass filter with narrow-band features based on an electromagnetic resonator at 6.4 GHz is presented. A prototype is manufactured and characterized in terms of transmission and reflection coefficient. The selective passband and suppression of the second harmonic make the filter suitable to be used in a C band frequency range for radar systems and satellite/terrestrial applications. To avoid substantial interference for this kind of applications, passive components with narrow band features and small dimensions are required. Between 3.6 GHz and 4.2 GHz the band-pass filter with harmonic suppression should have an attenuation of at least 35 dB, whereas for a passband, less than 10% is sufficient. PMID:28788412

First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds.

PubMed

Errea, Ion; Calandra, Matteo; Mauri, Francesco

2013-10-25

Palladium hydrides display the largest isotope effect anomaly known in the literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion, and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being mainly responsible for the isotope anomaly.

Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

NASA Astrophysics Data System (ADS)

Sikora, Roman; Markiewicz, Przemysław; Pabjańczyk, Wiesława

2018-04-01

The power systems usually include a number of nonlinear receivers. Nonlinear receivers are the source of disturbances generated to the power system in the form of higher harmonics. The level of these disturbances describes the total harmonic distortion coefficient THD. Its value depends on many factors. One of them are the deformation and change in RMS value of supply voltage. A modern LED luminaire is a nonlinear receiver as well. The paper presents the results of the analysis of the influence of change in RMS value of supply voltage and the level of dimming of the tested luminaire on the value of the current THD. The analysis was made using a mathematical model based on multivariable polynomial fitting.

On the solar cycle variation in the barometer coefficients of high latitude neutron monitors

NASA Technical Reports Server (NTRS)

Kusunose, M.; Ogita, N.

1985-01-01

Evaluation of barometer coefficients of neutron monitors located at high latitudes has been performed by using the results of the spherical harmonic analysis based on the records from around twenty stations for twelve years from January 1966 to December 1977. The average of data at eight stations, where continuous records are available for twelve years, show that the absolute value of barometer coefficient is in positive correlation with the cosmic ray neutron intensity. The variation rate of the barometer coefficient to the cosmic ray neutron intensity is influenced by the changes in the cutoff rigidity and in the primary spectrum.

Satellite borne gravity gradiometer study

NASA Technical Reports Server (NTRS)

Metzger, E.; Jircitano, A.; Affleck, C.

1976-01-01

Gravity gradiometry is recognized to be a very difficult instrumentation problem because extremely small differential acceleration levels have to be measured, 0.1 EU corresponds to an acceleration of 10 to the minus 11th power g at two points 1 meter apart. A feasibility model of a gravity gradiometer is being developed for airborne applications using four modified versions of the proven Model VII accelerometers mounted on a slowly rotating fixture. Gravity gradients are being measured to 1.07 EU in a vertical rotation axis orientation. Equally significant are the outstanding operational characteristics such as fast reaction time, low temperature coefficients and high degree of bias stability over long periods of time. The rotating accelerometer gravity gradiometer approach and its present status is discussed and it is the foundation for the orbital gravity gradiometer analyzed. The performance levels achieved in a 1 g environment of the earth and under relatively high seismic disturbances, lend the orbital gravity gradiometer a high confidence level of success.

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.

Numerical simulation of fluid flow and heat transfer in a thin liquid film over a stationary and rotating disk and comparison with experimental data

NASA Technical Reports Server (NTRS)

Faghri, Amir; Swanson, Theodore D.

1990-01-01

In the first section, improvements in the theoretical model and computational procedure for the prediction of film height and heat-transfer coefficient of the free surface flow of a radially-spreading thin liquid film adjacent to a flat horizontal surface of finite extent are presented. Flows in the presence and absence of gravity are considered. Theoretical results are compared to available experimental data with good agreement. In the presence of gravity, a hydraulic jump is present, isolating the flow into two regimes: supercritical upstream from the jump and subcritical downstream of it. In this situation, the effects of surface tension are important near the outer edge of the disk where the fluid experiences a free fall. A region of flow separation is present just downstream of the jump. In the absence of gravity, no hydraulic jump or separated flow region is present. The variation of the heat-transfer coefficient for flows in the presence and absence of gravity are also presented. In the second section, the results of a numerical simulation of the flow field and associated heat transfer coefficients are presented for the free surface flow of a thin liquid film adjacent to a horizontal rotating disk. The computation was performed for different flow rates and rotational velocities using a 3-D boundary-fitted coordinate system. Since the geometry of the free surface is unknown and dependent on flow rate, rate of rotation, and other parameters, an iterative procedure had to be used to ascertain its location. The computed film height agreed well with existing experimental measurements. The flow is found to be dominated by inertia near the entrance and close to the free surface and dominated by centrifugal force at larger radii and adjacent to the disk. The rotation enhances the heat transfer coefficient by a significant amount.

A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.

1982-01-01

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. A study is presented of the shock motion associated with an oscillating airfoil and its representation by the harmonic procedure. The effects of the shock motion and the resulting pressure pulse are shown to be included in the harmonic pressure distributions and the corresponding generalized forces. Analytical and experimental pressure distributions for the NACA 64A010 airfoil are compared for Mach numbers of 0.75, 0.80 and 0.842. A typical section, two-degree-of-freedom flutter analysis of a NACA 64A010 airfoil is performed. The results show a sharp transonic bucket in one case and abrupt changes in instability modes.

Imprints of fluctuating proton shapes on flow in proton-lead collisions at the LHC

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

Mantysaari, Heikki; Schenke, Bjorn; Shen, Chun

Results for particle production inmore » $$\\sqrt{s}$$ = 5.02 TeV p+Pb collisions at the Large Hadron Collider within a combined classical Yang-Mills and relativistic viscous hydrodynamic calculation are presented. We emphasize the importance of sub-nucleon scale fluctuations in the proton projectile to describe the experimentally observed azimuthal harmonic coefficients v n, demonstrating their sensitivity to the proton shape. We stress that the proton shape and its fluctuations are not free parameters in our calculations. Instead, they have been constrained using experimental data from HERA on exclusive vector meson production. Including temperature dependent shear and bulk viscosities, as well as UrQMD for the low temperature regime, we present results for mean trans-verse momenta, harmonic flow coefficients for charged hadrons and identified particles, as well as Hanbury-Brown-Twiss radii.« less

Kinematics and constraints associated with swashplate blade pitch control

NASA Technical Reports Server (NTRS)

Leyland, Jane A.

1993-01-01

An important class of techniques to reduce helicopter vibration is based on using a Higher Harmonic controller to optimally define the Higher Harmonic blade pitch. These techniques typically require solution of a general optimization problem requiring the determination of a control vector which minimizes a performance index where functions of the control vector are subject to inequality constraints. Six possible constraint functions associated with swashplate blade pitch control were identified and defined. These functions constrain: (1) blade pitch Fourier Coefficients expressed in the Rotating System, (2) blade pitch Fourier Coefficients expressed in the Nonrotating System, (3) stroke of the individual actuators expressed in the Nonrotating System, (4) blade pitch expressed as a function of blade azimuth and actuator stroke, (5) time rate-of-change of the aforementioned parameters, and (6) required actuator power. The aforementioned constraints and the associated kinematics of swashplate blade pitch control by means of the strokes of the individual actuators are documented.

Absolute and relative nonlinear optical coefficients of KDP, KD(asterisk)P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation

NASA Technical Reports Server (NTRS)

Eckardt, Robert C.; Byer, Robert L.; Masuda, Hisashi; Fan, Yuan Xuan

1990-01-01

Both absolute and relative nonlinear optical coefficients of six nonlinear materials measured by second-harmonic generation are discussed. A single-mode, injection-seeded, Q-switched Nd:YAG laser with spatially filtered output was used to generate the 1.064-micron fundamental radiation. The following results were obtained: d36(KDP) = 0.38 pm/V, d36(KD/asterisk/P) = 0.37 pm/V, (parallel)d22(BaB2O4)(parallel) = 2.2 pm/V, d31(LiIO3) = -4.1 pm/V, d31(5 percentMgO:MgO LiNbO3) = -4.7 pm/V, and d(eff)(KTP) = 3.2 pm/V. The accuracy of these measurements is estimated to be better than 10 percent.

Imprints of fluctuating proton shapes on flow in proton-lead collisions at the LHC

DOE PAGES

Mantysaari, Heikki; Schenke, Bjorn; Shen, Chun; ...

2017-07-21

Results for particle production inmore » $$\\sqrt{s}$$ = 5.02 TeV p+Pb collisions at the Large Hadron Collider within a combined classical Yang-Mills and relativistic viscous hydrodynamic calculation are presented. We emphasize the importance of sub-nucleon scale fluctuations in the proton projectile to describe the experimentally observed azimuthal harmonic coefficients v n, demonstrating their sensitivity to the proton shape. We stress that the proton shape and its fluctuations are not free parameters in our calculations. Instead, they have been constrained using experimental data from HERA on exclusive vector meson production. Including temperature dependent shear and bulk viscosities, as well as UrQMD for the low temperature regime, we present results for mean trans-verse momenta, harmonic flow coefficients for charged hadrons and identified particles, as well as Hanbury-Brown-Twiss radii.« less

Low-Cost Alternative for Signal Generators in the Physics Laboratory

NASA Astrophysics Data System (ADS)

Pathare, Shirish Rajan; Raghavendra, M. K.; Huli, Saurabhee

2017-05-01

Recently devices such as the optical mouse of a computer, webcams, Wii remote, and digital cameras have been used to record and analyze different physical phenomena quantitatively. Devices like tablets and smartphones are also becoming popular. Different scientific applications available at Google Play (Android devices) or the App Store (iOS devices) make them versatile. One can find many websites that provide information regarding various scientific applications compatible with these systems. A variety of smartphones/tablets are available with different types of sensors embedded. Some of them have sensors that are capable of measuring intensity of light, sound, and magnetic field. The camera of these devices has been used to study projectile motion, and the same device, along with a sensor, has been used to study the physical pendulum. Accelerometers have been used to study free and damped harmonic oscillations and to measure acceleration due to gravity. Using accelerometers and gyroscopes, angular velocity and centripetal acceleration have been measured. The coefficient of restitution for a ball bouncing on the floor has been measured using the application Oscilloscope on the iPhone. In this article, we present the use of an Android device as a low-cost alternative for a signal generator. We use the Signal Generator application installed on the Android device along with an amplifier circuit.

Tidal Response of Preliminary Jupiter Model

NASA Astrophysics Data System (ADS)

Wahl, Sean M.; Hubbard, William B.; Militzer, Burkhard

2016-11-01

In anticipation of improved observational data for Jupiter’s gravitational field, from the Juno spacecraft, we predict the static tidal response for a variety of Jupiter interior models based on ab initio computer simulations of hydrogen-helium mixtures. We calculate hydrostatic-equilibrium gravity terms, using the non-perturbative concentric Maclaurin Spheroid method that eliminates lengthy expansions used in the theory of figures. Our method captures terms arising from the coupled tidal and rotational perturbations, which we find to be important for a rapidly rotating planet like Jupiter. Our predicted static tidal Love number, {k}2=0.5900, is ˜10% larger than previous estimates. The value is, as expected, highly correlated with the zonal harmonic coefficient J 2, and is thus nearly constant when plausible changes are made to the interior structure while holding J 2 fixed at the observed value. We note that the predicted static k 2 might change, due to Jupiter’s dynamical response to the Galilean moons, and find reasons to argue that the change may be detectable—although we do not present here a theory of dynamical tides for highly oblate Jovian planets. An accurate model of Jupiter’s tidal response will be essential for interpreting Juno observations and identifying tidal signals from effects of other interior dynamics of Jupiter’s gravitational field.

Gravity Effects in Condensing and Evaporating Films

NASA Technical Reports Server (NTRS)

Hermanson, J. C.; Som, S. M.; Allen, J. S.; Pedersen, P. C.

2004-01-01

A general overview of gravity effects in condensing and evaporating films is presented. The topics include: 1) Research Overview; 2) NASA Recognizes Critical Need for Condensation & Evaporation Research to Enable Human Exploration of Space; 3) Condensation and Evaporation Research in Reduced Gravity is Enabling for AHST Technology Needs; 4) Differing Role of Surface Tension on Condensing/Evaporating Film Stability; 5) Fluid Mechanisms in Condensing and Evaporating Films in Reduced Gravity; 6) Research Plan; 7) Experimental Configurations for Condensing Films; 8) Laboratory Condensation Test Cell; 9) Aircraft Experiment; 10) Condensation Study Current Test Conditions; 11) Diagnostics; 12) Shadowgraph Images of Condensing n- pentane Film in Unstable (-1g) Configuration; 13) Condensing n-Pentane Film in Normal Gravity (-1g) at Constant Pressure; 14) Condensing n-Pentane Film in Normal Gravity (-1g) with Cyclic Pressure; 15) Non-condensing Pumped Film in Normal Gravity (-1g); 16) Heat Transfer Coefficient in Developing, Unstable Condensing Film in Normal Gravity; 17) Heat Transfer for Unsteady Condensing Film (-1g); 18) Ultrasound Measurement of Film Thickness N-pentane Film, Stable (+1g) Configuration; and 19) Ultrasound Measurement of Film Thickness N-pentane Film, Unstable (-1g) Configuration.

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.

Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO(4).

PubMed

Asaumi, K

1993-10-20

A simplified approximate expression for the effective nonlinear coefficient of type-II second-harmonicgeneration in KTiOPO(4) was obtained by observing that the difference between the refractive indices n(x) and n(y) is 1 order of magnitude smaller than the difference between n(z) and n(y) (or n(x)). The agreement of this approximate equation with the true definition is good, with a maximum discrepancy of 4%.

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.

Gravity and Heater Size Effects on Pool Boiling Heat Transfer

NASA Technical Reports Server (NTRS)

Kim, Jungho; Raj, Rishi

2014-01-01

The current work is based on observations of boiling heat transfer over a continuous range of gravity levels between 0g to 1.8g and varying heater sizes with a fluorinert as the test liquid (FC-72/n-perfluorohexane). Variable gravity pool boiling heat transfer measurements over a wide range of gravity levels were made during parabolic flight campaigns as well as onboard the International Space Station. For large heaters and-or higher gravity conditions, buoyancy dominated boiling and heat transfer results were heater size independent. The power law coefficient for gravity in the heat transfer equation was found to be a function of wall temperature under these conditions. Under low gravity conditions and-or for smaller heaters, surface tension forces dominated and heat transfer results were heater size dependent. A pool boiling regime map differentiating buoyancy and surface tension dominated regimes was developed along with a unified framework that allowed for scaling of pool boiling over a wide range of gravity levels and heater sizes. The scaling laws developed in this study are expected to allow performance quantification of phase change based technologies under variable gravity environments eventually leading to their implementation in space based applications.

Wood variables affecting the friction coefficient of spruce pine on steel

Treesearch

Truett J. Lemoine; Charles W. McMillin; Floyd G. Manwiller

1970-01-01

Wood of spruce pine, Pinus glabra Walk., was factorially segregated by moisture content (0, 10, and 18 percent), specific gravity (less than 0.45 and more than 0.45), and extractive content (unextracted and extractive-freE), and the kinetic coefficient of friction on steel (having surface roughness of 9 microinches RMS) determined for tangential...

Proportioning the airplane for lateral stability

NASA Technical Reports Server (NTRS)

Donlan, C. J.

1976-01-01

Proportioning for lateral aircraft control included: (1) directional stability (slope of curve of yawing moment coefficient against sideslip), and (2) effective dihedral factor (slope of curve of rolling moment coefficient against sideslip). Basic forces influencing the directional stability of aircraft are indicated. Propeller side force, basic fuselage yaw, and vertical tail side force contributed to yaw moment about center of gravity.

Properties of Interfacial Tribo-Films

DTIC Science & Technology

1993-06-01

cf these rods is such as to have the center of gravity of or the attraction of water into the re-entrant peripheral gap the whole sample as close as...difference between the fluid dynamics, acoustic effects in stringed musical static and the kinetic friction coefficients increases with instruments...interfacial fluid molecules to static minimize oscillations, the center of gravity of the sample friction have been explored and, in this regard, adsorbed

Search for Lorentz Violation in a Short-Range Gravity Experiment

NASA Astrophysics Data System (ADS)

Bennett, D.; Skavysh, V.; Long, J.

2011-12-01

An experimental test of the Newtonian inverse square law at short range has been used to set limits on Lorentz violation in the pure gravity sector of the Standard-Model Extension. On account of the planar test mass geometry, nominally null with respect to 1/r2 forces, the limits derived for the SME coefficients of Lorentz violation are on the order bar sJK ˜ 104 .

Some Applications of Holography to Study Strongly Correlated Systems

NASA Astrophysics Data System (ADS)

Bhatnagar, Neha

2018-04-01

In this work, we study the transport coefficients of strongly coupled condensed matter systems using gauge/gravity duality (holography). We consider examples from the real world and evaluate the conductivities from their gravity duals. Adopting the bottom-up approach of holography, we obtain the frequency response of the conductivity for (1+1)-dimensional systems. We also evaluate the DC conductivities for non-relativistic condensed matter systems with hyperscaling violating geometry.

Simulation of the Chang'E-5 mission contribution in lunar long wavelength gravity field improvement

NASA Astrophysics Data System (ADS)

Yan, Jianguo; Yang, Xuan; Ping, Jinsong; Ye, Mao; Liu, Shanhong; Jin, Weitong; Li, Fei; Barriot, Jean-Pierre

2018-06-01

The precision of lunar gravity field estimation has improved by means of three to five orders of magnitude since the successful GRAIL lunar mission. There are still discrepancies however, in the low degree coefficients and long wavelength components of the solutions developed by two space research centers (JPL and GSFC). These discrepancies hint at the possibilities for improving the accuracy in the long wavelength part of the lunar gravity field. In the near future, China will launch the Chang'E-5 lunar mission. In this sample-return mission, there will be a chance to do KBRR measurements between an ascending module and an orbiting module. These two modules will fly around lunar at an inclination of ˜49 degrees, with an orbital height of 100 km and an inter-satellite distance of 200 km. In our research, we simulated the contribution of the KBRR tracking mode for different GRAIL orbital geometries. This analysis indicated possible deficiencies in the low degree coefficient solutions for the polar satellite-to-satellite tracking mode at various orbital heights. We also investigated the potential contributions of the KBRR to the Chang'E-5 mission goal of lunar gravity field recovery, especially in the long wavelength component. Potential improvements were assessed using various power spectrums of the lunar gravity field models. In addition, we also investigated possible improvements in solving lunar tidal Love number K2. These results may assist the implementation of the Chang'E-5 mission.

Time series of low-degree geopotential coefficients from SLR data: estimation of Earth's figure axis and LOD variations

NASA Astrophysics Data System (ADS)

Luceri, V.; Sciarretta, C.; Bianco, G.

2012-12-01

The redistribution of the mass within the earth system induces changes in the Earth's gravity field. In particular, the second-degree geopotential coefficients reflect the behaviour of the Earth's inertia tensor of order 2, describing the main mass variations of our planet impacting the EOPs. Thanks to the long record of accurate and continuous laser ranging observations to Lageos and other geodetic satellites, SLR is the only current space technique capable to monitor the long time variability of the Earth's gravity field with adequate accuracy. Time series of low-degree geopotential coefficients are estimated with our analysis of SLR data (spanning more than 25 years) from several geodetic satellites in order to detect trends and periodic variations related to tidal effects and atmospheric/oceanic mass variations. This study is focused on the variations of the second-degree Stokes coefficients related to the Earth's principal figure axis and oblateness: C21, S21 and C20. On the other hand, surface mass load variations induce excitations in the EOPs that are proportional to the same second-degree coefficients. The time series of direct estimates of low degree geopotential and those derived from the EOP excitation functions are compared and presented together with their time and frequency analysis.

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.

Reciprocal relations for transmission coefficients - Theory and application

NASA Technical Reports Server (NTRS)

Qu, Jianmin; Achenbach, Jan D.; Roberts, Ronald A.

1989-01-01

The authors present a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water) to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.

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.

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.

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

The influence of gravity on the precise measurement of solute diffusion coefficients in dilute liquid metals and metalloids.

PubMed

Smith, Reginald W; Zhu, Xiaohe; Tunnicliffe, Mark C; Smith, Timothy J N; Misener, Lowell; Adamson, Josee

2002-10-01

It is now well known that the diffusion coefficient (D) measured in a laboratory in low earth orbit (LEO) is less than the corresponding value measured in a terrestrial laboratory. However, all LEO laboratories are subject to transient accelerations (g-jitter) superimposed on the steady reduced gravity environment of the space platform. In measurements of the diffusion coefficients for dilute binary alloys of Pb-(Ag, Au,Sb), Sb-(Ga,In), Bi-(Ag,Au,Sb), Sn-(Au,Sb), Al-(Fe, Ni,Si), and In-Sb in which g-jitter was suppressed, it was found that D proportional to T (temperature) if g-jitter was suppressed, rather than D proportional to T(2) as observed by earlier workers with g-jitter present. Furthermore, when a forced g-jitter was applied to a diffusion couple, the value measured for D increased. The significance of these results is reviewed in the light of recent work in which ab initio molecular dynamics simulations predicted a D proportional to T relationship.

Mixed quantum-classical simulation of the hydride transfer reaction catalyzed by dihydrofolate reductase based on a mapped system-harmonic bath model

NASA Astrophysics Data System (ADS)

Xu, Yang; Song, Kai; Shi, Qiang

2018-03-01

The hydride transfer reaction catalyzed by dihydrofolate reductase is studied using a recently developed mixed quantum-classical method to investigate the nuclear quantum effects on the reaction. Molecular dynamics simulation is first performed based on a two-state empirical valence bond potential to map the atomistic model to an effective double-well potential coupled to a harmonic bath. In the mixed quantum-classical simulation, the hydride degree of freedom is quantized, and the effective harmonic oscillator modes are treated classically. It is shown that the hydride transfer reaction rate using the mapped effective double-well/harmonic-bath model is dominated by the contribution from the ground vibrational state. Further comparison with the adiabatic reaction rate constant based on the Kramers theory confirms that the reaction is primarily vibrationally adiabatic, which agrees well with the high transmission coefficients found in previous theoretical studies. The calculated kinetic isotope effect is also consistent with the experimental and recent theoretical results.

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

Diffusive smoothing of surfzone bathymetry by gravity-driven sediment transport

NASA Astrophysics Data System (ADS)

Moulton, M. R.; Elgar, S.; Raubenheimer, B.

2012-12-01

Gravity-driven sediment transport often is assumed to have a small effect on the evolution of nearshore morphology. Here, it is shown that down-slope gravity-driven sediment transport is an important process acting to smooth steep bathymetric features in the surfzone. Gravity-driven transport can be modeled as a diffusive term in the sediment continuity equation governing temporal (t) changes in bed level (h): ∂h/∂t ≈ κ ▽2h, where κ is a sediment diffusion coefficient that is a function of the bed shear stress (τb) and sediment properties, such as the grain size and the angle of repose. Field observations of waves, currents, and the evolution of large excavated holes (initially 10-m wide and 2-m deep, with sides as steep as 35°) in an energetic surfzone are consistent with diffusive smoothing by gravity. Specifically, comparisons of κ estimated from the measured bed evolution with those estimated with numerical model results for several transport theories suggest that gravity-driven sediment transport dominates the bed evolution, with κ proportional to a power of τb. The models are initiated with observed bathymetry and forced with observed waves and currents. The diffusion coefficients from the measurements and from the model simulations were on average of order 10-5 m2/s, implying evolution time scales of days for features with length scales of 10 m. The dependence of κ on τb varies for different transport theories and for high and low shear stress regimes. The US Army Corps of Engineers Field Research Facility, Duck, NC provided excellent logistical support. Funded by a National Security Science and Engineering Faculty Fellowship, a National Defense Science and Engineering Graduate Fellowship, and the Office of Naval Research.

Harmonic regression based multi-temporal cloud filtering algorithm for Landsat 8

NASA Astrophysics Data System (ADS)

Joshi, P.

2015-12-01

Landsat data archive though rich is seen to have missing dates and periods owing to the weather irregularities and inconsistent coverage. The satellite images are further subject to cloud cover effects resulting in erroneous analysis and observations of ground features. In earlier studies the change detection algorithm using statistical control charts on harmonic residuals of multi-temporal Landsat 5 data have been shown to detect few prominent remnant clouds [Brooks, Evan B., et al, 2014]. So, in this work we build on this harmonic regression approach to detect and filter clouds using a multi-temporal series of Landsat 8 images. Firstly, we compute the harmonic coefficients using the fitting models on annual training data. This time series of residuals is further subjected to Shewhart X-bar control charts which signal the deviations of cloud points from the fitted multi-temporal fourier curve. For the process with standard deviation σ we found the second and third order harmonic regression with a x-bar chart control limit [Lσ] ranging between [0.5σ < Lσ < σ] as most efficient in detecting clouds. By implementing second order harmonic regression with successive x-bar chart control limits of L and 0.5 L on the NDVI, NDSI and haze optimized transformation (HOT), and utilizing the seasonal physical properties of these parameters, we have designed a novel multi-temporal algorithm for filtering clouds from Landsat 8 images. The method is applied to Virginia and Alabama in Landsat8 UTM zones 17 and 16 respectively. Our algorithm efficiently filters all types of cloud cover with an overall accuracy greater than 90%. As a result of the multi-temporal operation and the ability to recreate the multi-temporal database of images using only the coefficients of the fourier regression, our algorithm is largely storage and time efficient. The results show a good potential for this multi-temporal approach for cloud detection as a timely and targeted solution for the Landsat 8 research community, catering to the need for innovative processing solutions in the infant stage of the satellite.

The Bach equations in spin-coefficient form

NASA Astrophysics Data System (ADS)

Forbes, Hamish

2018-06-01

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

Averaged model to study long-term dynamics of a probe about Mercury

NASA Astrophysics Data System (ADS)

Tresaco, Eva; Carvalho, Jean Paulo S.; Prado, Antonio F. B. A.; Elipe, Antonio; de Moraes, Rodolpho Vilhena

2018-02-01

This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from J_2 up to J_6, and the tesseral harmonics \\overline{C}_{22} that is of the same magnitude than zonal J_2. In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury-Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury's gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits.

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.

Stability analysis of an F/A-18 E/F cable mount m odel

NASA Technical Reports Server (NTRS)

Thompson, Nancy; Farmer, Moses

1994-01-01

A full-span F/A-18 E/F cable mounted wind tunnel model is part of a flutter clearance program at the NASA Langley Transonic Dynamics Tunnel. Parametric analysis of this model using GRUMCBL software was conducted to assess stability for wind tunnel tests. Two configurations of the F/A-18 E/F were examined. The parameters examined were pulley-cable friction, mach number, dynamic pressure, cable geometry, center of gravity location, cable tension, snubbing the model, drag, and test medium. For the nominal cable geometry (Cable Geometry 1), Configuration One was unstable for cases with higher pulley-cable friction coefficients. A new cable geometry (Cable Geometry 3) was determined in which Configuration One was stable for all cases evaluated. Configuration Two with the nominal center of gravity position was found to be unstable for cases with higher pulley-cable friction coefficients; however, the model was stable when the center of gravity moved forward 1/2. The model was tested using the cable mount system during the initial wind tunnel entry and was stable as predicted.

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.

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.

Separation of Non-metallic Inclusions from a Fe-Al-O Melt Using a Super-Gravity Field

NASA Astrophysics Data System (ADS)

Song, Gaoyang; Song, Bo; Guo, Zhancheng; Yang, Yuhou; Song, Mingming

2018-02-01

An innovative method for separating non-metallic inclusions from a high temperature melt using super gravity was systematically investigated. To explore the separation behavior of inclusion particles with densities less than that of metal liquid under a super-gravity field, a Fe-Al-O melt containing Al2O3 particles was treated with different gravity coefficients. Al2O3 particles migrated rapidly towards the reverse direction of the super gravity and gathered in the upper region of the sample. It was hard to find any inclusion particles with sizes greater than 2 μm in the middle and bottom areas. Additionally, the oxygen content in the middle region of the sample could be reduced to 0.0022 mass pct and the maximum removal rate of the oxygen content reached 61.4 pct. The convection in the melt along the direction of the super gravity was not generated by the super-gravity field, and the fluid velocity in the molten melt consisted only of the rotating tangential velocity. Moreover, the motion behavior of the Al2O3 particles was approximatively determined by Stokes' law along the direction of super gravity.

Determination of rolling resistance coefficient based on normal tyre stiffness

NASA Astrophysics Data System (ADS)

Rykov, S. P.; Tarasuyk, V. N.; Koval, V. S.; Ovchinnikova, N. I.; Fedotov, A. I.; Fedotov, K. V.

2018-03-01

The purpose of the article is to develop analytical dependence of wheel rolling resistance coefficient based on the mathematical description of normal tyre stiffness. The article uses the methods of non-holonomic mechanics and plane section methods. The article shows that the abscissa of gravity center of tyre stiffness expansion by the length of the contact area is the shift of normal road response. It can be used for determining rolling resistance coefficient. When determining rolling resistance coefficient using ellipsis and power function equations, one can reduce labor costs for testing and increase assessment accuracy.

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

NASA Astrophysics Data System (ADS)

Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot

2018-05-01

The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.

THERMODYNAMIC PROPERTIES OF MC (M = V, Nb, Ta): FIRST-PRINCIPLES CALCULATIONS

NASA Astrophysics Data System (ADS)

Cao, Yong; Zhu, Jingchuan; Liu, Yong; Long, Zhishen

2013-07-01

Through the quasi-harmonic Debye model, the pressure and temperature dependences of linear expansion coefficient, bulk modulus, Debye temperature and heat capacity have been investigated. The calculated thermodynamic properties were compared with experimental data and satisfactory agreement is reached.

Instability of meridional axial system in f( R) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Yousaf, Z.

2015-05-01

We analyze the dynamical instability of a non-static reflection axial stellar structure by taking into account the generalized Euler equation in metric f( R) gravity. Such an equation is obtained by contracting the Bianchi identities of the usual anisotropic and effective stress-energy tensors, which after using a radial perturbation technique gives a modified collapse equation. In the realm of the gravity model, we investigate instability constraints at Newtonian and post-Newtonian approximations. We find that the instability of a meridional axial self-gravitating system depends upon the static profile of the structure coefficients, while f( R) extra curvature terms induce the stability of the evolving celestial body.

Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface - Part 1: Harmonic wave

NASA Astrophysics Data System (ADS)

Troitskaya, Yu. I.; Ezhova, E. V.; Zilitinkevich, S. S.

2013-10-01

The surface-drag and mass-transfer coefficients are determined within a self-consistent problem of wave-induced perturbations and mean fields of velocity and density in the air, using a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. Investigation of a harmonic wave propagating along the wind has disclosed that the surface drag is generally larger for shorter waves. This effect is more pronounced in the unstable and neutral stratification. The stable stratification suppresses turbulence, which leads to weakening of the momentum and mass transfer.

Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons

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

Menikoff, Ralph

2014-09-02

A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.

NONLINEAR AND FIBER OPTICS: Conversion of pulsed laser radiation from the 9.3-9.6 μm range to the second harmonic in ZnGeP2 crystals

NASA Astrophysics Data System (ADS)

Andreev, Yu M.; Bykanov, A. N.; Gribenyukov, A. I.; Zuev, V. V.; Karyshev, V. D.; Kisletsov, A. V.; Kovalev, I. O.; Konov, Vitalii I.; Kuz'min, G. P.; Nesterenko, A. A.; Osorgin, A. E.; Starodumov, Yu M.; Chapliev, N. I.

1990-04-01

A pulsed TEA CO2 laser was used in an investigation of the influence of the pump radiation parameters (mode composition, wavelength, pulse duration), of the focusing conditions, of the properties of the material (absorption coefficient), and of the operating conditions (temperature) on the efficiency of conversion to the second harmonic and on the angular dependences of phase matching in ZnGeP2 crystals. The calculated results were found to be in good agreement with the experimental data.

Some new methods in geomagnetic field modeling applied to the 1960 - 1980 epoch

NASA Technical Reports Server (NTRS)

Langel, R. A.; Estes, R. H.; Mead, G. H.

1981-01-01

The utilization of satellite and surface data together permitted the incorporation of a solution for the anomaly field at each observatory. The residuals of the observatory measurements to such models is commensurate with the actual measurment accuracy. Incorporation of the anomaly estimation enabled the inclusion of stable time derivatives of the spherical harmonic coefficients up to the third derivative. A spherical harmonic model is derived with degree and order 13 in its constant and first time derivative terms, six in its second derivative terms and four in its third derivative terms.

Chi 3 dispersion in planar tantalum pentoxide waveguides in the telecommunications window.

PubMed

Chen, Ruiqi Y; Charlton, Martin D B; Lagoudakis, Pavlos G

2009-04-01

We report on the dispersion of the third-order nonlinear susceptibility (chi(3) or "Chi 3") in planar Ta2O5 waveguides in the telecommunications spectral window. We utilize the observation of third-harmonic generation under ultrashort pulsed excitation as a reference-free characterization method of chi(3) and obtain a large nonlinear coefficient, 2x10(-13) esu, at 1550 nm. Our observation of efficient third-harmonic generation in Ta2O5 waveguides in the telecoms window reveals the potential of this material system in high-speed integrated nonlinear optical switches.

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

Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at √{s_{NN}}=2.76 TeV

NASA Astrophysics Data System (ADS)

Adam, J.; Adamová, D.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alexandre, D.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Alme, J.; Alt, T.; Altinpinar, S.; Altsybeev, I.; Alves Garcia Prado, C.; An, M.; Andrei, C.; Andrews, H. A.; Andronic, A.; Anguelov, V.; Antičić, T.; Antinori, F.; Antonioli, P.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Balasubramanian, S.; Baldisseri, A.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartke, J.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Belmont, R.; Belmont-Moreno, E.; Beltran, L. G. E.; Belyaev, V.; Bencedi, G.; Beole, S.; Berceanu, I.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Bjelogrlic, S.; Blair, J. T.; Blau, D.; Blume, C.; Bock, F.; Bogdanov, A.; Bøggild, H.; Boldizsár, L.; Bombara, M.; Bonora, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Bossú, F.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Breitner, T.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Cai, X.; Caines, H.; Calero Diaz, L.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cepila, J.; Cerello, P.; Cerkala, J.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Chelnokov, V.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Conesa Balbastre, G.; Conesa del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Crkovska, J.; Crochet, P.; Cruz Albino, R.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; De, S.; De Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; De Falco, A.; De Gruttola, D.; De Marco, N.; De Pasquale, S.; De Souza, R. D.; Deisting, A.; Deloff, A.; Dénes, E.; Deplano, C.; Dhankher, P.; Di Bari, D.; Di Mauro, A.; Di Nezza, P.; Di Ruzza, B.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erdemir, I.; Erhardt, F.; Espagnon, B.; Estienne, M.; Esumi, S.; Eulisse, G.; Eum, J.; Evans, D.; Evdokimov, S.; Eyyubova, G.; Fabbietti, L.; Fabris, D.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Francisco, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gajdosova, K.; Gallio, M.; Galvan, C. D.; Gangadharan, D. R.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Garg, K.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Germain, M.; Gheata, M.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Grachov, O. A.; Graczykowski, L. K.; Graham, K. L.; Grelli, A.; Grigoras, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grinyov, B.; Grion, N.; Gronefeld, J. M.; Grosse-Oetringhaus, J. F.; Grosso, R.; Gruber, L.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Guzman, I. B.; Haake, R.; Hadjidakis, C.; Haiduc, M.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Herrmann, F.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hippolyte, B.; Horak, D.; Hosokawa, R.; Hristov, P.; Hughes, C.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Ilkaev, R.; Inaba, M.; Incani, E.; Ippolitov, M.; Irfan, M.; Isakov, V.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacak, B.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jahnke, C.; Jakubowska, M. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Mohisin Khan, M.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Khatun, A.; Kileng, B.; Kim, D. W.; Kim, D. J.; Kim, D.; Kim, H.; Kim, J. S.; Kim, J.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Kopcik, M.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Ladron de Guevara, P.; Lagana Fernandes, C.; Lakomov, I.; Langoy, R.; Lapidus, K.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lea, R.; Leardini, L.; Lee, S.; Lehas, F.; Lehner, S.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; León Vargas, H.; Leoncino, M.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lindal, S.; Lindenstruth, V.; Lippmann, C.; Lisa, M. A.; Ljunggren, H. M.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lupi, M.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Maldonado Cervantes, I.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Mao, Y.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martinengo, P.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Mastroserio, A.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzilli, M.; Mazzoni, M. A.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Mhlanga, S.; Miake, Y.; Mieskolainen, M. M.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Mishra, T.; Miskowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Molnar, L.; Montaño Zetina, L.; Montes, E.; Moreira De Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Münning, K.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Negrao De Oliveira, R. A.; Nellen, L.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Oh, S. K.; Ohlson, A.; Okatan, A.; Okubo, T.; Oleniacz, J.; Oliveira Da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Ozdemir, M.; Pachmayer, Y.; Pagano, D.; Pagano, P.; Paić, G.; Pal, S. K.; Palni, P.; Pan, J.; Pandey, A. K.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, W. J.; Parmar, S.; Passfeld, A.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Peng, X.; Pereira Da Costa, H.; Peresunko, D.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Ploskon, M.; Planinic, M.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Poppenborg, H.; Porteboeuf-Houssais, S.; Porter, J.; Pospisil, J.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Qvigstad, H.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Ravasenga, I.; Read, K. F.; Redlich, K.; Reed, R. J.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rodríguez Cahuantzi, M.; Rodriguez Manso, A.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Ronchetti, F.; Ronflette, L.; Rosnet, P.; Rossi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rui, R.; Russo, R.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Sahlmuller, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Šándor, L.; Sandoval, A.; Sano, M.; Sarkar, D.; Sarkar, N.; Sarma, P.; Scapparone, E.; Scarlassara, F.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schmidt, M.; Schuchmann, S.; Schukraft, J.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shadura, O.; Shahoyan, R.; Shangaraev, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singhal, V.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Song, Z.; Soramel, F.; Sorensen, S.; Sozzi, F.; Spiriti, E.; Sputowska, I.; Spyropoulou-Stassinaki, M.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Steyn, G.; Stiller, J. H.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Swain, S.; Szabo, A.; Szarka, I.; Szczepankiewicz, A.; Szymanski, M.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thäder, J.; Thakur, D.; Thomas, D.; Tieulent, R.; Tikhonov, A.; Timmins, A. R.; Toia, A.; Trogolo, S.; Trombetta, G.; Trubnikov, V.; Trzaska, W. H.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; Valencia Palomo, L.; Van Der Maarel, J.; Van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vázquez Doce, O.; Vechernin, V.; Veen, A. M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Vickovic, L.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Virgili, T.; Vislavicius, V.; Viyogi, Y. P.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Vranic, D.; Vrláková, J.; Vulpescu, B.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Willems, G. A.; Williams, M. C. S.; Windelband, B.; Winn, M.; Yalcin, S.; Yang, P.; Yano, S.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Zaborowska, A.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zaporozhets, S.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zgura, I. S.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zyzak, M.

2016-09-01

The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for π±, K± and p+overline{p} in Pb-Pb collisions at √{s_{NN}}=2.76 TeV were measured with the ALICE detector at the Large Hadron Collider. The results were obtained with the Scalar Product method, correlating the identified hadrons with reference particles from a different pseudorapidity region. Effects not related to the common event symmetry planes (non-flow) were estimated using correlations in pp collisions and were subtracted from the measurement. The obtained flow coefficients exhibit a clear mass ordering for transverse momentum ( p T) values below ≈ 3 GeV/ c. In the intermediate p T region (3 < p T < 6 GeV/ c), particles group at an approximate level according to the number of constituent quarks, suggesting that coalescence might be the relevant particle production mechanism in this region. The results for p T < 3 GeV/ c are described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses initial conditions generated by A Multi-Phase Transport model (AMPT) and describes the expansion of the fireball using a value of 0.08 for the ratio of shear viscosity to entropy density ( η/s), coupled to a hadronic cascade model (UrQMD). Finally, expectations from AMPT alone fail to quantitatively describe the measurements for all harmonics throughout the measured transverse momentum region. However, the comparison to the AMPT model highlights the importance of the late hadronic rescattering stage to the development of the observed mass ordering at low values of p T and of coalescence as a particle production mechanism for the particle type grouping at intermediate values of p T for all harmonics. [Figure not available: see fulltext.

Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $$\\sqrt{s_{\\mathrm{NN}}}=2.76 $$ TeV

DOE PAGES

Adam, J.; Adamová, D.; Aggarwal, M. M.; ...

2016-09-28

The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for π ± , K ± and p +more » $$\\bar{p}$$ in Pb-Pb collisions at √s NN=2.76 TeV were measured with the ALICE detector at the Large Hadron Collider. The results were obtained with the Scalar Product method, correlating the identified hadrons with reference particles from a different pseudorapidity region. Effects not related to the common event symmetry planes (non-flow) were estimated using correlations in pp collisions and were subtracted from the measurement. The obtained flow coefficients exhibit a clear mass ordering for transverse momentum (p T ) values below ≈ 3 GeV/c. In the intermediate p T region (3 < p T < 6 GeV/c), particles group at an approximate level according to the number of constituent quarks, suggesting that coalescence might be the relevant particle production mechanism in this region. The results for p T < 3 GeV/c are described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses initial conditions generated by A Multi-Phase Transport model (AMPT) and describes the expansion of the fireball using a value of 0.08 for the ratio of shear viscosity to entropy density (η/s), coupled to a hadronic cascade model (UrQMD). Finally, expectations from AMPT alone fail to quantitatively describe the measurements for all harmonics throughout the measured transverse momentum region. However, the comparison to the AMPT model highlights the importance of the late hadronic rescattering stage to the development of the observed mass ordering at low values of p T and of coalescence as a particle production mechanism for the particle type grouping at intermediate values of p T for all harmonics.« less

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.

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

NASA Astrophysics Data System (ADS)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.; Espley, J. R.; Joergensen, J. L.; Joergensen, P. S.; Merayo, J. M. G.; Herceg, M.; Bloxham, J.; Moore, K. M.; Bolton, S. J.; Levin, S. M.

2018-03-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of 45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

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.

A novel approach for quantitative harmonization in PET.

PubMed

Namías, M; Bradshaw, T; Menezes, V O; Machado, M A D; Jeraj, R

2018-05-04

Positron emission tomography (PET) imaging allows for measurement of activity concentrations of a given radiotracer in vivo. The quantitative capabilities of PET imaging are particularly important in the context of monitoring response to treatment, where quantitative changes in tracer uptake could be used as a biomarker of treatment response. Reconstruction algorithms and settings have a significant impact on PET quantification. In this work we introduce a novel harmonization methodology requiring only a simple cylindrical phantom and show that it can match the performance of more complex harmonization approaches based on phantoms with spherical inserts. Resolution and noise measurements from cylindrical phantoms are used to simulate the spherical inserts from NEMA image quality phantoms. An optimization algorithm was used to find the optimal smoothing filters for the simulated NEMA phantom images to identify those that best harmonized the PET scanners. Our methodology was tested on seven different PET models from two manufacturers installed at five institutions. Our methodology is able to predict contrast recovery coefficients (CRCs) from NEMA phantoms with errors within  ±5.2% for CRCmax and  ±3.7% for CRCmean (limits of agreement  =  95%). After applying the proposed harmonization protocol, all the CRC values were within the tolerances from EANM. Quantitative harmonization in compliance with the EARL FDG-PET/CT accreditation program is achieved in a simpler way, without the need of NEMA phantoms. This may lead to simplified scanner harmonization workflows more accessible to smaller institutions.

Effect of Transport Coefficients on Excitation of Flare-induced Standing Slow-mode Waves in Coronal Loops

NASA Astrophysics Data System (ADS)

Wang, Tongjiang; Ofman, Leon; Sun, Xudong; Solanki, Sami K.; Davila, Joseph M.

2018-06-01

Standing slow-mode waves have been recently observed in flaring loops by the Atmospheric Imaging Assembly of the Solar Dynamics Observatory. By means of the coronal seismology technique, transport coefficients in hot (∼10 MK) plasma were determined by Wang et al., revealing that thermal conductivity is nearly suppressed and compressive viscosity is enhanced by more than an order of magnitude. In this study, we use 1D nonlinear MHD simulations to validate the predicted results from the linear theory and investigate the standing slow-mode wave excitation mechanism. We first explore the wave trigger based on the magnetic field extrapolation and flare emission features. Using a flow pulse driven at one footpoint, we simulate the wave excitation in two types of loop models: Model 1 with the classical transport coefficients and Model 2 with the seismology-determined transport coefficients. We find that Model 2 can form the standing wave pattern (within about one period) from initial propagating disturbances much faster than Model 1, in better agreement with the observations. Simulations of the harmonic waves and the Fourier decomposition analysis show that the scaling law between damping time (τ) and wave period (P) follows τ ∝ P 2 in Model 2, while τ ∝ P in Model 1. This indicates that the largely enhanced viscosity efficiently increases the dissipation of higher harmonic components, favoring the quick formation of the fundamental standing mode. Our study suggests that observational constraints on the transport coefficients are important in understanding both the wave excitation and damping mechanisms.

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.

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

NASA Astrophysics Data System (ADS)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

Characterization of second and third order optical nonlinearities of ZnO sputtered films

NASA Astrophysics Data System (ADS)

Larciprete, M. C.; Haertle, D.; Belardini, A.; Bertolotti, M.; Sarto, F.; Günter, P.

2006-03-01

We measured the second and third order optical nonlinearity of zinc oxide, grown on glass substrates by the ion beam sputtering technique. Second and third harmonic generation measurements were performed by means of the rotational Maker fringes technique for different polarization configurations, thus allowing the determination of all non-zero components of the second order susceptibility at three different fundamental beam wavelengths, i.e., 1064 nm, 1542 nm and 1907 nm. The dispersion of the nonlinear optical coefficients has been evaluated, while the nonlinear optical coefficients were found to range between 0.9 pm/V and 0.16 pm/V for d33, 0.53 pm/V and 0.08 pm/V for |d15|, 0.31 and 0.08 pm/V for |d31|, with increasing wavelength. Finally, one third order susceptibility, χijkl (3), has been determined by third harmonic generation measurements at a fundamental wavelength λ=1907 nm and a value for χ3333 (3) of 185×10-20 m2/V2 has been found.

Determining the strengths of HCP slip systems using harmonic analyses of lattice strain distributions

DOE PAGES

Dawson, Paul R.; Boyce, Donald E.; Park, Jun-Sang; ...

2017-10-15

A robust methodology is presented to extract slip system strengths from lattice strain distributions for polycrystalline samples obtained from high-energy x-ray diffraction (HEXD) experiments with in situ loading. The methodology consists of matching the evolution of coefficients of a harmonic expansion of the distributions from simulation to the coefficients derived from measurements. Simulation results are generated via finite element simulations of virtual polycrystals that are subjected to the loading history applied in the HEXD experiments. Advantages of the methodology include: (1) its ability to utilize extensive data sets generated by HEXD experiments; (2) its ability to capture trends in distributionsmore » that may be noisy (both measured and simulated); and (3) its sensitivity to the ratios of the family strengths. The approach is used to evaluate the slip system strengths of Ti-6Al-4V using samples having relatively equiaxed grains. These strength estimates are compared to values in the literature.« less

Math modeling for helicopter simulation of low speed, low altitude and steeply descending flight

NASA Technical Reports Server (NTRS)

Sheridan, P. F.; Robinson, C.; Shaw, J.; White, F.

1982-01-01

A math model was formulated to represent some of the aerodynamic effects of low speed, low altitude, and steeply descending flight. The formulation is intended to be consistent with the single rotor real time simulation model at NASA Ames Research Center. The effect of low speed, low altitude flight on main rotor downwash was obtained by assuming a uniform plus first harmonic inflow model and then by using wind tunnel data in the form of hub loads to solve for the inflow coefficients. The result was a set of tables for steady and first harmonic inflow coefficients as functions of ground proximity, angle of attack, and airspeed. The aerodynamics associated with steep descending flight in the vortex ring state were modeled by replacing the steady induced downwash derived from momentum theory with an experimentally derived value and by including a thrust fluctuations effect due to vortex shedding. Tables of the induced downwash and the magnitude of the thrust fluctuations were created as functions of angle of attack and airspeed.

An investigation of adaptive controllers for helicopter vibration and the development of a new dual controller

NASA Technical Reports Server (NTRS)

Mookerjee, P.; Molusis, J. A.; Bar-Shalom, Y.

1985-01-01

An investigation of the properties important for the design of stochastic adaptive controllers for the higher harmonic control of helicopter vibration is presented. Three different model types are considered for the transfer relationship between the helicopter higher harmonic control input and the vibration output: (1) nonlinear; (2) linear with slow time varying coefficients; and (3) linear with constant coefficients. The stochastic controller formulations and solutions are presented for a dual, cautious, and deterministic controller for both linear and nonlinear transfer models. Extensive simulations are performed with the various models and controllers. It is shown that the cautious adaptive controller can sometimes result in unacceptable vibration control. A new second order dual controller is developed which is shown to modify the cautious adaptive controller by adding numerator and denominator correction terms to the cautious control algorithm. The new dual controller is simulated on a simple single-control vibration example and is found to achieve excellent vibration reduction and significantly improves upon the cautious controller.