Phase delay of the solid earth tide
Phase delay of solid earth tide, minimizing ocean and atmosphere loading by strain seismograph measurement
Jungels, P.↗
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Geodesy by radio interferometry - Determinations of baseline vector, earth rotation, and solid earth tide parameters with the Mark I very long baseline radio interferometery system
Thirty-seven very long baseline radio interferometry experiments performed between 1972 and 1978 are analyzed and estimates of baseline vectors between six sites, five in the continental United States and one in Europe are derived. No evidence of significant changes in baseline length is found. For example, with a statistical level of confidence of approximately 85 percent, upper bounds on such changes within the United States ranged from a low of 10 mm/yr for the 850 km baseline between Westford, Massachusetts, and Green Bank, West Virginia, to a high of 90 mm/yr for the nearly 4000 km baseline between Westford and Goldstone, California. Estimates for universal time and for the x component of the position of the earth's pole are obtained. For the last 15 experiments, the only ones employing wideband receivers, the root-mean-square differences between the derived values and the corresponding ones published by the Bureau International de l'Heure are 0.0012 s and 0.018 arc sec respectively. The average value obtained for the radial Love number for the solid earth is 0.62 + or - 0.02 (estimated standard error).
Ryan, J. W.↗
Solid Earth Tide Modeling in VLBI
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Very Long Baseline Interferometry (VLBI) IERS Wahr↗
Tidal perturbations on the satellite 1967-92A
The orbit of the 1967-92A satellite was studied to ascertain the extent to which tidal forces contribute to orbital perturbations. Parameters describing the ocean tide potential-in particular for the M2 and S2 constituents-were estimated. Since the ocean tide potential is less well known than the solid Earth tide, the ocean tide parameter estimation is based upon the use of a value of 0.3 for the solid Earth tide Love number in the orbit determination procedure. These tidal parameter values are in good agreement with those appearing in numerical models of the M2 and S2 tides derived from surface data.
Felsentreger, T. L.↗
Long Term Mean Local Time of the Ascending Node Prediction
Significant error has been observed in the long term prediction of the Mean Local Time of the Ascending Node on the Aqua spacecraft. This error of approximately 90 seconds over a two year prediction is a complication in planning and timing of maneuvers for all members of the Earth Observing System Afternoon Constellation, which use Aqua's MLTAN as the reference for their inclination maneuvers. It was determined that the source of the prediction error was the lack of a solid Earth tide model in the operational force models. The Love Model of the solid Earth tide potential was used to derive analytic corrections to the inclination and right ascension of the ascending node of Aqua's Sun-synchronous orbit. Additionally, it was determined that the resonance between the Sun and orbit plane of the Sun-synchronous orbit is the primary driver of this error. The analytic corrections have been added to the operational force models for the Aqua spacecraft reducing the two-year 90-second error to less than 7 seconds.
McKinley, David P.↗
The Algorithm Theoretical Basis Document for Tidal Corrections
This Algorithm Theoretical Basis Document deals with the tidal corrections that need to be applied to range measurements made by the Geoscience Laser Altimeter System (GLAS). These corrections result from the action of ocean tides and Earth tides which lead to deviations from an equilibrium surface. Since the effect of tides is dependent of the time of measurement, it is necessary to remove the instantaneous tide components when processing altimeter data, so that all measurements are made to the equilibrium surface. The three main tide components to consider are the ocean tide, the solid-earth tide and the ocean loading tide. There are also long period ocean tides and the pole tide. The approximate magnitudes of these components are illustrated in Table 1, together with estimates of their uncertainties (i.e. the residual error after correction). All of these components are important for GLAS measurements over the ice sheets since centimeter-level accuracy for surface elevation change detection is required. The effect of each tidal component is to be removed by approximating their magnitude using tidal prediction models. Conversely, assimilation of GLAS measurements into tidal models will help to improve them, especially at high latitudes.
Fricker, Helen A.↗
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
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.
Parke, M. E.↗
M2, S2, K1 models of the global ocean tide
Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps 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 contituent are presented.
Parke, M. E.↗
Tidal perturbations on the satellite 1967-92A
The orbit of the 1967-92A satellite has been studied to ascertain the extent to which tidal forces contribute to orbital perturbations. This study has permitted an estimation of the magnitudes of ocean tide effects on the satellite's inclination, in particular for the M sub 2 and S sub 2 constituents. The ocean tide estimates are based upon the use of a value of 0.3 for the solid earth tide Love number and a lag angle of zero deg in the orbit determination procedure. The amplitudes and phases of these tidal effects are in good agreement with those calculated from numerical models of the tidal parameters derived from surface data.
Felsentreger, T. L.↗
A determination of the earth tidal amplitude and phase from the orbital perturbations of the Beacon Explorer C spacecraft
An analysis of the orbital inclination of the Beacon Explorer C spacecraft over a period of nearly five months in 1970 revealed a very clear and distinctive perturbation caused by the earth and ocean tides. The perturbation has a full amplitude of about 1.8 seconds of arc and a period of about 85 days. This amplitude is approximately 15% smaller than would be expected from the solid-earth tide alone and is shifted slightly in phase. The perturbation can be represented almost exactly by a Love number of k sub 2 = 0.245 with a phase lag of 3.2 degrees. The data used were laser range measurements obtained by a NASA Goddard Space Flight Center tracking system in Greenbelt, Maryland.
Smith, D. E.↗
Observation model and parameter partials for the JPL VLBI parameter estimation software MODEST, 19 94
This report is a revision of the document Observation Model and Parameter Partials for the JPL VLBI Parameter Estimation Software 'MODEST'---1991, dated August 1, 1991. It supersedes that document and its four previous versions (1983, 1985, 1986, and 1987). A number of aspects of the very long baseline interferometry (VLBI) model were improved from 1991 to 1994. Treatment of tidal effects is extended to model the effects of ocean tides on universal time and polar motion (UTPM), including a default model for nearly diurnal and semidiurnal ocean tidal UTPM variations, and partial derivatives for all (solid and ocean) tidal UTPM amplitudes. The time-honored 'K(sub 1) correction' for solid earth tides has been extended to include analogous frequency-dependent response of five tidal components. Partials of ocean loading amplitudes are now supplied. The Zhu-Mathews-Oceans-Anisotropy (ZMOA) 1990-2 and Kinoshita-Souchay models of nutation are now two of the modeling choices to replace the increasingly inadequate 1980 International Astronomical Union (IAU) nutation series. A rudimentary model of antenna thermal expansion is provided. Two more troposphere mapping functions have been added to the repertoire. Finally, corrections among VLBI observations via the model of Treuhaft and lanyi improve modeling of the dynamic troposphere. A number of minor misprints in Rev. 4 have been corrected.
Sovers, O. J.↗
Preliminary study of the application of the Timation 3 satellite to earth physics
The Timation 3 is a timing and navigation satellite originally planned for launch in December 1972 into a circular orbit at 98 deg inclination 14,000 km altitude with gravity gradient stabilization. An error analysis indicates a satellite position uncertainty of about one meter, 80 percent of which is attributable to the assumed gravity model errors. The remaining uncertainties have a period equal to that of the satellites and can be filtered out yielding an effective uncertainty of about 10 cm in the study of phenomena having different periodicities. The accomplishment of these results depends on a careful consideration of solar radiation pressure taking account of the spacecraft reflecting properties and variations in the presentation area. Consideration is also given to the displacement of the laser reflectors from the center of mass of the spacecraft and to the dynamic coupling of any libration in attitude with the orbital motion. The results indicate that a good set of well distribution laser observations of Timation 3 could yield determinations of polar motion, sea floor spreading, solid earth tides, and earth rotation at the 10 cm level.
Carpenter, L.↗
Polar motion
Tracking of the Beacon Explorer-C satellite by a precision laser system was used to measure the polar motion and solid earth tide. The tidal perturbation of satellite latitude is plotted as variation in maximum latitude in seconds of arc on earth's surface as a function of the date, and polar motion is shown by plotting the variation in latitude of the laser in seconds of arc along the earth's surface as a function of date
Kolenkiewicz, R.↗
Geodetic studies by laser ranging to satellites.
For three months in 1970, two Goddard Space Flight Center (GSFC) laser tracking systems were used to try to detect the motion of the pole of rotation of the earth. More than two hundred passes of the Beacon Explorer C spacecraft were observed as it passed between the two stations, and these data were used to determine the orbital inclination of the spacecraft. The analysis required the accurate determination of the relative positions of the two tracking stations and the identification of the perturbations to the spacecraft orbit, in particular, those due to the gravitational fields of the earth, sun, and moon and those caused by the solid-earth tides. The results to date indicate that the GSFC laser systems can determine interstation distances with a repeatability of about 25 cm and that a new value of the Love number k that represents the distortion of the earth's gravity field caused by the tidal deformation of the earth is 0.35 plus or minus 0.05.
Smith, D. E.↗
Computations of M sub 2 and K sub 1 ocean tidal perturbations in satellite elements
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.
Estes, R. H.↗
Tidal parameters from the variation of inclination of GEOS-1 and GEOS-2
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.
Douglas, B. C.↗
Transcontinental baselines and the rotation of the earth measured by radio interferometry
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.
Shapiro, I. I.↗
Geophysical and astronomical models applied in the analysis of very long baseline interferometry
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.
Ma, C.↗