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1.
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   

2.
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   

3.
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   

4.
Résumé Il s'agit de la détermination de l'aplatissement de la Terre et de la pesanteur équatoriale en utilisant la définition de l'ellipsoïde de référence donnée par l'auteur dans une publication antérieure et les anomalies isostatiques moyennes calculées parL. Tanni. Les résultats obtenus, e =978.055, =1/296.3, sont sensiblement égaux à ceux qui proviennent de la méthode habituelle des moindres carrés; l'aplatissement calculé est compris entre les limites déduites parA. Véronnet de la précession terrestre.
Summary This article contains the numerical computation of the Earth's flattening and the equatorial gravity on the basis of the definition of the reference ellipsoid, given by the author in a former work, and the mean isostatic anomalies computed byL. Tanni. The results, e =978.055, =1/296.3, show that the method of least squares is accurate enough under the present conditions; the flattening computed is bounded by the values derived byA. Véronnet from the terrestrial precession.
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5.
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   

6.
From the point of view of consistency with the Geodetic Reference System 1967, it would be desirable that the boundary surface of a Standard Earth Model is an exact equipotential ellipsoid. This is incompatible with the requirement that it be a figure of hydrostatic equilibrium. The report investigates the relation between equipotential ellipsoids and equilibrium figures. The principal conclusion is that it is possible to find an ellipsoidal model that has the same distribution of density and flattening (more precisely, of the parameter f′ as defined in the paper) as a hydrostatic model, the deviations being only of second order in the flattening.  相似文献   

7.
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   

8.
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   

9.
The concept of the strain ellipsoid is applied to indicate a possible regular shear pattern of earthquake distribution over the Earth's surface. A simple model of the Earth is assumed in the form of a rotating sphere with a plastic interior and a thin, fragile, crust. On this basis rotation of the Earth generates an internal radial pressure at the equator equivalent to 1/300g causing a proportionate distortion of the spherical shell. The system is in dynamic equilibrium with an increase in gravity at the equator. The ellipsoid representing the distortion, has orthogonal principal axes corresponding to the principal strains while radial directions at 54°44 from the poles are unchanged in length and are thus possible axes of shear generating the same distortion. The Alpide region of earthquakes extending from Lisbon to Tokyo and restriction of earthquakes mainly to the broad band between latitudes 55°N or S are in support of the proposed view.Four unique sets of orthogonal shear systems have been identified which form a regular pattern with a definite symmetry with respect to the plane of the ecliptic. This suggests that the hoop stress at the Equator associated with Earth rotation may be triggered off by tidal forces and that earthquake prediction may well be possible. Other implications of this new approach are also discussed.  相似文献   

10.
Summary Simple expressions for the deformation of equipotential surfaces and changes of the deflections of the vertical are derived at points of the Earth's surface, which are due to the variations of the rotational component of the gravity potential under free nutation of the Earth's axis of rotation (pole wandering). The results of the solution of this problem given in[1] are discussed. The values of the tilts and the changes of geoid heights for extreme deviations of the poles are considered from the point of view of the effect on measuring tilts and on levelling. An elastically deformable Earth is assumed. It is concluded that reductions with respect to the mean Earth's pole are not realistic at the present degree of accuracy of levelling. The necessity to reduce long-term tilt observations, or the possibility of determining the time variations of the rotational axis from the analysis of these observations is pointed out.  相似文献   

11.
For more than a decade, the global network of GPS stations whose measurements are part of the International GPS Service (IGS) have been recording cyclic variations in the radius vector of the geodetic ellipsoid with a period of one year and amplitude of ~10 mm. The analysis of the figure of the Earth carried out by us shows that the observed variations in the vertical component of the Earth’s surface displacements can induce small changes in the flattening of the Earth’s figure which are, in turn, caused by the instability of the Earth’s rotation. The variations in the angular velocity and flattening of the Earth change the kinetic energy of the Earth’s rotation. The additional energy is ~1021 J. The emerging variations in the flattening of the Earth’s ellipsoid lead to changes in the surface area of the Earth’s figure, cause the development of deformations in rocks, accumulation of damage, activation of seismotectonic processes, and preparation of earthquakes. It is shown that earthquakes can be caused by the instability of the Earth’s rotation which induces pulsations in the shape of the Earth and leads to the development of alternating-sign deformations in the Earth’s solid shell.  相似文献   

12.
In this paper, the definition of latitudinal density and density flattening of the level ellipsoid is given, and integral formulas of latitudinal density for pole gravity and equator gravity are derived. According to the pole gravity condition and equator gravity condition for the level ellipsoid, latitudinal density distribution function of the level ellipsoid is obtained. It is proved mathematically that latitudinal density of the earth’s equator is larger than that of the pole, the earth’s density flattening calculated preliminarily is 1/322, and hypothesis of the earth’s latitudinal normal density is further proposed, so that theoretical preparation for studying the forming cause of the earth gravity in problems such as continent drift, mantle convection, and submarine extension is made well.  相似文献   

13.
Summary A typical geodetic satellite orbit has been computed by numerical integration for a period of thirty hours. The gravitational potential of a standard orbit was represented by the SAO 1969 Standard Earth potential coefficients taken to degree 18. Other orbits were generated using the generalized Stokes' equations and the coating method applied to gravity anomalies and surface densities, in 5°, 10°, 15° and 30° equal-area blocks, derived from the given potential coefficients. The differences between these orbits yield the position differences to be expected when representing the potential field by using gravity data instead of potential coefficients. Using 10°, 15°, and 30° blocks and the generalized Stokes' equations, the position error at the end of thirty hours was 89 meters, 224 meters, and 2060 meters respectively. This error is primarily due to the integration error in computing the gravitational field by summation over a finite number of areas.  相似文献   

14.
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   

15.
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   

16.
Summary A relation between Stokes' constants (harmonic coefficients) J n (k) , S n (k) has been derived in the development for the external geopotential and the coefficients in the development for the single-layer density distributed over the surface of the external ellipsoid, the external equipotential surface, as well as the smoothed physical surface of the actual Earth. Terms of the 2nd order, (J 2 (0) ) 2 , were taken into account, terms of the 3rd and lower orders were neglected.  相似文献   

17.
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   

18.
A second-order hydrostatic theory is developed on the assumption that the trace of the Earth's inertia tensor, its mass and mean radius are invariant under any process causing deviations from the hydrostatic state.The hydrostatic flattening and the zonal coefficients of the hydrostatic gravitational field are obtained as ??1 = 299.638, J2 = 1072.618 × 10?6 and J4 = ?2.992 × 10?6, respectively.The internal theory using the preliminary reference earth model (PREM) of Dziewonski and Anderson (1981) yields ??1 = 299.627, J2 = 1072.701 × 10?6 and J4 = ?2.992 × 10?6. The agreement between these and the hydrostatic values indicate that PREM is suitable as a reference model as it represents the spheroidal density distribution in a state of zero non-hydrostatic stress while satisfying the fundamental geodetic observations of the invariant quantities.The small discrepancy between the hydrostatic flattening and the value deduced from PREM suggests that the density is underestimated at large depths and/or it is slightly overestimated in shallow regions of the Earth.The discrepancies between the hydrostatic and observed quantities persist after the removal of the accountable effects of isostatically compensated topography, permanent tidal deformation and the present mass anomalies associated with the Late-Pleistocene deglaciation. These ‘corrected’ discrepancies point to a triaxial non-hydrostatic figure which cannot be explained by the delayed response of the Earth to tidal deceleration.  相似文献   

19.
It is sometimes assumed that steric sea-level variations do not produce a gravity signal as no net mass change, thus no change of ocean bottom pressure is associated with it. Analyzing the output of two CO2 emission scenarios over a period of 2000 years in terms of steric sea-level changes, we try to quantify the gravitational effect of steric sea-level variations. The first scenario, computed with version 2.6 of the Earth System Climate Model developed at the University of Victoria, Canada (UVic ESCM), is implemented with a linear CO2 increase of 1% of the initial concentration of 365 ppm and shows a globally averaged steric effect of 5.2 m after 2000 years. In the second scenario, computed with UVic ESCM version 2.7, the CO2 concentration increases quasi-exponentially to a level of 3011 ppm and is hold fixed afterwards. The corresponding globally averaged steric effect in the first 2000 years is 2.3 m. We show, due to the (vertical) redistribution of ocean water masses (expansion or contraction), the steric effect results also in a small change in the Earth’s gravity field compared to usually larger changes associated with net mass changes. Maximum effects for computation points located on the initial ocean surface can be found in scenario 1, with the effect on gravitational attraction and potential ranging from 0.0 to −0.7·10−5 m s−2 and −3·10−3 to 6·10−3 m2 s−2, respectively. As expected, the effect is not zero but negligible for practical applications.  相似文献   

20.
On the basis of the GRIM4-S1 satellite-only Earth gravity model, being accomplished in a common effort by DGFI and GRGS, a combination solution, called GRIM4-C1, has been derivcd using 1° × 1° mean gravity anomalies and 1° × 1° Seasat altimeter derived mean geoid undulations. In the meantime improvements could be achieved by incorporating more tracking data (GEOSAT, SPOT2-DORIS) into the solution, resulting in the two new parallel versions, the satellite-only gravity model GRIM4-S2 and the combined solution GRIM4-C2p (preliminary). All GRIM4 Earth gravity models cover the spectral gravitational constituents complete up to degree and order 50.In this report the emphasis is on the discussion of the combined gravity models: combination and estimation techniques, capabilities for application in precise satellite orbit computation and accuracies in long wavelength geoid representation. It is shown that with the new generation of global gravity models general purpose satellite-only models are no longer inferior to combination solutions if applied to satellite orbit restitution.  相似文献   

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