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1.
The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on
reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential
coefficients
n,m
. In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal
harmonic series is developed for the geopotential and then its coefficients
n,m
e
are transformed to the unknown
n,m
. The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral
formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied
numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From
two sets of
n,m
(n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation
are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution
appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics
of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential
model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068)
by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to
apply the LS technique for evaluating geopotential coefficients.
Received: 12 December 2000 / Accepted: 21 June 2001 相似文献
2.
A synthetic Earth for use in geodesy 总被引:1,自引:0,他引:1
R. Haagmans 《Journal of Geodesy》2000,74(7-8):503-511
A synthetic Earth and its gravity field that can be represented at different resolutions for testing and comparing existing
and new methods used for global gravity-field determination are created. Both the boundary and boundary values of the gravity
potential can be generated. The approach chosen also allows observables to be generated at aircraft flight height or at satellite
altitude. The generation of the synthetic Earth shape (SES) and gravity-field quantities is based upon spherical harmonic
expansions of the isostatically compensated equivalent rock topography and the EGM96 global geopotential model. Spherical
harmonic models are developed for both the synthetic Earth topography (SET) and the synthetic Earth potential (SEP) up to
degree and order 2160 corresponding to a 5′×5′ resolution. Various sets of SET, SES and SEP with boundary geometry and boundary
values at different resolutions can be generated using low-pass filters applied to the expansions. The representation is achieved
in point sets based upon refined triangulation of a octahedral geometry projected onto the chosen reference ellipsoid. The
filter cut-offs relate to the sampling pattern in order to avoid aliasing effects. Examples of the SET and its gravity field
are shown for a resolution with a Nyquist sampling rate of 8.27 degrees.
Received: 6 August 1999 / Accepted: 26 April 2000 相似文献
3.
L. E. Sjöberg 《Journal of Geodesy》2001,75(5-6):283-290
The topographic and atmospheric effects of gravimetric geoid determination by the modified Stokes formula, which combines
terrestrial gravity and a global geopotential model, are presented. Special emphasis is given to the zero- and first-degree
effects. The normal potential is defined in the traditional way, such that the disturbing potential in the exterior of the
masses contains no zero- and first-degree harmonics. In contrast, it is shown that, as a result of the topographic masses,
the gravimetric geoid includes such harmonics of the order of several centimetres. In addition, the atmosphere contributes
with a zero-degree harmonic of magnitude within 1 cm.
Received: 5 November 1999 / Accepted: 22 January 2001 相似文献
4.
A technique for the analysis of low–low intersatellite range-rate data in a gravity mapping mission is explored. The technique
is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the
12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters
is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types
without large simultaneous multiple-data-type solutions. The technique appears especially valuable for estimating gravity
from short arcs (e.g. less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those
using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably
well, although higher-order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or
short arcs of the Gravity Recovery and Climate Experiment (GRACE) data are likely to improve parts of the geopotential spectrum
by orders of magnitude.
Received: 26 June 2001 / Accepted: 21 January 2002 相似文献
5.
The passive satellite GFZ-1 has been orbiting the Earth since April 1995. The purpose of this mission is to improve the current
knowledge of the Earth's gravity field by analysing gravitational orbit perturbations observed at unique low altitudes, below
400 km. GFZ-1 is one target of the international satellite laser ranging ground network. An evaluation of the first 30 months
of GFZ-1 laser tracking data led to a new version of the global GRIM4-S4 satellite-only gravity field model: GRIM4-S4G. Information
was obtained from GFZ-1 data for spherical harmonic coefficients up to degree 100, which was not possible in any earlier satellite-only
gravity field solution. GFZ-1's contribution to a global 5 × 5° geoid and gravity field representations is moderate but visible
with a 1 cm and 0.1 mGal gain in accuracy on a level of 75 cm and 5 mGal, respectively.
Received: 10 November 1998 / Accepted: 19 April 1999 相似文献
6.
Downward continuation and geoid determination based on band-limited airborne gravity data 总被引:4,自引:3,他引:4
The downward continuation of the harmonic disturbing gravity potential, derived at flight level from discrete observations
of airborne gravity by the spherical Hotine integral, to the geoid is discussed. The initial-boundary-value approach, based
on both the direct and inverse solution to Dirichlet's problem of potential theory, is used. Evaluation of the discretized
Fredholm integral equation of the first kind and its inverse is numerically tested using synthetic airborne gravity data.
Characteristics of the synthetic gravity data correspond to typical airborne data used for geoid determination today and in
the foreseeable future: discrete gravity observations at a mean flight height of 2 to 6 km above mean sea level with minimum
spatial resolution of 2.5 arcmin and a noise level of 1.5 mGal. Numerical results for both approaches are presented and discussed.
The direct approach can successfully be used for the downward continuation of airborne potential without any numerical instabilities
associated with the inverse approach. In addition to these two-step approaches, a one-step procedure is also discussed. This
procedure is based on a direct relationship between gravity disturbances at flight level and the disturbing gravity potential
at sea level. This procedure provided the best results in terms of accuracy, stability and numerical efficiency. As a general
result, numerically stable downward continuation of airborne gravity data can be seen as another advantage of airborne gravimetry
in the field of geoid determination.
Received: 6 June 2001 / Accepted: 3 January 2002 相似文献
7.
The results from 14 satellite orbit analyses, two of which are new objects, are used to determine individual tesseral harmonic coefficients of 30th-order and even degree. Six C, S pairs are evaluated by solving the equations using a modified least-squares technique. The results are compared with comprehensive geopotential models. The recent models GRIM4-C1, GEM-T3 and JGM-2 emerge well from such tests and are generally closest to the resonance values. A tentative solution is found for four pairs of harmonic coefficients of 30th-order and odd degree. 相似文献
8.
W. E. Featherstone J. F. Kirby A. H. W. Kearsley J. R. Gilliland G. M. Johnston J. Steed R. Forsberg M. G. Sideris 《Journal of Geodesy》2001,75(5-6):313-330
The AUSGeoid98 gravimetric geoid model of Australia has been computed using data from the EGM96 global geopotential model,
the 1996 release of the Australian gravity database, a nationwide digital elevation model, and satellite altimeter-derived
marine gravity anomalies. The geoid heights are on a 2 by 2 arc-minute grid with respect to the GRS80 ellipsoid, and residual
geoid heights were computed using the 1-D fast Fourier transform technique. This has been adapted to include a deterministically
modified kernel over a spherical cap of limited spatial extent in the generalised Stokes scheme. Comparisons of AUSGeoid98
with GPS and Australian Height Datum (AHD) heights across the continent give an RMS agreement of ±0.364 m, although this apparently
large value is attributed partly to distortions in the AHD.
Received: 10 March 2000 / Accepted: 21 February 2001 相似文献
9.
Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt 总被引:1,自引:0,他引:1
C. C. Tscherning Awar Radwan A. A. Tealeb S. M. Mahmoud M. Abd El-Monum Ramdan Hassan I. El-Syaed K. Saker 《Journal of Geodesy》2001,75(7-8):343-348
The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and
the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity
data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not
using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with
gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general
gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan
Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using
only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was
in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used,
as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave
difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the
agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances
and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account
for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads.
Received: 14 August 2000 / Accepted: 28 February 2001 相似文献
10.
The single- and dual-satellite crossover (SSC and DSC) residuals between and among Geosat, TOPEX/Poseidon (T/P), and ERS
1 or 2 have been used for various purposes, applied in geodesy for gravity field accuracy assessments and determination as
well as in oceanography. The theory is presented and various examples are given of certain combinations of SSC and DSC that test for residual altimetry data errors, mostly of non-gravitational origin, of the order of a few centimeters.
There are four types of basic DSCs and 12 independent combinations of them in pairs which have been found useful in the present
work. These are defined in terms of the `mean' and `variable' components of a satellite's geopotential orbit error from Rosborough's
1st-order analytical theory. The remaining small errors, after all altimeter data corrections are applied and the relative
offset of coordinate frames between altimetry missions removed, are statistically evaluated by means of the Student distribution.
The remaining signal of `non-gravitational' origin can in some cases be attributed to the main ocean currents which were not
accounted for among the media or sea-surface corrections. In future, they may be resolved by a long-term global circulation
model. Experience with two current models, neither of which are found either to cover the most critical missions (Geosat &
TOPEX/Poseidon) or to have the accuracy and resolution necessary to account for the strongest anomalies found across them,
is described. In other cases, the residual signal is due to errors in tides, altimeter delay corrections or El Ni?o. (Various
examples of these are also presented.) Tests of the combinations of the JGM 3-based DSC residuals show that overall the long-term
data now available are well suited for a gravity field inversion refining JGM 3 for low- and resonant-order geopotential harmonics
whose signatures are clearly seen in the basic DSC and SSC sets.
Received: 15 January 1999 / Accepted: 9 September 1999 相似文献
11.
Regularization of geopotential determination from satellite data by variance components 总被引:11,自引:18,他引:11
Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination
of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming
mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed
or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance
components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected
with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large
linear systems. The posterior density function for the variance components, weighting factors and regularization parameters
are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer
observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach.
Received: 5 June 2001 / Accepted: 28 November 2001 相似文献
12.
The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational
task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing
the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned
conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different
concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding
the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the
coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical
results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative
adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns
out to be a feasible method for practical applications.
Received: 17 December 2001 / Accepted: 17 July 2002
Acknowledgments. We would like to thank Prof. W.-D. Schuh, Institute of Theoretical Geodesy, University of Bonn, for providing us with the
serial version of the PCGMA algorithm, which forms the basis for the parallel PCGMA package developed at our institute. This
study was partially performed in the course of the GOCE project `From E?tv?s to mGal+', funded by the European Space Agency
(ESA) under contract No. 14287/00/NL/DC.
Correspondence to: R. Pail 相似文献
13.
The structure of normal matrices occurring in the problem of weighted least-squares spherical harmonic analysis of measurements
scattered on a sphere with random noises is investigated. Efficient algorithms for the formation of the normal matrices are
derived using fundamental relations inherent to the products of two surface spherical harmonic functions. The whole elements
of a normal matrix complete to spherical harmonic degree L are recursively obtained from its first row or first column extended to degree 2L with only O(L
4) computational operations. Applications of the algorithms to the formation of surface normal matrices from geoid undulations
and surface gravity anomalies are discussed in connection with the high-degree geopotential modeling.
Received: 22 March 1999 / Accepted: 23 December 1999 相似文献
14.
Gravitational perturbation theory for intersatellite tracking 总被引:7,自引:0,他引:7
M. K. Cheng 《Journal of Geodesy》2002,76(3):169-185
An analytical gravitational perturbation theory for the intersatellite tracking range and range-rate measurement between
two satellites is developed. The satellite-to-satellite tracking (SST) range data measure the difference between the position
perturbations of two satellites along the direction of the intersatellite range. The SST range-rate data measure the difference
between the velocity perturbations along the direction of the intersatellite range, and the difference of the position perturbation
along the direction perpendicular to the intersatellite range (cross-range). The SST range and range rate depend on different
orbital excitations for mapping the gravity field. For the Gravity Recovery and Climate Experiment (GRACE), approximately
97% of the geopotential coefficient pairs produce perturbations with a root-mean-square larger than 1 m on the range and 0.1
m/sec on the range rate based on the EGM96 gravity field truncated at degree and order 140. Results in this study showed that
ocean tides produce significant perturbations in the range and range-rate measurements. An ocean tide field with a higher
degree and order (>70) is required to model the ocean tide perturbations on the intersatellite range and range-rate measurement.
Received: 17 May 2000 / Accepted: 3 September 2001 相似文献
15.
H. Nahavandchi 《Journal of Geodesy》2002,76(6-7):345-352
It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might
be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient
model. A `direct' method of geoidal height determination from a global Earth gravity model coefficient alone and an `indirect'
approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In
both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and
indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which
are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield
better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such
improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the
application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is
also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction
terms used for the indirect determination of geoidal heights from height anomalies.
Received: 26 July 2001 / Accepted: 21 February 2002 相似文献
16.
One of the aims of the Earth Explorer Gravity Field and Steady-State Ocean Circulation (GOCE) mission is to provide global
and regional models of the Earth's gravity field and of the geoid with high spatial resolution and accuracy. Using the GOCE
error model, simulation studies were performed in order to estimate the accuracy of datum transfer in different areas of the
Earth. The results showed that with the GOCE error model, the standard deviation of the height anomaly differences is about
one order of magnitude better than the corresponding value with the EGM96 error model. As an example, the accuracy of the
vertical datum transfer from the tide gauge of Amsterdam to New York was estimated equal to 57 cm when the EGM96 error model
was used, while in the case of GOCE error model this accuracy was increased to 6 cm. The geoid undulation difference between
the two places is about 76.5 m. Scaling the GOCE errors to the local gravity variance, the estimated accuracy varied between
3 and 7 cm, depending on the scaling model.
Received: 1 March 2000 / Accepted: 21 February 2001 相似文献
17.
Geoid determination using adapted reference field, seismic Moho depths and variable density contrast 总被引:4,自引:0,他引:4
The traditional remove-restore technique for geoid computation suffers from two main drawbacks. The first is the assumption
of an isostatic hypothesis to compute the compensation masses. The second is the double consideration of the effect of the
topographic–isostatic masses within the data window through removing the reference field and the terrain reduction process.
To overcome the first disadvantage, the seismic Moho depths, representing, more or less, the actual compensating masses, have
been used with variable density anomalies computed by employing the topographic–isostatic mass balance principle. In order
to avoid the double consideration of the effect of the topographic–isostatic masses within the data window, the effect of
these masses for the used fixed data window, in terms of potential coefficients, has been subtracted from the reference field,
yielding an adapted reference field. This adapted reference field has been used for the remove–restore technique. The necessary
harmonic analysis of the topographic–isostatic potential using seismic Moho depths with variable density anomalies is given.
A wide comparison among geoids computed by the adapted reference field with both the Airy–Heiskanen isostatic model and seismic
Moho depths with variable density anomaly and a geoid computed by the traditional remove–restore technique is made. The results
show that using seismic Moho depths with variable density anomaly along with the adapted reference field gives the best relative
geoid accuracy compared to the GPS/levelling geoid.
Received: 3 October 2001 / Accepted: 20 September 2002
Correspondence to: H.A. Abd-Elmotaal 相似文献
18.
Fast spherical collocation: theory and examples 总被引:2,自引:4,他引:2
It has long been known that a spherical harmonic analysis of gridded (and noisy) data on a sphere (with uniform error for
a fixed latitude) gives rise to simple systems of equations. This idea has been generalized for the method of least-squares
collocation, when using an isotropic covariance function or reproducing kernel. The data only need to be at the same altitude
and of the same kind for each latitude. This permits, for example, the combination of gravity data at the surface of the Earth
and data at satellite altitude, when the orbit is circular. Suppose that data are associated with the points of a grid with
N values in latitude and M values in longitude. The latitudes do not need to be spaced uniformly. Also suppose that it is required to determine the
spherical harmonic coefficients to a maximal degree and order K. Then the method will require that we solve K systems of equations each having a symmetric positive definite matrix of only N × N. Results of simulation studies using the method are described.
Received: 18 October 2001 / Accepted: 4 October 2002
Correspondence to: F. Sansò 相似文献
19.
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
20.
Considering a GPS satellite and two terrestrial stations, two types of equations are derived relating the heights of the
two stations to the measured data (frequency ratio or clock rate differences) and the coordinates and velocity components
of all three participating objects. The potential possibilities of using such relations for the determination of heights (in
terms of geopotential numbers or orthometric heights) are discussed.
Received: 6 December 2000 / Accepted: 9 July 2001 相似文献