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1.
M. S. Petrovskaya 《Journal of Geodesy》1979,53(3):259-271
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. 相似文献
2.
E. Groten 《Journal of Geodesy》1968,42(2):227-239
Summary It is shown that the divergence of the spherical harmonics series of the geopotential V at the earth’s surface does not have
any limiting consequences for the corresponding finite series in satellite geodesy as well as for the solution of the boundary
value problem of physical geodesy if a finite set of observations is used. The usefulness of the multiples series of V for
the study of secular variations of the gravity field is stressed.
Publ. No. 49, Institut für Astronomische und Physikalische Geod?sie, Technische Hochschule München. 相似文献
3.
Richard H. Rapp 《Journal of Geodesy》1975,49(1):57-63
For proper computation of the Stokes’ constants, or the evaluation of potential coefficients from terrestrial gravity data,
surface free-air anomalies should be corrected to sea level. Such a correction is composed of two parts; the first, the Molodensky
correction, G1, and a second, a term depending on the degree (n) and the expansion of (hΔg). This paper examines these terms numerically,
computing for 1654 5° equal area blocks values of G1 and the total correction based on spherical harmonic expansions to degree 20. The largest correction found was 0.37 mgals.
Corrections to potential coefficients caused by the anomaly correction were computed and compared to the original coefficients.
The ratio between the coefficient corrections and the full coefficients generally increased by degree having a maximum ratio
of 0.21 percent at degree 14 indicating that at the present time the corrections considered are negligible up to at least
degree 20. 相似文献
4.
J. C. Bhattacharji 《Journal of Geodesy》1980,54(2):225-233
The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian
geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the
Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms
on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding
generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were
also considered before actual finalization of the results of the present determination. 相似文献
5.
Any errors in digital elevation models (DEMs) will introduce errors directly in gravity anomalies and geoid models when used
in interpolating Bouguer gravity anomalies. Errors are also propagated into the geoid model by the topographic and downward
continuation (DWC) corrections in the application of Stokes’s formula. The effects of these errors are assessed by the evaluation
of the absolute accuracy of nine independent DEMs for the Iran region. It is shown that the improvement in using the high-resolution
Shuttle Radar Topography Mission (SRTM) data versus previously available DEMs in gridding of gravity anomalies, terrain corrections
and DWC effects for the geoid model are significant. Based on the Iranian GPS/levelling network data, we estimate the absolute
vertical accuracy of the SRTM in Iran to be 6.5 m, which is much better than the estimated global accuracy of the SRTM (say
16 m). Hence, this DEM has a comparable accuracy to a current photogrammetric high-resolution DEM of Iran under development.
We also found very large differences between the GLOBE and SRTM models on the range of −750 to 550 m. This difference causes
an error in the range of −160 to 140 mGal in interpolating surface gravity anomalies and −60 to 60 mGal in simple Bouguer
anomaly correction terms. In the view of geoid heights, we found large differences between the use of GLOBE and SRTM DEMs,
in the range of −1.1 to 1 m for the study area. The terrain correction of the geoid model at selected GPS/levelling points
only differs by 3 cm for these two DEMs. 相似文献
6.
John A. OKeefe III 《Journal of Geodesy》1974,48(1):81-84
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. 相似文献
7.
Margarita Petrovskaya 《Journal of Geodesy》1988,62(2):161-170
A non-conventional treatment of Stokes’integral enables significant simplification of formulas for both the regional and global
contributions of the gravity field to the geoidal height. 相似文献
8.
J. Li 《Journal of Geodesy》2005,79(1-3):64-70
Integral formulas are derived which can be used to convert the second-order radial gradient of the disturbing potential, as boundary values, into the disturbing potential, gravity anomaly and the deflection of the vertical. The derivations are based on the fundamental differential equation as the boundary condition in Stokes’s boundary-value problem and the modified Poisson integral formula in which the zero and first-degree spherical harmonics are excluded. The rigorous kernel functions, corresponding to the integral operators, are developed by the methods of integration. 相似文献
9.
J. C. Bhattacharji 《Journal of Geodesy》1984,58(1):31-36
The concept of an idealised earth having 1° averaged heights over its land surface is introduced as a means to improve upon
the existing geopotential coefficient solutions without the use of additional observed data, in order to provide more precise
knowledge of the earth’s gravity field in the form of 1° global geoid and 1° mean free-air gravity anomalies especially over
the mountainous regions with the visible topography condensed into the actual geoid, first by referring them to the idealised
earth and then by reducing the same to the actual earth on applying appropriate corrections for the differences between the
two earths. 相似文献
10.
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. 相似文献
11.
Y. M. Wang 《Journal of Geodesy》1999,73(1):29-34
The formulas of the ellipsoidal corrections to the gravity anomalies computed using the inverse Stokes integral are derived.
The corrections are given in the integral formulas and expanded in the spherical harmonics series. If a coefficient model
such as the OSU91A is given, the corrections can be easily computed.
Received: 19 August 1996 / Accepted: 28 September 1998 相似文献
12.
L. E. Sjöberg 《Journal of Geodesy》2007,81(5):345-350
This study emphasizes that the harmonic downward continuation of an external representation of the Earth’s gravity potential
to sea level through the topographic masses implies a topographic bias. It is shown that the bias is only dependent on the
topographic density along the geocentric radius at the computation point. The bias corresponds to the combined topographic
geoid effect, i.e., the sum of the direct and indirect topographic effects. For a laterally variable topographic density function,
the combined geoid effect is proportional to terms of powers two and three of the topographic height, while all higher order
terms vanish. The result is useful in geoid determination by analytical continuation, e.g., from an Earth gravity model, Stokes’s
formula or a combination thereof. 相似文献
13.
K. Lambeck 《Journal of Geodesy》1971,45(3):263-281
The methods of using earth satellites for determining the motion of the earth’s axis of rotation and of the earth’s principal
axis of maximum inertia are discussed.
Some simple formulae are also presented for evaluating the influence of various error sources in the orbital calculations
on the pole coordinates and these offer some explanations of the frequencies found in the spectrum of the pole coordinates
obtained by Anderle and Beuglass (1970). Initial calculations with existing laser data were attempted but the results were
quite unsatisfactory due to the poor distribution of the data along the orbit. Some conclusions have however been drawn from
these calculations that may be useful for future studies when better distributed data becomes available. 相似文献
14.
Lars E. Sj?berg 《Journal of Geodesy》1988,62(2):93-101
The spherical harmonic coefficients of the Earth’s gravitational potential are conveniently determined by integration of gravity
data or potential data (derived from satellite altimetry) over a sphere. The major problem of such a method is that the data,
given on the non-spherical surface of the Earth, must be reduced to the sphere.
A new integral formula over the surface of the Earth is derived. With this formula improved first order topographic corrections
to the spherical formulas are obtained. 相似文献
15.
L. de Witte 《Journal of Geodesy》1967,41(1):41-53
When the values of gravity anomalies are given at the geoid, Ag can be calculated at altitude by application of Poisson’s
integral theorem. The process requires integration of Δg multiplied by the Poisson kernel function over the entire globe.
It is common practice to add to the kernel function terms that will ensure removal of any zeroth and first order components
of Δg that may be present. The effects of trancating the integration at the boundary of a spherical cap of earth central half
angle ψo have been analyzed using an adaptation of Molodenskii’s procedure. The extension process without removal terms retains the
correct effects of inaccuracies in the constant term of the gravity reference model used in the definition of Δg. Furthermore,
the effects of ignoring remote zones or unmapped areas in the integration process are very much smaller for the extension
without removal terms than for the commonly used formula with removal terms. For these reasons the Poisson vertical extension
process without removal terms is to be preferred over the extension with the zeroth order term removal. Truncation of this
process at the point recommended for the Stokes integration, namely, the first zero crossing of the Stokes kernel function,
leaves negligible truncation errors. 相似文献
16.
Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography 总被引:1,自引:1,他引:0
The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at
airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic
and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the
geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potential T fulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses
can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward
continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based
on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation
time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation
point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global
spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original
approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for
Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography
on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented
and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes.
Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these
effects. 相似文献
17.
Spherical harmonic expansions of the geopotential are frequently used for modelling the earth’s gravity field. Degree and
order of recently available models go up to 360, corresponding to a resolution of about50 km. Thus, the high degree potential coefficients can be verified nowadays even by locally distributed sets of terrestrial gravity
anomalies. These verifications are important when combining the short wavelength model impact, e.g. for regional geoid determinations
by means of collocation solutions. A method based on integral formulae is presented, enabling the improvement of geopotential
models with respect to non-global distributed gravity anomalies. To illustrate the foregoing, geoid computations are carried
out for the area of Iran, introducing theGPM2 geopotential model in combination with available regional gravity data. The accuracy of the geoid determination is estimated
from a comparison with Doppler and levelling data to ±1.4m. 相似文献
18.
The impact of errors in polar motion and nutation on UT1 determinations from VLBI Intensive observations 总被引:2,自引:2,他引:0
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. 相似文献
19.
Lars E. Sjöberg 《Journal of Geodesy》2006,79(12):675-681
The application of Stokes’s formula to determine the geoid height requires that topographic and atmospheric masses be mathematically removed prior to Stokes integration. This corresponds to the applications of the direct topographic and atmospheric effects. For a proper geoid determination, the external masses must then be restored, yielding the indirect effects. Assuming an ellipsoidal layering of the atmosphere with 15% increase in its density towards the poles, the direct atmospheric effect on the geoid height is estimated to be −5.51 m plus a second-degree zonal harmonic term with an amplitude of 1.1 cm. The indirect effect is +5.50 m and the total geoid correction thus varies between −1.2 cm at the equator to 1.9 cm at the poles. Finally, the correction needed to the atmospheric effect if Stokes’s formula is used in a spherical approximation, rather than an ellipsoidal approximation, of the Earth varies between 0.3 cm and 4.0 cm at the equator and pole, respectively. 相似文献
20.
The design and construction are described of an experimental strainmeter. This observes changes in the number of waves of
light standing in a one-kilometer gap between points on the earth’s surface. Strain is observed over a frequency range of
zero to several hundred hertz, to an accuracy of an arbitrarily-small fraction of a wave-length of light. Frequency-dependent
phase and amplitude distortion are absent. As the read-out is of the nature of a servo device, dynamic range limitations are
not encountered.
The prototype instrument is located in a region affected by the world rift system. 相似文献