The absolute value of the geopotential

It is suggested that it would be worthwhile to determine the absolute value of the geopotential on the geopotential surface which corresponds to mean sea level. This number would replace the earth’s semi-major axis as the parameter which fixes the earth’s size; but slight variations in the parameter might be employed to study the dynamics of the sea. Fixing this number involves knowing the geopotential for a point on the orbit of a satellite whose true gravitational potential is also known.     

Modeling of earth’s gravity fields visualization based on Quad Tree

The problems of the earth’s gravity fields’ visualization are both focus and puzzle currently. Aiming at multiresolution rendering, modeling of the Earth’s gravity fields’ data is discussed in the paper by using LOD algorithm based on Quad Tree. First, this paper employed the method of LOD based on Quad Tree to divide up the regional gravity anomaly data, introduced the combined node evaluation system that was composed of viewpoint related and roughness related systems, and then eliminated the T-cracks that appeared among the gravity anomaly data grids with different resolutions. The test results demonstrated that the gravity anomaly data grids’ rendering effects were living, and the computational power was low. Therefore, the proposed algorithm was a suitable method for modeling the gravity anomaly data and has potential applications in visualization of the earth’s gravity fields.     

Solution of the geodetic boundary value problem

Summary The possibility of improving the convergence of Molodensky’s series is considered. Then new formulas are derived for the solution of the geodetic boundary value problem. One of them presents an expression for the boundary condition which involves a linear combination of Stokes’ constants and surface gravity anomalies. This differs from the usually used relation by the appearance of additional terms dependent on second order terns with respect to the elevations of the earth’s surface. The formulas are derived for Stokes’ constants and the anomalous potential in terms of surface anomalies. As compared to the Taylor’s series of Molodensky, they are presented in the form of surface harmonic series. Due regard is made to the earth’s oblateness, in addition to the terrain topography.     

Upward and downward continuations in the geopotential determination

Summary The geopotential on and outside the earth is represented as a series in surface harmonics. The principal terms in it correspond to the solid harmonics of the external potential expansion with the coefficients being Stokes’ constantsC _nm andS _nm . The additional terms which occur near the earth’s surface due to its non-sphericity and topography are expressed in terms of Stokes’ constants too. This allows performing downward continuation of the potential derived from satellite observations. In the boundary condition which correlates Stokes’ constants and the surface gravity anomalies there occur additional terms due to the earth’s non-sphericity and topography. They are expressed in terms of Stokes’ constants as well. This improved boundary condition can be used for upward and downward continuations of the gravity field. Simple expressions are found representingC _nm andS _nm as explicit functions of the surface anomalies and its derivatives. The formula for the disturbing potential on the surface is derived in terms of the surface anomalies. All the formulas do not involve the earth’s surface in clinations.     

The impact of errors in polar motion and nutation on UT1 determinations from VLBI Intensive observations

The earth’s phase of rotation, expressed as Universal Time UT1, is the most variable component of the earth’s rotation. Continuous monitoring of this quantity is realised through daily single-baseline VLBI observations which are interleaved with VLBI network observations. The accuracy of these single-baseline observations is established mainly through statistically determined standard deviations of the adjustment process although the results of these measurements are prone to systematic errors. The two major effects are caused by inaccuracies in the polar motion and nutation angles introduced as a priori values which propagate into the UT1 results. In this paper, we analyse the transfer of these components into UT1 depending on the two VLBI baselines being used for short duration UT1 monitoring. We develop transfer functions of the errors in polar motion and nutation into the UT1 estimates. Maximum values reach 30 [μs per milliarcsecond] which is quite large considering that observations of nutation offsets w.r.t. the state-of-the-art nutation model show deviations of as much as one milliarcsecond.     

1949．0至1979．0 ILS地极坐标的均匀化

自１９８４年起在天文计算中都采用ＦＫ５基本星表和新天文常数,这些变动直接影响了用天顶仪等光学仪器观测订定的地极坐标。本文论述了基本星表和天文常数变动后,对国际纬度服务（ＩＬＳ）订定的地极坐标的影响。结果表明：１）星表系统差对地极坐标的影响在ｘ和ｙ方向最大,分别约－０．００６”和－０．００４”;２）章动序列变动的影响在ｘ、ｙ方向最大波动分别为０．０１２”和０．０１０”。     

The secular variantion of longitudes and plate tectonic motion

Summary According to the plate tectonic theory of Le Pichon [1968] we summarized the absolute values of the angular rate of rotation of the Eurasia and America plates determined by astronomical latitude observations. The authors then tried to use the data of longitude observation so far available to emphasize the existence of similar crust movements. The analysis of longitude data has shown the minor homogeneity of these astronomical observations especially as far as the observations obtained by means of PZT are concerned. By using particularly accurate observational data [Torao & Okasahi, 1965, 1969] the data of longitude variations confirm the existence of movements in the earth’s crust, exactly equal to those deduced by the analysis of latitude observations and in agreement with the results of geophysical measurements.     

Methods for the computation of geoid undulations from potential coefficients

The undulations of the geoid may be computed from spherical harmonic potential coefficients of the earth’s gravitational field. This paper examines three procedures that reflect various points of view on how this computation should be carried out. One method requires only the flattening of a reference ellipsoid to be defined while the other two methods require a complete definition of the parameters of the ellipsoid. It was found that the various methods give essentially the same undulations provided that correct parameters are chosen for the reference ellipsoid. A discussion is given on how these parameters are chosen and numerical results are reported using recent potential coefficient determinations.     

An analytical method to transform geocentric into geodetic coordinates

A closed-form analytical method needing no approximation and deduced from a single quartic equation is offered to transform geocentric into geodetic coordinates. It is valid at any point inside and outside the Earth including the polar axis, the equatorial plane and the Earth’s center. Comparison with the method of extrema with constraints to obtain this quartic equation is made.     

The corridor correction concept

Atmospheric delays are contributors to the GNSS error budget in precise GNSS positioning that can reduce positioning accuracy considerably if not compensated appropriately. Both ionospheric and tropospheric delay corrections can be determined with help of reference stations in active GNSS networks. One approach to interpolate these error terms to the user’s location that is employed in Germany’s SAPOS network is the determination of area correction parameters (ACP, German: “Fl?chenkorrekturparameter—FKP”). A 2D interpolation scheme using data from at least 3 reference stations surrounding the rover is employed. A modification of this method was developed which only makes use of as few as 2 reference stations and provides 1D linear correction parameters along a “corridor” in which the user’s rover is moving. We present the results of a feasibility study portraying results from use of corridor correction parameters for precise RTK-like positioning. The differences to the reference coordinates (3D) attained in average for 1 h of data employing selected network nodes in Germany are between 0.8 and 2.0 cm, which compares well with the traditional area correction method that yields an error of 0.7 up to 1.1 cm.