The impact of tidal errors on the determination of the Lense-Thirring effect from satellite laser ranging

The general relativistic Lense-Thirring effect can be detected by means of a suitable combination of orbital residuals of the laser-ranged LAGEOS and LAGEOS II satellites. While this observable is not affected by the orbital perturbation induced by the zonal Earth solid and ocean tides, it is sensitive to those generated by the tesseral and sectorial tides. The assessment of their influence on the measurement of the parameter mu, with which the gravitomagnetic effect is accounted for, is the goal of this paper. After simulating the combined residual curve by calculating accurately the mismodeling of the more effective tidal perturbations, it has been found that, while the solid tides affect the recovery of mu at a level always well below 1%, for the ocean tides and the other long-period signals Delta mu depends strongly on the observational period and the noise level: Delta mu(tides) amounts to almost 2% after 7 years. The aliasing effect of K1 l=3 p=1 tide and SRP(4241) solar radiation pressure harmonic, with periods longer than 4 years, on the perigee of LAGEOS II yield to a maximum systematic uncertainty on \m_{LT} of less than 4% over different observational periods. The zonal 18.6-year tide does not affect the combined residuals.Comment: 24 pages, 4 tables, 6 figures, submitted to Int. Journal of Mod. Phys. D. Changes in auctorship, references and conten

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the GEM-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient by coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment

Measuring the relativistic perigee advance with Satellite Laser Ranging

One of the most famous classical tests of General Relativity is the gravitoelectric secular advance of the pericenter of a test body in the gravitational field of a central mass. In this paper we explore the possibility of performing a measurement of the gravitoelectric pericenter advance in the gravitational field of the Earth by analyzing the laser-ranged data to some existing, or proposed, laser-ranged geodetic satellites. At the present level of knowledge of various error sources, the relative precision obtainable with the data from LAGEOS and LAGEOS II, suitably combined, is of the order of $10^{\rm -3}$. Nevertheless, these accuracies could sensibly be improved in the near future when the new data on the terrestrial gravitational field from the CHAMP and GRACE missions will be available. The use of the perigee of LARES (LAser RElativity Satellite), in the context of a suitable combination of orbital residuals including also LAGEOS II, should further raise the precision of the measurement. As a secondary outcome of the proposed experiment, with the so obtained value of \ppn and with \et=4\beta-\gamma-3 from Lunar Laser Ranging it could be possible to obtain an estimate of the PPN parameters $\gamma$ and $\beta$ at the $10^{-2}-10^{-3}$ level.Comment: LaTex2e, 14 pages, no figures, 2 tables. To appear in Classical and Quantum Gravit

Status of Precise Orbit Determination for Jason-2 Using GPS

The JASON-2 satellite, launched in June 2008, is the latest follow-on to the successful TOPEX/Poseidon (T/P) and JASON-I altimetry missions. JASON-2 is equipped with a TRSR Blackjack GPS dual-frequency receiver, a laser retroreflector array, and a DORIS receiver for precise orbit determination (POD). The most recent time series of orbits computed at NASA GSFC, based on SLR/DORIS data have been completed using both ITRF2005 and ITRF2008. These orbits have been shown to agree radially at 1 cm RMS for dynamic vs SLRlDORIS reduced-dynamic orbits and in comparison with orbits produced by other analysis centers (Lemoine et al., 2010; Zelensky et al., 2010; Cerri et al., 2010). We have recently upgraded the GEODYN software to implement model improvements for GPS processing. We describe the implementation of IGS standards to the Jason2 GEODYN GPS processing, and other dynamical and measurement model improvements. Our GPS-only JASON-2 orbit accuracy is assessed using a number of tests including analysis of independent SLR and altimeter crossover residuals, orbit overlap differences, and direct comparison to orbits generated at GSFC using SLR and DORIS tracking, and to orbits generated externally at other centers. Tests based on SLR and the altimeter crossover residuals provide the best performance indicator for independent validation of the NASAlGSFC GPS-only reduced dynamic orbits. For the ITRF2005 and ITRF2008 implementation of our GPS-only obits we are using the IGS05 and IGS08 standards. Reduced dynamic versus dynamic orbit differences are used to characterize the remaining force model error and TRF instability. We evaluate the GPS vs SLR & DORIS orbits produced using the GEODYN software and assess in particular their consistency radially and the stability of the altimeter satellite reference frame in the Z direction for both ITRF2005 and ITRF2008 as a proxy to assess the consistency of the reference frame for altimeter satellite POD

Gravitational model improvement at the Goddard Space Flight Center

Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment

An improved model of the Earth's gravitational field: GEM-T1

Goddard Earth Model T1 (GEM-T1), which was developed from an analysis of direct satellite tracking observations, is the first in a new series of such models. GEM-T1 is complete to degree and order 36. It was developed using consistent reference parameters and extensive earth and ocean tidal models. It was simultaneously solved for gravitational and tidal terms, earth orientation parameters, and the orbital parameters of 580 individual satellite arcs. The solution used only satellite tracking data acquired on 17 different satellites and is predominantly based upon the precise laser data taken by third generation systems. In all, 800,000 observations were used. A major improvement in field accuracy was obtained. For marine geodetic applications, long wavelength geoidal modeling is twice as good as in earlier satellite-only GEM models. Orbit determination accuracy has also been substantially advanced over a wide range of satellites that have been tested

Coherence-based approaches for estimating the composition of the seismic wavefield

As new techniques exploiting the Earth's ambient seismic noise field are developed and applied, such as for the observation of temporal changes in seismic velocity structure, it is crucial to quantify the precision with which wave‐type measurements can be made. This work uses array data at the Homestake mine in Lead, South Dakota, and an array at Sweetwater, Texas, to consider two aspects that control this precision: the types of seismic wave contributing to the ambient noise field at microseism frequencies and the effect of array geometry. Both are quantified using measurements of wavefield coherence between stations in combination with Wiener filters. We find a strong seasonal change between body‐wave and surface‐wave content. Regarding the inclusion of underground stations, we quantify the lower limit to which the ambient noise field can be characterized and reproduced; the applications of the Wiener filters are about 4 times more successful in reproducing ambient noise waveforms when underground stations are included in the array, resulting in predictions of seismic time series with less than a 1% residual, and are ultimately limited by the geometry and aperture of the array, as well as by temporal variations in the seismic field. We discuss the implications of these results for the geophysics community performing ambient seismic noise studies, as well as for the cancellation of seismic Newtonian gravity noise in ground‐based, sub‐Hertz, gravitational‐wave detectors

LAGEOS geodetic analysis-SL7.1

Laser ranging measurements to the LAGEOS satellite from 1976 through 1989 are related via geodetic and orbital theories to a variety of geodetic and geodynamic parameters. The SL7.1 analyses are explained of this data set including the estimation process for geodetic parameters such as Earth's gravitational constant (GM), those describing the Earth's elasticity properties (Love numbers), and the temporally varying geodetic parameters such as Earth's orientation (polar motion and Delta UT1) and tracking site horizontal tectonic motions. Descriptions of the reference systems, tectonic models, and adopted geodetic constants are provided; these are the framework within which the SL7.1 solution takes place. Estimates of temporal variations in non-conservative force parameters are included in these SL7.1 analyses as well as parameters describing the orbital states at monthly epochs. This information is useful in further refining models used to describe close-Earth satellite behavior. Estimates of intersite motions and individual tracking site motions computed through the network adjustment scheme are given. Tabulations of tracking site eccentricities, data summaries, estimated monthly orbital and force model parameters, polar motion, Earth rotation, and tracking station coordinate results are also provided

The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96

The NASA Goddard Space Flight Center (GSFC), the National Imagery and Mapping Agency (NIMA), and The Ohio State University (OSU) have collaborated to develop an improved spherical harmonic model of the Earth's gravitational potential to degree 360. The new model, Earth Gravitational Model 1996 (EGM96), incorporates improved surface gravity data, altimeter-derived gravity anomalies from ERS-1 and from the GEOSAT Geodetic Mission (GM), extensive satellite tracking data-including new data from Satellite Laser Ranging (SLR), the Global Postioning System (GPS), NASA's Tracking and Data Relay Satellite System (TDRSS), the French DORIS system, and the US Navy TRANET Doppler tracking system-as well as direct altimeter ranges from TOPEX/POSEIDON (T/P), ERS-1, and GEOSAT. The final solution blends a low-degree combination model to degree 70, a block-diagonal solution from degree 71 to 359, and a quadrature solution at degree 360. The model was used to compute geoid undulations accurate to better than one meter (with the exception of areas void of dense and accurate surface gravity data) and realize WGS84 as a true three-dimensional reference system. Additional results from the EGM96 solution include models of the dynamic ocean topography to degree 20 from T/P and ERS-1 together, and GEOSAT separately, and improved orbit determination for Earth-orbiting satellites