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1.
G. Ramillien 《Journal of Geodesy》2002,76(3):139-149
A fast spherical harmonic approach enables the computation of gravitational or magnetic potential created by a non-uniform
shell of material bounded by uneven topographies. The resulting field can be evaluated outside or inside the sphere, assuming
that density of the shell varies with latitude, longitude, and radial distance. To simplify, the density (or magnetization)
source inside the sphere is assumed to be the product of a surface function and a power series expansion of the radial distance.
This formalism is applied to compute the gravity signal of a steady, dry atmosphere. It provides geoid/gravity maps at sea
level as well as satellite altitude. Results of this application agree closely with those of earlier studies, where the atmosphere
contribution to the Earth's gravity field was determined using more time-consuming methods.
Received: 14 August 2000 / Accepted: 19 March 2001 相似文献
2.
High-resolution atmospheric angular momentum functions related to Earth rotation parameters during CONT08 总被引:1,自引:1,他引:0
Michael Schindelegger Johannes Böhm David Salstein Harald Schuh 《Journal of Geodesy》2011,85(7):425-433
Due to the temporal resolution of available numerical weather analyses, the effect of the atmosphere on Earth rotation at
daily and sub-daily periods is usually investigated using 6-hourly atmospheric angular momentum (AAM) functions. During the
period of CONT08, however, atmospheric analysis data were provided by the European Centre for Medium-Range Weather Forecasts
(ECMWF) also on an hourly basis. In this paper, we, therefore, determine two sets of AAM functions from ECMWF data—one for
CONT08 with hourly resolution and one for the year 2008 with 6-hourly resolution. The comparisons of the AAM functions to
high-resolution Earth rotation parameters (ERP) from VLBI and GPS observations are carried out in the frequency domain. Special
attention is paid to the preparation of the high-resolution data sets for the geodetic purposes, as there are jump discontinuities
at 12 h intervals. Hence, the hourly AAM functions need to be concatenated. The revised functions yield much smaller amplitudes
than their 6-hourly counterparts, as can be seen from the equatorial and the axial frequency spectra of atmospheric excitation
in Earth rotation. This decrease of spectral power in the hourly AAM functions is found to be associated with a strong counteraction
of pressure and wind terms, which originates from atmospheric circulation on short time scales. The results are compared to
previous findings published by Brzeziński and Petrov (IERS Tech Note 28:53–60, 2000) based on the data from the U.S. National Centers for Environmental Prediction (NCEP). 相似文献
3.
J. Höpfner 《Journal of Geodesy》2001,75(2-3):137-150
The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth–atmosphere system reflect
significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind
term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still
missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the
total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular
momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the
Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM)
data derived for the 10–0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated
by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and
from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations,
the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263–270]. Using
vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within
the estimated uncertainties of the momentum quantities on seasonal time scales.
Received: 6 April 2000 / Accepted: 13 December 2000 相似文献
4.
A potential-type Molodensky telluroid based upon a minimum-distance mapping is derived. With respect to a reference potential
of Somigliana–Pizzetti type which relates to the World Geodetic Datum 2000, it is shown that a point-wise minimum-distance
mapping of the topographical surface of the Earth onto the telluroid surface, constrained to the gauge W(P)=u(p), leads to a system of four nonlinear normal equations. These normal equations are solved by a fast Newton–Raphson iteration.
Received: 7 February 2000 / Accepted: 23 October 2001 相似文献
5.
In the framework of a boundary value problem (BVP), when areas on the boundary are void of data the solution of the problem
becomes undetermined and clearly more difficult. Physically, this could be the situation in which a gradiometer on a satellite
on a perfectly circular orbit covers a sphere with measured second radial derivatives: if the satellite orbit is not polar,
there are caps at satellite altitude which are not covered by data. A solution is presented based on an iterative algorithm,
under the hypothesis of using a finite-dimensional model as is usually done in the time-wise approach. The convergence of
the iterative solution is proved and a numerical example is shown to confirm the theoretical result.
Received: 14 August 2000 / Accepted: 12 April 2001 相似文献
6.
I. N. Tziavos 《Journal of Geodesy》1987,61(2):177-197
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point
gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same
area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data,
the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation,
an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the
comparison between observed and predicted values. 相似文献
7.
The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational
field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients
of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to
a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation
law allows a representation of the incremental mass density by the respective excitation function. A representation of an
arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing
these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In
particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments
of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely:
(1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application
of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of
inertia.
Received: 27 July 1999 / Accepted: 24 May 2000 相似文献
8.
Gravity recovery using COSMIC GPS data: application of orbital perturbation theory 总被引:14,自引:0,他引:14
C. Hwang 《Journal of Geodesy》2001,75(2-3):117-136
COSMIC is a joint Taiwan–US mission to study the atmosphere using the Global Positioning System (GPS) occultation technique.
Improved formulas are developed for the radial, along-track, and cross-track perturbations, which are more accurate than the
commonly used order-zero formulas. The formulas are used to simulate gravity recovery using the geodetic GPS data of COSMIC
in the operational phase. Results show that the EGM96 model can be improved up to degree 26 using 1 year of COSMIC data. TOPEX/POSEIDON
altimeter data are used to derive a temporal gravity variation. COSMIC cannot reproduce this gravity variation perfectly because
of data noise and orbital configuration, but the recovered field clearly shows the gravity signature due to mass movement
in an El Ni?o.
Received: 3 March 2000 / Accepted: 10 November 2000 相似文献
9.
A new approach for airborne vector gravimetry using GPS/INS 总被引:2,自引:2,他引:2
A new method for airborne vector gravimetry using GPS/INS has been developed and the results are presented. The new algorithm
uses kinematic accelerations as updates instead of positions or velocities, and all calculations are performed in the inertial
frame. Therefore, it is conceptually simpler, easier, more straightforward and computationally less expensive compared to
the traditional approach in which the complex navigation equations should be integrated. Moreover, it is a unified approach
for determining all three vector components, and no stochastic gravity modeling is required. This approach is based on analyzing
the residuals from the Kalman filter of sensor errors, and further processing with wavenumber coefficient filterings is applied
in case closely parallel tracks of data are available. An application to actual test-flight data is performed to test the
validity of the new algorithm. The results yield an accuracy in the down component of about 3–4 mGal. Also, comparable results
are obtained for the horizontal components with accuracies of about 6 mGal. The gravity modeling issue is discussed and alternative
methods are presented, none of which improves on the original approach.
Received: 18 April 2000 / Accepted: 14 August 2000 相似文献
10.
Willi Freeden 《Journal of Geodesy》1980,54(1):1-20
Summary Let S be the (regular) boundary-surface of an exterior regionE
e
in Euclidean space ℜ3 (for instance: sphere, ellipsoid, geoid, earth's surface). Denote by {φn} a countable, linearly independent system of trial functions (e.g., solid spherical harmonics or certain singularity functions)
which are harmonic in some domain containingE
e
∪ S. It is the purpose of this paper to show that the restrictions {ϕn} of the functions {φn} onS form a closed system in the spaceC (S), i.e. any functionf, defined and continuous onS, can be approximated uniformly by a linear combination of the functions ϕn.
Consequences of this result are versions of Runge and Keldysh-Lavrentiev theorems adapted to the chosen system {φn} and the mathematical justification of the use of trial functions in numerical (especially: collocational) procedures. 相似文献
11.
Giuseppe Arbia 《Journal of Geographical Systems》2001,3(3):271-281
Economists have recently devoted an increasing attention to the issue of spatial concentration of economic activities. However,
surprisingly enough, most of the empirical work is still based on the computation of very basic statistical measures in which
the geographical characteristics of data play no role. By making use of a series of empirical examples we show that spatial
concentration consists of two different features that are rarely kept as separate in the statistical analysis: an a-spatial
concept of variability which is invariant to permutations, and the concept of polarization that refers to the geographical
position of observations.
Received: 8 August 2000 / Accepted: 20 June 2001 相似文献
12.
D. Arabelos 《Journal of Geodesy》1985,59(2):109-123
The evaluation of deflections of the vertical for the area of Greece is attempted using a combination of topographic and astrogeodetic
data. Tests carried out in the area bounded by 35°≤ϕ≤42°, 19°≤λ≤27° indicate that an accuracy of ±3″.3 can be obtained in
this area for the meridian and prime vertical deflection components when high resolution topographic data in the immediate
vicinity of computation points are used, combined with high degree spherical harmonic expansions of the geopotential and isostatic
reduction potential. This accuracy is about 25% better than the corresponding topographic-Moho deflection components which
are evaluated using topographic and Moho data up to 120 km around each station, without any combination with the spherical
harmonic expansion of the geopotential or isostatic reduction potential. The accuracy in both cases is increased to about
2″.6 when the astrogeodetic data available in the area mentioned above are used for the prediction of remaining values. Furthermore
the estimation of datum-shift parameters is attempted using least squares collocation. 相似文献
13.
A model for adjustment of differential gravity measurements with simultaneous gravimeter calibration
A mathematical model is proposed for adjustment of differential or relative gravity measurements, involving simultaneously
instrumental readings, coefficients of the calibration function, and gravity values of selected base stations. Tests were
performed with LaCoste and Romberg model G gravimeter measurements for a set of base stations located along a north–south
line with 1750 mGal gravity range. This line was linked to nine control stations, where absolute gravity values had been determined
by the free-fall method, with an accuracy better than 10 μGal. The model shows good consistence and stability. Results show
the possibility of improving the calibration functions of gravimeters, as well as a better estimation of the gravity values,
due to the flexibility admitted to the values of the calibration coefficients.
Received: 15 November 1999 / Accepted: 31 October 2000 相似文献
14.
The gravitational attraction of any polygonally shaped vertical prism with inclined top and bottom faces 总被引:2,自引:0,他引:2
D. A. Smith 《Journal of Geodesy》2000,74(5):414-420
A closed formula for computing the gravitational attraction of a general vertical prism with N+2 faces (N faces are vertical planes, the other two are the inclined top and bottom planes) in Cartesian coordinates is presented. In
addition, the special case of a triangular prism is discussed. Algebraic differences and overlooked singularity conditions
of a previously published formula of this computation (which was only for the triangular special case) were identified and
are also presented.
Received: 22 March 1999 / Accepted: 2 February 2000 相似文献
15.
D. A. Smith 《Journal of Geodesy》2002,76(3):150-168
A new method for computing gravitational potential and attraction induced by distant, global masses on a global scale has
been developed. The method uses series expansions and the well known one-dimensional fast Fourier transform (1-D FFT) method.
It has been proven to be significantly faster than quadrature while being equally accurate. Various quantities were studied
to cover the two primary applications of the Stokes–Helmert scheme of modeling effects. These two applications (or paths),
given the names R/r/D and R/D/r, are briefly discussed, although the primary objective of the paper is to provide computational
information to either path, rather than choosing one path as preferable to the other. It is further shown that the impact
of masses outside a 4-degree cap can impact the absolute computation of the geoid at more than 1 cm, and should therefore
be included in all local geoid computations seeking that accuracy.
Received: 13 December 2000 / Accepted: 3 September 2001 相似文献
16.
Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm 总被引:4,自引:0,他引:4
Erik W. Grafarend 《GPS Solutions》2000,4(2):31-44
In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange
observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued
parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review
the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference
operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated
by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined
by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities)
and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to
the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove
that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued
unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated
by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')−1[L'◯] ∈ ℤ
m
where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ
m
, the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc. 相似文献
17.
The analysis of lunar laser ranging (LLR) data enables the determination of many parameters of the Earth–Moon system, such
as lunar gravity coefficients, reflector and station coordinates which contribute to the realisation of the International
Terrestrial Reference Frame 2000 (ITRF 2000), Earth orientation parameters [EOPs, which contribute to the global EOP solutions
at the International Earth Rotation Service (IERS)] or quantities which parameterise relativistic effects in the solar system.
The big advantage of LLR is the long time span of lunar observations (1970–2000). The accuracy of the normal points nowadays
is about 1 cm.
The capability of LLR to determine tidal parameters is investigated. In principle, it could be assumed that LLR would contribute
greatly to the investigation of tidal effects, because the Moon is the most important tide-generating body. In this respect
some special topics such as treatment of the permanent tide and the effect of atmospheric loading are addressed and results
for the tidal parameters h
2 and l
2 as well as values for the eight main tides are given.
Received: 14 August 2000 / Accepted: 15 October 2001 相似文献
18.
In October 1998 the IGEX field campaign, the first coordinated international effort to monitor GLONASS satellites on global
basis, was started. Currently about 40 institutions worldwide support this effort either by providing GLONASS tracking data
or in operating related data and analysis centers. The increasing quality and consistency of the calculated GLONASS orbits
(about 25 cm early in 2000), even after the end of the official IGEX field campaign, are shown. Particular attention is drawn
to the combination of precise ephemerides in order to generate a robust, reliable and complete IGEX orbits product. Some problems
in modeling the effect of solar radiation pressure on GLONASS satellites are demonstrated. Finally, the expected benefits
and prospects of the upcoming International GLOnass Service-Pilot Project (IGLOS-PP) of the International GPS Service (IGS)
are discussed in more detail.
Received: 17 August 2000 / Accepted: 12 April 2001 相似文献
19.
A special class of regularization methods for satellite gravity gradiometry based on Tikhonov spherical regularization wavelets
is considered, with particular emphasis on the case of data blurred by random noise. A convergence rate is proved for the
regularized solution, and a method is discussed for choosing the regularization level a posteriori from the gradiometer data.
Received: 23 March 2000 / Accepted: 20 September 2000 相似文献
20.
The spacetime gravitational field of a deformable body 总被引:3,自引:0,他引:3
The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation
of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation
of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body
are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental
spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents:
the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference
mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both
in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential
is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement
multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces.
The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position
of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution,
emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus
surface Love-Shida functions (h(r),l(r) versus h
′(r),l
′(r)) and Love functions k(r) versus k
′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential,
proving an excellent agreement with experimental results.
Received: December 1995 / Accepted: 1 February 1997 相似文献