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1.
Summary Four parameters defining the Earth's tri-axial ellipsoid (E) have been derived on the basis of the condition that the gravity potential on E be constant and equal to the actual geopotential value (W0) on the geoid. The geocentric gravitational constant, the angular velocity of the Earth's rotation, the actual 2nd degree geopotential Stokes parameters and W0 are taken to be the primary geodetic constants defining E and its (normal) gravity field.  相似文献   

2.
The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U 0 ) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U 0 should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U 0 , can be adopted as reference for realizing the Major Vertical Datum.  相似文献   

3.
The topic of the Earth's reference body, which has now been established as Pizzetti's level rotational ellipsoid, is analysed. Such a body is fully determined by four parameters: a, GM, J 2 and . At present, the largest discrepancy in determining these parameters occurs in the value of a, which may in future be replaced by the gravity potential of the mean sea level W o, with respect to Brovar's condition.Pizzetti's four parameters of the reference body are determined by solving the Dirichlet boundary value problem. The Dirichlet problem has only a unique solution, which, however, can be expressed in infinitely many ways. It turns out that the most important part in the form of the solution is played by Lamé's conditions, which determine the type of ellipsoidal coordinates.The solutions given by Pizzetti, Molodensky and another variant are considered. The last variant leads to a simple formula for the potential of the reference ellipsoid, but the formulae for Lamé's coefficients are inconvenient. Of course, all the methods lead to identical solutions, but some of them are more convenient for the historical use of logarithms, whereas others are more appropriate for use in computers.  相似文献   

4.
Summary A relation is established between coefficients of an expansion of the gravitational potential into a series of Legendre's function of the second kind and coefficients of an expansion of gravity anomalies on the surface of the reference ellipsoid into a series of the same functions. This connection can be useful in geodetic computations which take into account the Earth's flattening.  相似文献   

5.
Summary Using the geocentric constant GM=398 601.3 × 10 9 m 3s –2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J n (k) and S n (k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid Wo, the scale factor for lengths Ro=GM/Wo, the radius-vector of the surface W=Wo, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.  相似文献   

6.
论述了物理大地测量与地球物理中分别对应的正常重力场源的构成、物理与几何上的意义以及对两者之间的差别进行了论述 ,分析了同源性研究在物理大地测量与地球物理相互结合以及定量描述地球内部密度分布的过程中的重要意义 .给出了同源性分析可遵循的途径及其所应满足的条件与约束 .最后 ,以正常椭球的扁率变化率具有最小模为约束 ,应用PREM模型 （PreliminaryReferenceEarthModel）密度为大地测量中正常椭球赋值 ,其结果以正常椭球的内部扁率的多项式表达式给出 .  相似文献   

7.
The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W 0 and the geopotential scale factor R 0 = GM÷W 0 (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W 0 = (62 636 856.161 ± 0.002) m2s-2, R 0 = (6 363 672.5448 ± 0.0002) m. The actual accuracy is limited by the altimeter calibration error (2–3 cm) and it is conservatively estimated to be about ± 0.5 m2s-2 (± 5 cm). The differences between the yearly mean sea surface (MSS) levels came out as follows: 1993–1994: –(1.2 ± 0.7) mm, 1994–1995: (0.5 ± 0.7) mm, 1995–1996: (0.5 ± 0.7) mm, 1996–1997: (0.1 ± 0.7) mm, 1997–1998: –(0.5 ± 0.7) mm, 1998–1999: (0.0 ± 0.7) mm and 1999–2000: (0.6 ± 0.7) mm. The corresponding rate of change in the MSS level (or R 0) during the whole period of 1993–2000 is (0.02 ± 0.07) mm÷y. The value W 0 was found to be quite stable, it depends only on the adopted GM, and the volume enclosed by surface W = W 0. W 0 can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W 0 is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W 0 provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W 0, the semi-major axis a of the Earth's general ellipsoid can easily be derived. However, an a priori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W 0 in the least squares sense and an ellipsoid which has the global geopotential average equal to W 0. It is demonstrated that both a-values are practically equal to the value obtained by the Pizzetti's theory of the level ellipsoid: a = (6 378 136.7 ± 0.05) m.  相似文献   

8.
The geoidal geopotential value of W 0 = 62 636 856.0 ± 0.5m 2 s –2 , determined from the 1993 –1998 TOPEX/POSEIDON altimeter data, can be used to practically define and realize the World Height System. The W 0 -value can also uniquely define the geoidal surface and is required for a number of applications, including General Relativity in precise time keeping and time definitions. Furthermore, the W 0 -value provides a scale parameter for the Earth that is independent of the tidal reference system. All of the above qualities make the geoidal potential W 0 ideally suited for official adoption as one of the fundamental constants, replacing the currently adopted semi-major axis a of the mean Earth ellipsoid. Vertical shifts of the Local Vertical Datum (LVD) origins can easily be determined with respect to the World Height System (defined by W 0 ), in using the recent EGM96 gravity model and ellipsoidal height observations (e.g. GPS) at levelling points. Using this methodology the LVD vertical displacements for the NAVD88 (North American Vertical Datum 88), NAP (Normaal Amsterdams Peil), AMD (Australian Height Datum), KHD (Kronstadt Height Datum), and N60 (Finnish Height Datum) were determined with respect to the proposed World Height System as follows: –55.1 cm, –11.0 cm, +42.4 cm, –11.1 cm and +1.8 cm, respectively.  相似文献   

9.
Temporal variations in the nine elements of the Earth's inertia ellipsoid due to sea surface topography dynamics were derived from TOPEX/POSEIDON altimeter data 1993 - 1996. The variations amount to about 10 mm in the position of the center of the Earth's inertia ellipsoid (E i ), 0.15' in the polar axis direction of E i and to about 0.0003 in the denominator of its polar flattening. The approach used is based on the temporal variations of distortions computed by means of the geopotential model EGM96 which is used as reference.  相似文献   

10.
Satellite orbital data yield reliable values of low degree and order coefficients in the spherical harmonic expansion of the Earth's gravity field. The second degree coefficient yields the shape of the Earth — probably the most important single parameter in geodesy. It is crucial in the numerical evaluation of different forms of the theoretical gravity formula. The new information requires the standardization of gravity anomalies obtained from satellite gravity and terrestrial gravity data in the context of three most commonly used reference figures, e.g.,International Reference Ellipsoid, Reference Ellipsoid 1967, andEquilibrium Reference Ellipsoid. This standardization is important in the comparison and combination of satellite gravity and gravimetric data as well as the integration of surface gravity data, collected with different objectives, in a single reference system.Examination of the nature of satellite gravity anomalies aids in the geophysical and geodetic interpretation of these anomalies in terms of the tectonic features of the Earth and the structure of the Earth's crust and mantle. Satellite results also make it possible to compute the Potsdam correction and Earth's equatorial radius from the satellite-determined geopotential. They enable the decomposition of the total observed gravity anomaly into components of geophysical interest. They also make it possible to study the temporal variations of the geogravity field. In addition, satellite results make significant contributions in the prediction of gravity in unsurveyed areas, as well as in providing a check on marine gravity profiles.On leave from University of Hawaii, Honolulu.  相似文献   

11.
Summary Adopting thePizzetti-Somigliana method and using elliptic integrals we have obtained closed formulas for the space gravity field in which one of the equipotential surfaces is a triaxial ellipsoid. The same formulas are also obtained in first approximation of the equatorial flattening avoiding the use of the elliptic integrals. Using data from satellites and Earth gravity data the gravitational and geometric bulge of the Earth's equator are computed. On the basis of these results and on the basis of recent gravity data taken around the equator between the longitudes 50° to 100° E, 155° to 180° E, and 145° to 180° W, we question the advantage of using a triaxial gravity formula and a triaxial ellipsoid in geodesy. Closed formulas for the space field in which a biaxial ellipsoid is an equipotential surface are also derived in polar coordinates and its parameters are specialized to give the international gravity formula values on the international ellipsoid. The possibility to compute the Earth's dimensions from the present Earth gravity data is the discussed and the value ofMG=(3.98603×1020 cm3 sec–2) (M mass of the Earth,G gravitational constant) is computed. The agreement of this value with others computed from the mean distance Earth-Moon is discussed. The Legendre polinomials series expansion of the gravitational potential is also added. In this series the coefficients of the polinomials are closed formulas in terms of the flattening andMG.Publication Number 327, and Istituto di Geodesia e Geofisica of Università di Trieste.  相似文献   

12.
Towards the end of the 19th century, geodetic observation techniques allowed it to create geodetic networks of continental size. The insight that big networks can only be set up through international collaboration led to the establishment of an international collaboration called “Central European Arc Measurement”, the predecessor of the International Association of Geodesy (IAG), in 1864. The scope of IAG activities was extended already in the 19th century to include gravity.At the same time, astrometric observations could be made with an accuracy of a few tenths of an arcsecond. The accuracy stayed roughly on this level, till the space age opened the door for milliarcsecond (mas) astrometry. Astrometric observations allowed it at the end of the 19th century to prove the existence of polar motion. The insight that polar motion is almost unpredictable led to the establishment of the International Latitude Service (ILS) in 1899.The IAG and the ILS were the tools (a) to establish and maintain the terrestrial and the celestial reference systems, including the transformation parameters between the two systems, and (b) to determine the Earth's gravity field.Satellite-geodetic techniques and astrometric radio-interferometric techniques revolutionized geodesy in the second half of the 20th century. Satellite Laser Ranging (SLR) and methods based on the interferometric exploitation of microwave signals (stemming from Quasars and/or from satellites) allow it to realize the celestial reference frame with (sub-)mas accuracy, the global terrestrial reference frame with (sub-)cm accuracy, and to monitor the transformation between the systems with a high time resolution and (sub-)mas accuracy. This development led to the replacement of the ILS through the IERS, the International Earth Rotation Service in 1989.In the pre-space era, the Earth's gravity field could “only” be established by terrestrial methods. The determination of the Earth's gravitational field was revolutionized twice in the space era, first by observing geodetic satellites with optical, Laser, and Doppler techniques, secondly by implementing a continuous tracking with spaceborne GPS receivers in connection with satellite gradiometry. The sequence of the satellite gravity missions CHAMP, GRACE, and GOCE allow it to name the first decade of the 21st century the “decade of gravity field determination”.The techniques to establish and monitor the geometric and gravimetric reference frames are about to reach a mature state and will be the prevailing geodetic tools of the following decades. It is our duty to work in the spirit of our forefathers by creating similarly stable organizations within IAG with the declared goal to produce the geometric and gravimetric reference frames (including their time evolution) with the best available techniques and to make accurate and consistent products available to wider Earth sciences community as a basis for meaningful research in global change. IGGOS, the Integrated Global Geodetic Observing System, is IAG's attempt to achieve these goals. It is based on the well-functioning and well-established network of IAG services.  相似文献   

13.
The geopotential value of W 0 = (62 636 855.611 ± 0.008) m 2 s –2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W 0 to about (0.2 - 0.5) m 2 s –2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m 2 s –2 (±2.5 mm).  相似文献   

14.
本文研究由内核超速旋转引起的地球重力场的变化.论述了内核具有三个主要特征：椭球形状,各向异性对称轴与内核自转轴重合,内核自转轴与地球自转轴之间存在夹角并绕地球自转轴进动.内核超速旋转引起地球体系物质的重新分布,导致重力场变化.通过研究内核超速旋转的运动规律,建立了内核超速旋转导致重力场变化的模型,给出了由于内核超速旋转而引起的整个地球表面的重力变化,其中,在假定了内核超速旋转速率为1°/a的前提下,历经一年的最大重力变化量级约为037 μGal.  相似文献   

15.
Summary For precise geodetic computations over larger distances the reference surface of an ellipsoid of rotation should be used. However it is often replaced by a sphere of an adequate radius. The formulae are derived from figures which usually represent the conditions in a cross-section of the ellipsoid and the reference sphere through the normal plane. Equation (9) is given for the differences s of the length of the ellipse arc of the normal section and the corresponding arc of the circle with radius R. Also Eq. (19) is given for the distance d between the ellipse of the normal section and the circle (at the end point). Both equations are applied for various radii of the reference sphere. Table 1 shows the values s, Tab. 2 and Fig. 2 give the d-values for chosen lengths. It was found that especially the distance between the ellipsoid and the sphere need not always be negligible.  相似文献   

16.
So far the recent Earth's gravity model, EGM08, has been successfully applied for different geophysical and geodetic purposes. In this paper, we show that the computation of geoid and gravity anomaly on the reference ellipsoid is of essential importance but error propagation of EGM08 on this surface is not successful due to downward continuation of the errors. Also we illustrate that some artefacts appear in the computed geoid and gravity anomaly to lower degree and order than 2190. This means that the role of higher degree harmonics than 2160 is to remove these artefacts from the results. Consequently, EGM08 must be always used to degree and order 2190 to avoid the numerical problems.  相似文献   

17.
Summary Mean equatorial gravity has been computed from geopotential models GEM-10C, GEM-7, GEM-T1, GEM-T2, GEM-T3, JGM-1, JGM-2, JGM-3 and OSU91A and compared to the normal equatorial gravity, e=978 032·699 × 10–5 m s–2, computed from four given parameters defining the Earth's level ellipsoid. In all models ge>e.  相似文献   

18.
Résumé Ces remarques ont le but de compléter l'article antérieur; on trouve ici que les erreurs de l'inverse de l'aplatissement et de la pesanteur équatoriale, provenant de l'utilisation de moyennes des anomalies de la pesanteur dans le calcul de la pesanteur ellipsoïdique, n'excèdent pas 0.3 et 1.3 mgal respectivement. Il faut évaluer encore le reste du développement en série de fonctions sphériques de l'anomalie de la pesanteur régularisée et deux petites corrections qui résultent de la transition de la sphère de référence à la surface terrestre, pour obtenir les erreurs totales. La théorie du sphéroïde normal n'est pas plus simple que la théorie de l'ellipsoïde, et celle-ci est indispensable.
Summary These notes serve to complete the previous article; we find now that the inverse of the flattening and the equatorial gravity are affected with errors, owing to the utilisation of the mean gravity anomalies in the computation of the ellipsoidic gravity, that don't exceed 0.3 and 1.3 mgal. It is still necessary to appreciate the rest of the development in series of spherical functions of the regulated gravity anomaly and two small corrections, coming from the transition of the reference sphere to the Earth's surface, in order to compute the total errors. The theory of the ellipsoid is indispensable for the reduction of the bases and the angles in the geodetic nets and is as simple as the theory of the spheroid.

Cette Revue, Vol. XVI (1950). Fasc. 1–2, p. 7 et suiv.  相似文献   

19.
The Earth's gravity field can be determined from gravity measurements made on the surface of the Earth, and through the analysis of the motion of Earth satellites. Gravity data can be used to solve the boundary value problem of gravimetric geodesy in various ways, from the classical formulation using a geoid to the concept of a reference surface interior to the masses of the Earth to a statistical method. We now have gravity information for 10 data blocks over 46% of the Earth's surface and more than several million point measurements available.Satellite observations such as range, range-rate, and optical data have been analyzed to determine potential coefficients used to describe the Earth's gravitational potential field. Coefficients, in a spherical harmonic expansion to degree 12, can be determined from satellite data alone, and to at least degree 20 when the satellite data is combined with surface gravity material. Recent solutions for potential coefficients agree well to degree 4, but with increasing disagreement at higher degrees.  相似文献   

20.
武汉台重力潮汐长期观测结果   总被引：5，自引：1，他引：4       下载免费PDF全文
采用武汉台超导重力仪(SG C032)14年多的长期连续观测资料,研究了固体地球对二阶和三阶引潮力的响应特征,精密测定了重力潮汐参数,系统研究了最新的固体潮模型和海潮模型在中国大陆的有效性.采用最新的8个全球海潮模型计算了海潮负荷效应,从武汉台SG C032的观测中成功分离出63个2阶潮汐波群和15个3阶潮汐波群信号,3阶潮波涵盖了周日、半日和1/3日三个频段.重力潮汐观测的精度非常高,标准偏差达到1.116 nm·s-2,系统反映了非流体静力平衡、非弹性地球对2阶和3阶引潮力的响应特征.结果表明,现有的武汉国际重力潮汐基准在半日频段非常精确,但在周日频段存在比较明显的偏差,需要进一步精化.对于中国大陆的大地测量观测,固体潮可以采用Dehant等考虑地球内部介质非弹性和非流体静力平衡建立的固体潮理论模型或Xu 等基于全球SG观测建立的重力潮汐全球实验模型作为参考和改正模型,海潮负荷效应应该采用Nao99作为改正模型.  相似文献   

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