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Semi-analytic perturbation equations for the influence of M2 and K1 ocean tidal constituents on satellite motion are expanded into multi-dimensional Fourier series and calculations made for the BE-C satellite. Perturbation in the orbital elements are compared to those of the long period solid earth tides.
Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 and GEOS-2 has yielded the values 0.22 and 0.31 respectively for the apparent second degree Love number. For GEOS-1 a new purely numerical method involving osculating elements was employed. For GEOS-2 it was necessary to analyze the variations of the mean elements because of the very long period (450 days) of the dominant solar tidal perturbation. The disparate values indicate that the simple second degree zonal harmonic model of the tidal potential is accommodating other effects in addition to those caused by the solid earth tides. A recent paper by Lambeck et al. (1973) indicates that ocean tide effects have significant perturbations on satellite orbits and cannot be neglected.
Nine separate very-long-baseline interferometry experiments, carried out in 1972 and 1973 with radio telescopes 3900 kilometers apart, yielded values for the baseline length with an rms deviation about the mean of less than 20 centimeters. The corresponding fractional spread is about five parts in 100,000,000. Changes in universal time and in polar motion were also determined accurately from these data. The rms scatter of these results with respect to those based on optical methods was 2.9 msec and 1.3 m, respectively. Solid-earth tides were apparently detected, but no useful estimate of their amplitude was extracted.
Very long baseline interferometry presents an opportunity to measure at the centimeter level such geodetic parameters as baseline length and instantaneous pole position. In order to achieve such precision, the geophysical and astronomical models used in data analysis must be as accurate as possible. The Mark-3 interactive data analysis system includes a number of refinements beyond conventional practice in modeling precession, nutation, diurnal polar motion, UT1, solid Earth tides, relativistic light deflection, and reduction to solar system barycentric coordinates. The algorithms and their effects on the recovered geodetic, geophysical, and astrometric parameters are discussed.
The theory of the Earth's rotation and the geophysical phenomena affecting it is examined. First principles are reviewed and the problem of polar motion and UT1 variations is formulated in considerable generality and detail. The effects of Earth deformations and the solid Earth tides are analyzed.
A series of experiments was conducted during the last decade to explore the capability of very long baseline interferometry (VLBI) to measure the crustal and rotational motions of the Earth with accuracies at the centimeter level. The observing stations are those of NASA's Deep Space Network in California, Spain and Australia. A multiparameter fit to the observed values of delay and delay rate yields radio source positions, polar motion, universal time, the precession constant, baseline vectors, and solid Earth tides. Source positions are obtained with formal errors of the order of 0''.01. UT1-UTC and polar motion are determined at 49 epochs, with formal error estimates for the more recent data of 0.5 msec for UT1-UTC and 2 to 6 mas for polar motion. Intercontinental baseline lengths are determined with formal errors of 5 to 10 cm. The Love numbers and Earth tide phase lag agree with the commonly accepted values.
Approximately 2400 observations of extragalactic radio sources were made between August 1971 and February 1980 during 48 separate sessions. These consisted of 259 delay rate observations at 2.3 GHz (S-band), 796 delay and delay rate observations at either S-band of 8.3 GHz (X-band) and 1325 delay and delay rate observations recorded simultaneously at both S- and X-band. A single multiparameter fit has been applied to the observed values of delay and delay rate to extract astrometric and geophysical parameters from this decade-long sequence. The fit produced estimates of 784 parameters, including station locations, radio source positions, polar motion, Universal Time, the precession constant, and solid earth tides. The a priori model included gravitational bending, the 1980 IAU nutation series, the 1976 IAU expressions for Greenwich mean sidereal time and precession, BIH estimates of Universal Time and polar motion, and monthly mean values for zenith troposphere delay. The rms residuals were 0.52 nsec for delay and 0.30 psec/sec for delay rate. Intercontinental baseline lengths were determined with formal uncertainties of 5 to 10 cm. Universal Time and polar motion were measured at 49 epochs, with formal uncertainties (for the more recent data) of 0.5 msec for UT1 and 6 and 2 mas, respectively, for the X and Y components of polar motion.
Short pulse multicolor laser ranging systems are currently being developed for satellite ranging applications. These systems use Q-switched pulsed lasers and streak tube cameras to provide timing accuracies approaching a few picoseconds. Satellite laser ranging systems was used to evaluate many important geophysical phenomena such as fault motion, polar motion and solid earth tides, by measuring the orbital perturbations of retroreflector equipped satellites. Some existing operational systems provide range resolution approaching a few millimeters. There is currently considerable interest in adapting these highly accurate systems for use as airborne and satellite based altimeters. Potential applications include the measurement of sea state, ground topography and atmospheric pressure. This paper reviews recent progress in the development of multicolor laser altimeters for use in monitoring sea state and atmospheric pressure.
Approximately 2400 observations of extragalactic radio sources were made between August 1971 and February 1980 during 48 separate sessions. These consisted of 259 delay rate observations at 2.3 GHz (S-band), 796 delay and delay rate observations at either S-band of 8.3 GHz (X-band) and 1325 delay and delay rate observations recorded simultaneously at both S- and X-band. A single multiparameter fit has been applied to the observed values of delay and delay rate to extract astrometric and geophysical parameters from this decade-long sequence. The fit produced estimates of 784 parameters, including station locations, radio source positions, polar motion, Universal Time, the precession constant, and solid earth tides. The a priori model included gravitational bending, the 1980 IAU nutation series, the 1976 IAU expressions for Greenwich mean sidereal time and precession, BIH estimates of Universal Time and polar motion, and monthly mean values for zenith troposphere delay. The rms residuals were 0.52 nsec for delay and 0.30 psec/sec for delay rate. Intercontinental baseline lengths were determined with formal uncertainties of 5 to 10 cm. Universal Time and polar motion were measured at 49 epochs, with formal uncertainties (for the more recent data) of 0.5 msec for UT1 and 6 and 2 mas, respectively, for the X and Y components of polar motion. Previously announced in STAR as N83-28038
A summary of the results obtained for a new comprehensive geodetic parameter solution from the analysis of Lageos laser ranging data for the period May 1976 to the end of 1982 is presented. Estimates of each component of the polar motion and earth rotation, the station coordinates, the value of the earth's gravitational constant GM, and the elements of the Lageos orbit comprise this SL5.1AP solution. The results differ from previously published values primarily through incorporation of more rigorous dynamic models for the ocean and solid earth tides. The precision of the geodetic parameters are on average 5-marc sec polar motion, 0.2-ms length of day, better than 5-cm center-of-mass geodetic positioning, 3-cm global baselines, and 2-cm regional baselines. An assessment of the contribution of systematic errors in the interstation distance determination is presented.
Short-pulse multicolor laser ranging systems are currently being developed for satellite ranging applications. These systems use Q-switched pulsed lasers and streak-tube cameras to provide timing accuracies approaching a few picoseconds. Satellite laser ranging systems have been used to evaluate many important geophysical phenomena such as fault motion, polar motion and solid earth tides, by measuring the orbital perturbations of retroreflector equipped satellites. Some existing operational systems provide range resolution approaching a few millimeters. There is currently considerable interest in adapting these highly accurate systems for use as airborne and satellite based altimeters. Potential applications include the measurement of sea state, ground topography and atmospheric pressure. This paper reviews recent progress in the development of multicolor laser altimeters for use in monitoring sea state and atmospheric pressure.
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.
A revision is presented of MASTERFIT-1987, which it supersedes. Changes during 1988 to 1991 included introduction of the octupole component of solid Earth tides, the NUVEL tectonic motion model, partial derivatives for the precession constant and source position rates, the option to correct for source structure, a refined model for antenna offsets, modeling the unique antenna at Richmond, FL, improved nutation series due to Zhu, Groten, and Reigber, and reintroduction of the old (Woolard) nutation series for simulation purposes. Text describing the relativistic transformations and gravitational contributions to the delay model was also revised in order to reflect the computer code more faithfully.
Continual refinement of models and estimation methods is an integral part of improving VLBI measurements of Earth orientation and position along with advances in instrumentation and observing strategy. The modeling of the troposphere continues to be challenging with recent improvements in treating the mean gradient and gradient variations affecting the terrestrial reference frame scale and celestial declinations near the current limits of accuracy. Revised models of nutation and solid Earth tides are implemented in CALC 9.0 to conform to the latest IERS Conventions along with other changes to facilitate use by VLBI correlators. Using data since 1995 the celestial reference frame has been extended and improved consistent with the definition and 0.25 mas accuracy limit of the ICRF. The current definition of the VLBI terrestrial reference frame places a floor on the accuracy of station velocities at the 0.4 mm/yr level. The establishment of the IVS (International VLBI Service for Geodesy and Astrometry) in the past year will provide a forum for further improvements of VLBI data analysis.
The few millimeter per year level accuracy of radial global velocity estimates with the Global Positioning System (GPS) is at least an order of magnitude poorer than the accuracy of horizontal global motions. An improvement in the accuracy of radial global velocities would have a very positive impact on a number of geophysical studies of current general interest such as global sea-level and climate change, coastal hazards, glacial isostatic adjustment, atmospheric and oceanic loading, glaciology and ice mass variability, tectonic deformation and volcanic inflation, and geoid variability. The goal of this project is to improve our current understanding of GPS error sources associated with estimates of radial velocities at global scales. GPS error sources relevant to this project can be classified in two broad categories: (1) those related to the analysis of the GPS phase observable, and (2) those related to the combination of the positions and velocities of a set of globally distributed stations as determined from the analysis of GPS data important aspect in the first category include the effect on vertical rate estimates due to standard analysis choices, such as orbit modeling, network geometry, ambiguity resolution, as well as errors in models (or simply the lack of models) for clocks, multipath, phase-center variations, atmosphere, and solid-Earth tides. The second category includes the possible methods of combining and defining terrestrial reference flames for determining vertical velocities in a global scale. The latter has been the subject of our research activities during this reporting period.
Long-period tidal variations of the Earth's rotation rate are caused by the redistribution of mass associated with the respective elastic solid Earth tides, the ocean tide heights, and the anelasticity of the Earth's mantle, and by the relative angular momentum associated with the long-period ocean tide currents.
Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness
Since 2008 the VLBI group at the Institute of Geodesy and Geophysics at TU Vienna has focused on the development of a new VLBI data analysis software called VieVS (Vienna VLBI Software). One part of the program, currently under development, is a unit for parameter estimation in so-called global solutions, where the connection of the single sessions is done by stacking at the normal equation level. We can determine time independent geodynamical parameters such as Love and Shida numbers of the solid Earth tides. Apart from the estimation of the constant nominal values of Love and Shida numbers for the second degree of the tidal potential, it is possible to determine frequency dependent values in the diurnal band together with the resonance frequency of Free Core Nutation. In this paper we show first results obtained from the 24-hour IVS R1 and R4 sessions.