共查询到10条相似文献,搜索用时 156 毫秒
1.
Y. M. Wang 《Journal of Geodesy》1989,63(4):359-370
The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of
the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies
have to be analytically downward continued from the earth's surface to a sphere—at least to the ellipsoid. The goal of this
paper is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models.
The basic method for the downward continuation is the gradient solution (theg
1 term). The terrain correction has also been computed because of the role it can play as a correction term when calculating
harmonic coefficients from surface gravity data.
Theg
1 term and the terrain correction were expanded into the spherical harmonics up to180
th
order. The corrections (theg
1 term and the terrain correction) have the order of about 2% of theRMS value of degree variance of the disturbing potential per degree. The influences of theg
1 term and the terrain correction on the geoid take the order of 1 meter (RMS value of corrections of the geoid undulation) and on the deflections of the vertical is of the order 0.1″ (RMS value of correction of the deflections of the vertical). 相似文献
2.
R. H. Rapp 《Journal of Geodesy》1977,51(4):301-323
A set of 38406 1°×1° mean free air anomalies were used to derive a set of 1507 5° equal area anomalies that were supplemented
by 147 predicted anomalies to form a global coverage of 1654 anomalies. These anomalies were used to derive potential coefficients
to degree 52 using the summation formulae. In these computations, a smoothing operator was introduced and found to significantly
effect the results at higher degrees. In addition, the effects of the atmosphere, spherical approximation and terrain were
studied. It was found that the atmospheric effects and spherical approximation effects were about 0.3% of the actual coefficients.
The terrain correction effects amounted to 10 to 25% of the low degree coefficients depending on a specific terrain correction
model chosen; however, the correction terms found from the models did not yield solutions that agreed better with current
satellite derived potential coefficient determinations.
Anomalies were computed from the derived potential coefficients for comparison to the original anomalies. These comparisons
showed that the agreement between the two anomalies became significantly better as the degree of expansion increased to the
maximum considered. These comparisons shed some doubt on the rule of thumb that a block of size θ° can be represented by a spherical harmonic expansion to 180°/θ°. 相似文献
3.
Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution 总被引:4,自引:0,他引:4
Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative
(the standardized harmonic coefficients) characteristics of the behavior of the potential V
2(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors
problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients
and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination
of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients
are estimated in addition to ˙Cˉ
20, ˙Cˉ
21, and ˙Sˉ
21 of the EGM96 gravity model. In addition, a non-linear hyperbolic model for Cˉ
2m
(t), Sˉ
2m
(t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V
2(ψ) instead of V
2(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V
2(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval.
Received: 25 September 1998 / Accepted: 28 June 2000 相似文献
4.
Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic
stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric
heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W
0(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted
into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal
potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational
potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients
into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order
360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed
by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms
of the spheroidal “free-air” potential reduction in order to produce the spheroidal W
0(1993.4) value. As a mean of those 25 W
0(1993.4) data as well as a root mean square error estimation we computed W
0(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W
0 data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level
ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made.
Received: 7 November 1996 / Accepted: 27 March 1997 相似文献
5.
This paper generalizes the Stokes formula from the spherical boundary surface to the ellipsoidal boundary surface. The resulting
solution (ellipsoidal geoidal height), consisting of two parts, i.e. the spherical geoidal height N
0 evaluated from Stokes's formula and the ellipsoidal correction N
1, makes the relative geoidal height error decrease from O(e
2) to O(e
4), which can be neglected for most practical purposes. The ellipsoidal correction N
1 is expressed as a sum of an integral about the spherical geoidal height N
0 and a simple analytical function of N
0 and the first three geopotential coefficients. The kernel function in the integral has the same degree of singularity at
the origin as the original Stokes function. A brief comparison among this and other solutions shows that this solution is
more effective than the solutions of Molodensky et al. and Moritz and, when the evaluation of the ellipsoidal correction N
1 is done in an area where the spherical geoidal height N
0 has already been evaluated, it is also more effective than the solution of Martinec and Grafarend.
Received: 27 January 1999 / Accepted: 4 October 1999 相似文献
6.
Christopher Jekeli 《Journal of Geodesy》1980,54(2):137-147
Errors are considered in the outer zone contribution to oceanic undulation differences as obtained from a set of potential
coefficients complete to degree 180. It is assumed that the gravity data of the inner zone (a spherical cap), consisting of
either gravity anomalies or gravity disturbances, has negligible error. This implies that error estimates of the total undulation
difference are analyzed. If the potential coefficients are derived from a global field of 1°×1° mean anomalies accurate to
εΔg=10 mgal, then for a cap radius of 10°, the undulation difference error (for separations between 100 km and 2000 km) ranges
from 13 cm to 55 cm in the gravity anomaly case and from 6 cm to 36 cm in the gravity disturbance case. If εΔg is reduced to 1 mgal, these errors in both cases are less than 10 cm. In the absence of a spherical cap, both cases yield
identical error estimates: about 68 cm if εΔg=1 mgal (for most separations) and ranging from 93 cm to 160 cm if εΔg=10 mgal. Introducing a perfect 30-degree reference field, the latter errors are reduced to about 110 cm for most separations. 相似文献
7.
Demosthenes C. Christodoulidis 《Journal of Geodesy》1979,53(1):61-77
Seasonal and latitude dependent corrections to the gravity and height anomalies are developed in order to account for the
neglect of the atmospheric masses outside the geold, when using Stokes’ equation. It is shown that the atmospheric correction
to gravity at sea level is almost constant, equal to0.871 mgals with a variation of2 μ gals whereas the height anomaly correction varies between −0.1 cm and −1.3 cm. Further, when the combined latitudinal/seasonal dependence is neglected in the atmospheric corrections, the maximum error
introduced is of the order of40 μ gals for the gravity corrections and0.7 cm for the height anomaly corrections. 相似文献
8.
L. E. Sjöberg 《Journal of Geodesy》2003,77(3-4):139-147
Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e
2 (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e
2/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question. 相似文献
9.
S. M. Kudryavtsev 《Journal of Geodesy》1999,73(9):448-451
Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference
frame. In this frame the mean values for gravity coefficients of the second degree and first order, C
21(IERS) and S
21(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it
is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure
their values as given by the same source. The relevant error of the normalized mean values for C
21(IERS) and S
21(IERS) is 3×10−12, far above the adopted cutoff (10−13) for variations of these coefficients. Such an error in C
21 and S
21 can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable
to the accuracy of current tracking measurements.
Received: 14 September 1998 / Accepted: 20 May 1999 相似文献
10.
Low-degree earth deformation from reprocessed GPS observations 总被引:3,自引:1,他引:2
Mathias Fritsche R. Dietrich A. Rülke M. Rothacher P. Steigenberger 《GPS Solutions》2010,14(2):165-175
Surface mass variations of low spherical harmonic degree are derived from residual displacements of continuously tracking
global positioning system (GPS) sites. Reprocessed GPS observations of 14 years are adjusted to obtain surface load coefficients
up to degree n
max = 6 together with station positions and velocities from a rigorous parameter combination. Amplitude and phase estimates of
the degree-1 annual variations are partly in good agreement with previously published results, but also show interannual differences
of up to 2 mm and about 30 days, respectively. The results of this paper reveal significant impacts from different GPS observation
modeling approaches on estimated degree-1 coefficients. We obtain displacements of the center of figure (CF) relative to the
center of mass (CM), Δr
CF–CM, that differ by about 10 mm in maximum when compared to those of the commonly used coordinate residual approach. Neglected
higher-order ionospheric terms are found to induce artificial seasonal and long-term variations especially for the z-component of Δr
CF–CM. Daily degree-1 estimates are examined in the frequency domain to assess alias contributions from model deficiencies with
regard to satellite orbits. Finally, we directly compare our estimated low-degree surface load coefficients with recent results
that involve data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission. 相似文献