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1.
The satellite missions CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) provide
accurate data that are routinely inverted into spherical harmonic coefficients of the geopotential forming a global geopotential
model (GGM). Mean square errors of these coefficients, in some cases even entire covariance matrices, are included in the
GGM. Due to estimation procedures with a large redundancy and insufficiently propagated observation errors, they often do
not represent the actual accuracy of the harmonic coefficients, thus also gravity field parameters synthesized from the respective
GGM. Since in most cases standard methods validating the GGMs reached their limits, new procedures and independent data are
being currently sought. This article discusses an alternative validation procedure based on comparison of the GGMs with independent
data represented by a set of GPS/leveling stations. Due to a different spectral content of the height anomalies synthesized
from the GGMs and of those derived by combination of GPS-based ellipsoidal and leveled normal heights, the GGM-based low frequency
height anomaly is enhanced for a high frequency component computed from local ground gravity and elevation data. The methodology
is applied on a set of selected points of the European Vertical Reference Network and Czech trigonometric stations. In accordance
with similar tests based on entirely independent data of cross-over altimetry, obtained results seem to indicate low-frequency
deficiencies in the current GGMs, namely in those estimated from data of single-satellite missions. 相似文献
2.
Robert Tenzer Pavel Novák Ilya Prutkin Artu Ellmann Peter Vajda 《Studia Geophysica et Geodaetica》2009,53(2):157-167
To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric
geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration
sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions
to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical
harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation
coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in
solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s
integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly.
We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used
in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities
is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model
and a detailed digital terrain model are used as input data. 相似文献
3.
FFT-based high-performance spherical harmonic transformation 总被引：6，自引：0，他引：6
Spherical harmonic transformation is of practical interest in geodesy for transformation of globally distributed quantities such as gravity between space and frequency domains. The increasing spatial resolution of the latest and forthcoming gravitational models pose true computational challenges for classical algorithms since serious numerical instabilities arise during the computation of the respective base functions of the spherical harmonic expansion. A possible solution is the evaluation of the associated Legendre functions in the Fourier domain where numerical instabilities can be circumvented by an independent frequency-wise scaling of numerical coefficients into a numerically suitable double precision range. It is then rather straightforward to commit global fast data transformation into the Fourier domain and to evaluate subsequently spherical harmonic coefficients. For the inverse, the computation of respective Fourier coefficients from a given spherical harmonic model is performed as an inverse Fast Fourier Transform into globally distributed data points. The two-step formulation turns out to be stable even for very high resolutions as well as efficient when using state-of-the-art shared memory/multi-core architectures. In principle, any functional of the geopotential can be computed in this way. To give an example for the overall performance of the algorithm, we transformed an equiangular 1 arcmin grid of terrain elevation data corresponding to spherical harmonic degree and order 10800. 相似文献
4.
5.
提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。给出球谐函数展开式的Walsh变换及快速算法,讨论了Walsh变换和Walsh-Fourier变换、Fourier变换之间的差异,分析了用地球重力场模型OSU81的位系数作出的Walsh变换和Fourier变换的结果。研究表明:Walsh变换与Walsh-Fourier变换、Fourier变换对应向量在数量方面的差值通常都小于士10~(-5);对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;1°×1°等网格数据和Walsh函数形状相近。在重力场研究中Walsh级数会比Fourier级数收敛得更快;Walsh变换在计算速度、计算准确度、数据储存、收敛速度和方法简单方面都好于Fourier变换。 相似文献
6.
Summary The calibrated variance-covariance matrices of the harmonic geopotential coefficients of the recent combined model JGM 2 has
been tested and verified by independent crossover altimetry from TOPEX/Poseidon and ERS 1 using the Latitude Lumped Coefficients
in the southern oceans area. Although orbits are not yet available for these missions with other recent models for which error
matrices have been released, by comparison with JGM 2 results and field differences we also confirm that the error matrices
for the satellite model GRIM 4S4p and the combined data model JGM 3 are also generally valid. Projections of these matrices
for a variety of inclinations show that many unused orbits of even moderate altitude (≈ 800 km) will still yield trajectory
crossover errors at a level of many tens of centimeters even with the latest orbitgeopotential models. 相似文献
7.
Angel Martin Ana Belén Anquela Jorge Padín José Luís Berné 《Studia Geophysica et Geodaetica》2010,54(3):347-366
A new generation of global geopotential models (GGM) is being developed. These solutions offer a file with fully-normalized
spherical harmonic coefficients of the Earth’s gravitational potential up to a degree greater than 2000 with very low commission
errors. This paper analyses the recent Earth Gravitational Model EGM2008, developed up to degree and order 2159 with additional
coefficients to degree 2190 and order 2159, which means recovering the gravitational field up to approximately 20 km wavelengths.
223 GPS/levelling points of the new Spanish High Precision Levelling Network in the Valencia region (Eastern Spain) are used
as external tool for evaluation in that particular region. The same evaluation has been performed to other different global
(EGM96 and EIGENCG03C), continental (EGG97), regional (IGG2005 and IBERGEO2006) and local (GCV07) geoid models for comparison
purposes only. These comparisons show that EGM2008 is the geoid model that best fits to the GPS/levelling data in that region. 相似文献
8.
从两个方面模拟研究了低低卫-卫跟踪观测技术恢复地球重力场的空间分辨率. 利用重力位系数作为扰动量，积分30天的轨道，研究重力位系数变化引起低低卫-卫跟踪星间距离和速率变化，结果表明，对于地球重力场模型EGM96的前120阶，998%和97%的位系数扰动引起星间距离和速率变化的均方差大于1×１０-５m和１×１０-７m/s，并且星间距离观测值对地球重力场的反应更为敏感. 不考虑非保守力误差的影响，用随机误差为１×１０－５m和１×１０－６m/s的星间距离和速率变化作模拟观测量，恢复了78阶地球重力场位系数，结果表明，采用随机误差为１×１０－５m的星间距离恢复地球重力场的精度明显高于１×１０－６m/s的星间速率结果，但是如果考虑非保守力误差影响，则星间测速的优越性大大增强. 相似文献
9.
Pavel Novák 《Surveys in Geophysics》2010,31(1):1-21
During the General Assembly of the European Geosciences Union in April 2008, the new Earth Gravitational Model 2008 (EGM08)
was released with fully-normalized coefficients in the spherical harmonic expansion of the Earth’s gravitational potential
complete to degree and order 2159 (for selected degrees up to 2190). EGM08 was derived through combination of a satellite-based
geopotential model and 5 arcmin mean ground gravity data. Spherical harmonic coefficients of the global height function, that
describes the surface of the solid Earth with the same angular resolution as EGM08, became available at the same time. This
global topographical model can be used for estimation of selected constituents of EGM08, namely the gravitational potentials
of the Earth’s atmosphere, ocean water (fluid masses below the geoid) and topographical masses (solid masses above the geoid),
which can be evaluated numerically through spherical harmonic expansions. The spectral properties of the respective potential
coefficients are studied in terms of power spectra and their relation to the EGM08 potential coefficients is analyzed by using
correlation coefficients. The power spectra of the topographical and sea water potentials exceed the power of the EGM08 potential
over substantial parts of the considered spectrum indicating large effects of global isostasy. The correlation analysis reveals
significant correlations of all three potentials with the EGM08 potential. The potential constituents (namely their functionals
such as directional derivatives) can be used for a step known in geodesy and geophysics as the gravity field reduction or
stripping. Removing from EGM08 known constituents will help to analyze the internal structure of the Earth (geophysics) as
well as to derive the Earth’s gravitational field harmonic outside the geoid (geodesy). 相似文献
10.
本文试图采用卫星重力资料和一种新的反演方法来研究地幔的横向密度异常分布.先将密度异常△（r,,（?））在一个三维正交函数系下进行展开,其展开系数待定.然后,根据密度异常与重力扰动位之间的关系建立观测方程组,其中未知向量由密度异常展开系数组成,重力扰动观测向量由 GEM10B 重力模型中的位系数计算而得,并通过适当选取重力位系数的阶数,对观测向量进行滤波.最后,就下地幔（670km——CM 界面）作了实际计算.计算中,重力扰动位阶数取为2——11阶,密度异常展开式的截断阶数取为 K=4和 L=6,求解观测方程组时采用阻尼最小二乘法.结果表明:密度扰动值在670km 不连续面及核幔界面处达到极大值,且在环太平洋地区存在一高密度带,太平洋中部对应于一低密度区,这些特征与 Dziewonski 得到的下地幔三维波速异常分布特征相一致.但是,在南极地区、大西洋及印度洋部分地区,所得的密度异常分布与三维波速异常分布呈负相关,文章就其原因作了初步分析. 相似文献
11.
M.A. Khan 《Physics of the Earth and Planetary Interiors》1983,31(3):231-240
Accuracy tests on the most recent GEM (Goddard Earth Model) gravity models for the representation of the Earth's gravity field, using specially devised statistical techniques of comparative evaluation, show that there is steady improvement in these models with time. On this comparative basis, the accuracy of determination for the spherical harmonic coefficients of the Earth's gravity field is ～ 100% for n = 2–6, 90–99% for n = 7–10, 55–80% for n = 11–14 and ? 50% for n ? 15, deteriorating rapidly with increasing n. The higher degree coefficients corresponding to n ≥ 15 do not seem to be determined accurately enough to be useful from a geophysical standpoint, though their cumulative contribution is undoubtedly useful for specific orbital computations. The estimated errors are 0.3 mGal for n = 2–6, 1.5 mgal for the frequency range n = 2–10, 3 mGal for n = 2–14 and 5–6 mGal for n = 2–22. These error estimates, especially the ones for the higher frequency range, may have been affected by possible errors in the comparison standards used for this evaluation. Consequently, some of the higher degree coefficients of recent GEM models may be more accurate than predicted by these tests.Due to the inherent deficiency of the comparison standards, the errors given in this paper should be treated as error estimates. The steady and progressive improvement, shown by the various GEM gravity models when tested against comparison standards 10E and WGS 72, i.e. the more recent a gravity model, the better it tests against the comparison standards in contrast to its predecessors, is remarkable, as the comparison standards themselves are several years older than the gravity models tested here. This clearly validates our choice of comparison standards, as well as the premises and predictions of our evaluation techniques. It also demonstrates the power and potential of these techniques, which only seem to be limited by the level of accuracy of the available standard of comparison. 相似文献
12.
This paper demonstrates estimation of time-varying gravity harmonic coefficients from GPS data of COSMIC and GRACE satellite missions. The kinematic orbits of COSMIC and GRACE are determined to the cm-level accuracy. The NASA Goddard's GEODYN II software is used to model the orbit dynamics of COSMIC and GRACE, including the effect of a static gravity field. The surface forces are estimated per one orbital period. Residual orbits generated from kinematic and reference orbits serve as observables to determine the harmonic coefficients in the weighted-constraint least-squares. The monthly COSMIC and GRACE GPS data from September 2006 to December 2007 (16 months) are processed to estimate harmonic coefficients to degree 5. The geoid variations from the GPS and CSR RL04 (GRACE) solutions show consistent patterns over space and time, especially in regions of active hydrological changes. The monthly GPS-derived second zonal coefficient closely resembles the SLR-derived and CSR RL04 values, and third and fourth zonal coefficients resemble the CSR RL04 values. 相似文献
13.
P. Novák 《Studia Geophysica et Geodaetica》2007,51(3):351-367
Satellite missions CHAMP and GRACE dedicated to global mapping of the Earth’s gravity field yield accurate satellite-to-satellite
tracking (SST) data used for recovery of global geopotential models usually in a form of a finite set of Stokes’s coefficients.
The US-German Gravity Recovery And Climate Experiment (GRACE) yields SST data in both the high-low and low-low mode. Observed
satellite positions and changes in the intersatellite range can be inverted through the Newtonian equation of motion into
values of the unknown geopotential. The geopotential is usually approximated in observation equations by a truncated harmonic
series with unknown coefficients. An alternative approach based on integral inversion of the SST data of type GRACE into discrete
values of the geopotential at a geocentric sphere is discussed in this article. In this approach, observation equations have
a form of Green’s surface integrals with scalar-valued integral kernels. Despite their higher complexity, the kernel functions
exhibit features typical for other integral kernels used in geodesy for inversion of gravity field data. The two approaches
are discussed and compared based on their relative advantages and intended applications. The combination of heterogeneous
gravity data through integral equations is also outlined in the article.
panovak@kma.zcu.cz 相似文献
14.
The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth. 相似文献
15.
A methodology for improving geopotential models has been developed. Theoretical relations have been derived converting coefficients in harmonic expansions for radial distortions due to geopotential models into geopotential Stokes coefficients. Terms of the order of 10
–10
in magnitude have been retained. 相似文献
16.
An investigation is made of the changes produced in the spherical harmonic coefficients of a geomagnetic main field model when values of the total intensity synthesized from the model are systematically perturbed. Corresponding differences between the values of the field components from the original model and those from the perturbed model are also derived. The effects of varying the altitude of the perturbed point and of including a small proportion of component data are discussed. It is shown that significant errors can arise in the region of the dip equator when only scalar data are used, but that these errors can be eliminated if the data set contains 10% of well-distributed component data, some of which refers to the equatorial zone. 相似文献
17.
《Journal of Geodynamics》2009,47(3-5):144-154
Monthly geopotential spherical harmonic coefficients from the GRACE satellite mission are used to determine their usefulness and limitations for studying glacial isostatic adjustment (GIA) in North-America. Secular gravity rates are estimated by unweighted least-squares estimation using release 4 coefficients from August 2002 to August 2007 provided by the Center for Space Research (CSR), University of Texas. Smoothing is required to suppress short wavelength noise, in addition to filtering to diminish geographically correlated errors, as shown in previous studies. Optimal cut-off degrees and orders are determined for the destriping filter to maximize the signal to noise ratio. The halfwidth of the Gaussian filter is shown to significantly affect the sensitivity of the GRACE data (with respect to upper mantle viscosity and ice loading history). Therefore, the halfwidth should be selected based on the desired sensitivity.It is shown that increase in water storage in an area south west of Hudson Bay, from the summer of 2003 to the summer of 2006, contributes up to half of the maximum estimated gravity rate. Hydrology models differ in the predictions of the secular change in water storage, therefore even 4-year trend estimates are influenced by the uncertainty in water storage changes. Land ice melting in Greenland and Alaska has a non-negligible contribution, up to one-fourth of the maximum gravity rate.The estimated secular gravity rate shows two distinct peaks that can possibly be due to two domes in the former Pleistocene ice cover: west and south east of Hudson Bay. With a limited number of models, a better fit is obtained with models that use the ICE-3G model compared to the ICE-5G model. However, the uncertainty in interannual variations in hydrology models is too large to constrain the ice loading history with the current data span. For future work in which GRACE will be used to constrain ice loading history and the Earth's radial viscosity profile, it is important to include realistic uncertainty estimates for hydrology models and land ice melting in addition to the effects of lateral heterogeneity. 相似文献
18.
The Use of Resonant Orbits in Satellite Geodesy: A Review 总被引：1，自引：0，他引：1
J. Klokočník R. H. Gooding C. A. Wagner J. Kostelecký A. Bezděk 《Surveys in Geophysics》2013,34(1):43-72
Dynamic resonance, arising from commensurate (orbital or rotational) periods of satellites or planets with each other, has been a strong force in the development of the solar system. The repetition of conditions over the commensurate periods can result in amplified long-term changes in the positions of the bodies involved. Such resonant phenomena driven by the commensurability between the mean motion of certain artificial Earth satellites and the Earth’s rotation originally contributed to the evaluation and assessment of the Stokes parameters (harmonic geopotential coefficients) that specify the Earth’s gravitational field. The technique constrains linear combinations of the harmonic coefficients that are of relevant resonant order (lumped coefficients). The attraction of the method eventually dwindled, but the very accurate orbits of CHAMP and GRACE have recently led to more general insights for commensurate orbits applied to satellite geodesy involving the best resolution for all coefficients, not just resonant ones. From the GRACE mission, we learnt how to explain and predict temporary decreases in the resolution and accuracy of derived geopotential parameters, due to passages through low-order commensurabilities, which lead to low-density ground-track patterns. For GOCE we suggest how to change a repeat orbit height slightly, to achieve the best feasible recovery of the field parameters derived from on-board gradiometric measurements by direct inversion from the measurements to the harmonic geopotential coefficients, not by the way of lumped coefficients. For orbiters of Mars, we have suggestions which orbits should be avoided. The slow rotation of Venus results in dense ground-tracks and excellent gravitational recovery for almost all orbiters. 相似文献
19.
Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America 总被引：3，自引：1，他引：2
Monthly geopotential spherical harmonic coefficients from the GRACE satellite mission are used to determine their usefulness and limitations for studying glacial isostatic adjustment (GIA) in North-America. Secular gravity rates are estimated by unweighted least-squares estimation using release 4 coefficients from August 2002 to August 2007 provided by the Center for Space Research (CSR), University of Texas. Smoothing is required to suppress short wavelength noise, in addition to filtering to diminish geographically correlated errors, as shown in previous studies. Optimal cut-off degrees and orders are determined for the destriping filter to maximize the signal to noise ratio. The halfwidth of the Gaussian filter is shown to significantly affect the sensitivity of the GRACE data (with respect to upper mantle viscosity and ice loading history). Therefore, the halfwidth should be selected based on the desired sensitivity.It is shown that increase in water storage in an area south west of Hudson Bay, from the summer of 2003 to the summer of 2006, contributes up to half of the maximum estimated gravity rate. Hydrology models differ in the predictions of the secular change in water storage, therefore even 4-year trend estimates are influenced by the uncertainty in water storage changes. Land ice melting in Greenland and Alaska has a non-negligible contribution, up to one-fourth of the maximum gravity rate.The estimated secular gravity rate shows two distinct peaks that can possibly be due to two domes in the former Pleistocene ice cover: west and south east of Hudson Bay. With a limited number of models, a better fit is obtained with models that use the ICE-3G model compared to the ICE-5G model. However, the uncertainty in interannual variations in hydrology models is too large to constrain the ice loading history with the current data span. For future work in which GRACE will be used to constrain ice loading history and the Earth's radial viscosity profile, it is important to include realistic uncertainty estimates for hydrology models and land ice melting in addition to the effects of lateral heterogeneity. 相似文献
20.
Summary An algorithm is derived to compute the coefficients of a spherical harmonic series for the geoid radius vector that are a solution to a system of linear equations, containing Stokes' constants of the geopotential. 相似文献