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1.
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
2.
We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based
on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations.
The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity
field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal
energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite.
Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential
at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy
spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation
by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges
to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite
altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical
experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n
max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting
spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical
evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting
the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute
the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics
of satellite coverage, which could not be done using a global spherical harmonic representation.
The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577. 相似文献
3.
A preliminary error analysis of the gravity field recovery from a lunar Satellite-to-Satellite mission 总被引：2，自引：0，他引：2
Hüseyin Bâki Iz 《Journal of Geodesy》1993,67(3):173-177
Summary A low cost lunar Satellite-to-Satellite radio tracking mission in a low-low configuration could considerably improve the existing knowledge about the lunar gravity field. The impact of various mission parameters that may contribute to the recovery of the gravity field, such as satellite altitude, satellite separation, mission duration, measurement precision and sampling interval were quantified using the Jekeli-Rapp algorithm. Preliminary results indicate that the gravity field resolution up to harmonic degree 40 to 80 is feasible depending on various mission configurations. Radio tracking data from a six-month mission with a precision of 1 mm s–1 every 10 s and 300 km satellite separation at 150 km altitude will permit the determination of 5o×5o mean gravity anomalies with an error of approximately 15 mgals. Consideration of other unaccounted error sources of instrumental, operational as well as environmental nature may lower this resolution. 相似文献
4.
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
5.
GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。 相似文献
6.
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
7.
Minimization and estimation of geoid undulation errors 总被引：2，自引：1，他引：1
The objective of this paper is to minimize the geoid undulation errors by focusing on the contribution of the global geopotential model and regional gravity anomalies, and to estimate the accuracy of the predicted gravimetric geoid.The geopotential model's contribution is improved by (a) tailoring it using the regional gravity anomalies and (b) introducing a weighting function to the geopotential coefficients. The tailoring and the weighting function reduced the difference (1) between the geopotential model and the GPS/levelling-derived geoid undulations in British Columbia by about 55% and more than 10%, respectively.Geoid undulations computed in an area of 40° by 120° by Stokes' integral with different kernel functions are analyzed. The use of the approximated kernels results in about 25 cm () and 190 cm (maximum) geoid errors. As compared with the geoid derived by GPS/levelling, the gravimetric geoid gives relative differences of about 0.3 to 1.4 ppm in flat areas, and 1 to 2.5 ppm in mountainous areas for distances of 30 to 200 km, while the absolute difference (1) is about 5 cm and 20 cm, respectively.A optimal Wiener filter is introduced for filtering of the gravity anomaly noise, and the performance is investigated by numerical examples. The internal accuracy of the gravimetric geoid is studied by propagating the errors of the gravity anomalies and the geopotential coefficients into the geoid undulations. Numerical computations indicate that the propagated geoid errors can reasonably reflect the differences between the gravimetric and GPS/levelling-derived geoid undulations in flat areas, such as Alberta, and is over optimistic in the Rocky Mountains of British Columbia.Paper presented at the IAG General Meeting, Beijing, China, August 8–13, 1993. 相似文献
8.
Latitude-lumped coefficients (LLC) are defined, representing geopotential-orbit variations for dual-satellite crossovers (DSC). Formulae are derived for their standard errors from the covariances of geopotential field models. Numerical examples are
presented for pairs of the altimeter-bearing satellites TOPEX/Poseidon, ERS 1, and Geosat, using the error matrices of recent
gravity models. The DSC, connecting separate missions, will play an increasingly important role in oceanography spanning decades
only when its nonoceanographic signals are thoroughly understood. In general, the content of even the long-term averaged DSC
is more complex then their single satellite crossover (SSC) counterpart. The LLC, as the spatial spectra for the geopotential-caused
crossover effects, discriminate these source-differences sharply. Thus, the zero-order LLC in DSC data contains zonal gravity
information not present in SSC data. In addition, zero- and first-order LLC of DSC data can reveal a geocenter discrepancy
between the orbit tracking of the separate satellite missions. For example, DSC analysis from orbits computed with JGM 2 show
that the y-axis of the geocenter for Geosat in 1986–1988 is shifted with respect to T/P by 6–9 cm towards the eastern Pacific. Also,
where the time-gap is necessarily large (as between, say, Geosat and T/P missions) oceanographic (sea-level) differences in
DSC may corrupt the geopotential interpretation of the data. Most importantly, as we illustrate, media delays for the altimeter
(from the ionosphere, wet troposphere and sea-state bias) are more likely sources of contamination across two missions than
in SSC analyses. Again, the LLC of zero order best shows this contrast. Using the higher-order LLC of DSC for both Geosat-T/P
and ERS 1-T/P as likely representation of geopotential-only error, we show by comparison with the predicted standard errors
of JGM 2 that the latter's previously calibrated covariance matrix is generally valid.
Received: 14 February 1996 / Accepted: 27 March 1997 相似文献
9.
Performance of three types of Stokes's kernel in the combined solution for the geoid 总被引：8，自引：6，他引：2
When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes
implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion
is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for
the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is
shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the
geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer
a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in
terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best
source of this information.
Received: 11 August 1997 / Accepted: 18 August 1998 相似文献
10.
S. M. Nakiboglu 《Journal of Geodesy》1978,52(2):93-100
A variational principle for the Stokesian boundary value problem is derived using the Euler-Lagrange theory. The resulting
variational principle is then transformed into an equation determining the semi-major axis of the best fitting ellipsoid which
fulfills the conditionU
0
=W
0
.
The computations using three different geopotential models yields the semi-major axis of the earth ellipsoid asa=6378145.4 metres for the flatteningf=1/298.2564. The corresponding equatorial gravity and the geopotential number are computed as γa=978029.59 mgals andU
0=W
0=6.26367371 106 kgalmeters respectively. 相似文献
11.
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
12.
The geopotential coefficients of a number of recent and past models have been examined with the aim of calibrating their formal
(or published) errors, principally by direct comparison with the same coefficients of a precise and wholly independent satellite-only
reference field determined (in 2010) predominantly from over 7 years of μ/s low–low GRACE inter-satellite range rate observations
(ITG-GRACE2010S). In all of these comparisons the reference field used, over specified spectral ranges, has much smaller reported
errors than the ones to be calibrated. In particular we find that a recently published field (in 2010) using gravity gradient
and position data from ESA’s GOCE satellite, GO_CONS_GCF_2_TIM_R1, has formal errors which are significantly optimistic for
the lowest degrees (n) but with increasing realism where the gradiometer gains influence over the position information (15 < n < 120). Other GOCE models do not afford an unbiased error calibration. Validating error calibration with the independent
reference model, of two past comprehensive fields (containing both satellite and surface data), confirms that one of them
(JGM3, published in 1994, complete to n = 70) reported generally realistic formal errors while another (EGM96, published in 1998, complete to n = 360, tested only for n < 150) had significantly optimistic ones for most n < 100 but with better realism when affected only by the surface information. 相似文献
13.
A new gravity map, a new marine geoid around Japan and the detection of the Kuroshio current 总被引：3，自引：0，他引：3
About half a million marine gravity measurements over a 30∘×30∘ area centered on Japan have been processed and adjusted to produce a new free-air gravity map from a 5′×5′ grid. This map
seems to have a better resolution than those previously published as measured by its correlation with bathymetry. The grid
was used together with a high-degree and -order spherical harmonics geopotential model to compute a detailed geoid with two
methods: Stokes integral and collocation. Comparisons with other available geoidal surfaces derived either from gravity or
from satellite altimetry were made especially to test the ability of this new geoid at showing the sea surface topography
as mapped by the Topex/Poseidon satellite. Over 2 months (6 cycles) the dynamic topography at ascending passes in the region
(23∘47∘N and 123∘147∘E) was mapped to study the variability of the Kuroshio current.
Received: 15 July 1994 / Accepted: 17 February 1997 相似文献
14.
A function having some properties of a wavelet and being harmonic around a given point in R
3 is defined, and three models showing the local relationships between the disturbing density, the disturbing potential and
the disturbing gravity are established by using the function as the kernel function of the integrals in the models. The local
relationship has two meanings. One is that we can evaluate with a high accuracy the integrals in the models by using mainly
high-accuracy and high-resolution data in a local area. The other is that we can obtain a stable solution with high resolution
when we invert the integrals in the models because of the rapid decrease of the kernel function of the integrals. As a result,
with these models we evaluate one quantity with high resolution, in a band limited by the maximum degree of a set of geopotential
coefficients or by the resolution (spacing) of the local data, from another quantity (or quantities) in a local area, and
the resulting solution is stable.
Received: 6 April 1998 / Accepted: 16 June 1999 相似文献
15.
给出了勒让德函数4种模式的Clenshaw求和公式,在此基础上得到由全球位系数模型计算重力场参数的二阶Clenshaw求和公式,分析了EGM96与WDM94应用于某试验测区局部重力场的精度,为该测区在构建高精度局部重力场时初始全球位系数模型的选取提供了借鉴。 相似文献
16.
A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission
data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular
geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical
region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable
signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected
to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And
Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused
by great earthquakes such as the 2004 Sumatra–Andaman earthquake can be detected by the low-low tracking and the gradiometer
data within the bandwidths of spherical degrees 15–30 and 25–100, respectively. However, the detection of terrestrial water
storage variation by GOCE gradiometer is equivocal even after localization. 相似文献
17.
The multiresolution character of collocation 总被引：3，自引：0，他引：3
C. Kotsakis 《Journal of Geodesy》2000,74(3-4):275-290
An interesting theoretical connection between the statistical (non-stochastic) collocation principle and the multiresolution/wavelet
framework of signal approximation is presented. The rapid developments in multiresolution analysis theory over the past few
years have provided very useful (theoretical and practical) tools for approximation and spectral studies of irregularly varying
signals, thus opening new possibilities for `non-stationary' gravity field modeling. It is demonstrated that the classic multiresolution
formalism according to Mallat's pioneering work lies at the very core of some of the general approximation principles traditionally
used in physical geodesy problems. In particular, it is shown that the use of a spatio-statistical (non-probabilistic) minimum
mean-square-error criterion for optimal linear estimation of deterministic signals, in conjunction with regularly gridded
data, always gives rise to a generalized multiresolution analysis in the Hilbert space L
2(R), under some mild constraints on the spatial covariance function and the power spectrum of the unknown field under consideration.
Using the theory and the actual approximation algorithms associated with statistical collocation, a new constructive framework
for building generalized multiresolution analyses in L
2(R) is presented, without the need for the usual dyadic restriction that exists in classic wavelet theory. The multiresolution and `non-stationary' aspects of the statistical collocation approximation
procedure are also discussed, and finally some conclusions and recommendations for future work are given.
Received: 26 January 1999 / Accepted: 16 August 1999 相似文献
18.
The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid
(the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern
gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise
Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10−10 Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10−10 Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti
gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new
international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet.
Received: 23 June 2000 / Accepted: 2 January 2001 相似文献
19.
Summary The least-squares collocation method has been used for the computation of a geoid solution in central Spain, combining a geopotential model complete to degree and order 360, gravity anomalies and topographic information. The area has been divided in two 1°× 1° blocks and predictions have been done in each block with gravity data spacing about 5 × 5 within each block, extended 1/2°. Topographic effects have been calculated from 6 × 9 heights using an RTM reduction with a reference terrain model of 30 × 30 mean heights. 相似文献
20.
Erwin Groten 《Journal of Geodesy》1975,49(1):41-56
The application of a Sartorius 4104 microbalance after Gast in vertical gradiometry was tested. A small mass of about 20 grams
is suspended on thin fibers of different lengths Δℓ≤80 cm. From the weight difference of the small mass obtained at different
levels along the plumb line the corresponding differences of gravity along the plumb line are inferred. The microbalance is
mounted on a steal rack; measurements at constant low pressure (moderate vacuum) show the applicability of the balance as
gravity difference sensor for field work. When environmental effects are further reduced (i,e, temperature is kept constant
within ±0.1°C; pressure is controlled within 0.1 Torr etc.) the resolution of the balance can be fully exploited so a relative
accuracy of ±10−9 should be feasible and for laboratory experiments should be of the order of a few parts in ±10−10.
Vertical gravity gradients as observed on an improved moving platform with a LaCoste model G gravimeter are discussed. New
possibilities of microgravimetry are pointed out.
High precision observations and establishment of a system in an area of tectonic interest for detecting secular gravity changes
are described.
Paper presented at the meeting of the “International Gravity Commission”, Paris, September 1974. 相似文献