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1.
National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals. 相似文献
2.
3.
高精度高程基准重力位的确定往往依赖于高精度全球重力场模型,其对全球和区域高程基准的高精度统一非常关键,GRACE、GOCE卫星重力计划极大地提高了全球重力场模型中长波的精度.本文首先对GRACE/GOCE卫星重力场模型的内符合和外符合精度进行讨论分析,结果说明卫星重力模型的截断误差影响可达到分米级水平,在确定高程基准重力位时该影响不可忽略.利用EGM2008模型扩展GRACE/GOCE卫星重力场模型至2190阶,可有效减弱卫星重力模型的截断误差影响,但不同模型扩展时的最优拼接阶次不同,其中DIR-1、DIR-5模型对应的最优拼接阶次分别为180阶和220阶,以GPS水准数据检验,扩展模型在中国区域的精度均优于18cm.最后,基于最优拼接阶次获得的扩展重力场模型对我国1985高程基准重力位进行了估计,DIR-5和TIM-5模型对应数值分别为62636853.47m~2·s~(-2)和62636853.49m~2·s~(-2),精度均为1.51m~2·s~(-2);发现在中国区域模型大地水准面与GPS/水准数据的差值存在微弱的系统性倾斜,东西向倾斜约为9cm,南北向倾斜约为1.4cm,考虑倾斜改正后基于DIR-5和TIM-5模型估计我国1985高程基准重力位的精度提高了0.16m~2·s~(-2). 相似文献
4.
G. Rodríguez-Caderot M. C. Lacy A. J. Gil B. Blázquez 《Studia Geophysica et Geodaetica》2006,50(4):619-631
This work focuses on the comparison between satellite-only and combined Global Geopotential Models (GGMs) derived from the
CHAMP and GRACE satellite missions with land gravity anomalies, geoid undulations provided by the gravimetric geoid ANDALUSGeoid2002
and GPS/levelling geoid undulations in Andalusia in order to find the GGM that best fits this area in order to be used in
a further geoid computation. The results show that the EIGEN-CG01C model or the combined models GGM02C/EIGEN-CG01C and ITG-CHAMP01E/EIGEN-CG01C
should be used. 相似文献
5.
Determining the maximum degree of harmonic coefficients in geopotential models by Monte Carlo methods 总被引：1，自引：0，他引：1
K. R. Koch r 《Studia Geophysica et Geodaetica》2005,49(3):259-275
Random errors for the harmonic coefficients of a geopotential model are generated from the matrix of normal equations by a parallel computer applying the Gibbs sampler. This leads to random values for the harmonic coefficients. They are transformed by nonlinear, quadratic transformations to random values for the square roots of degree variances, of mean squares of geoid undulations and gravity anomalies. The expected values of these quantities are not equal to the values of these quantities computed by the estimated harmonic coefficients, due to correlations and errors in the estimation. By hypothesis tests estimated harmonic coefficients distorted by correlations and errors are detected. Applying the tests to the geopotential model ITG-CHAMP01 of the Institute of Theoretical Geodesy in Bonn it is concluded that above the degree 62 the harmonic coefficients cannot add any information to the geopotential model. 相似文献
6.
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
7.
This work presents a validation study of global geopotential models (GGM) in the region of Fagnano Lake, located in the southern Andes. This is an excellent area for this type of validation because it is surrounded by the Andes Mountains, and there is no terrestrial gravity or GNSS/levelling data. However, there are mean lake level (MLL) observations, and its surface is assumed to be almost equipotential. Furthermore, in this article, we propose improved geoid solutions through the Residual Terrain Modelling (RTM) approach. Using a global geopotential model, the results achieved allow us to conclude that it is possible to use this technique to extend an existing geoid model to those regions that lack any information (neither gravimetric nor GNSS/levelling observations). As GGMs have evolved, our results have improved progressively. While the validation of EGM2008 with MLL data shows a standard deviation of 35 cm, GOCO05C shows a deviation of 13 cm, similar to the results obtained on land. 相似文献
8.
The aim of this paper is to evaluate the effects of residual terrain model (RTM) on potential and on gravity and to point out how significant can the omission error of global geopotential models (GGMs) be and how it can influence their testing. The RTM for Central Europe is computed in the spherical approximation. The topography is modelled by spherical tesseroids and the gravitational effect of the topography is obtained as a sum of their partial gravitational effects. A detailed picture of RTM in Slovakia is shown. The testing of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) global geopotential models in Central Europe published earlier is re-evaluated with the more rigorous omission error estimation. Experimental results show significantly better agreement between the gravity anomalies computed from global geopotential models with the omission-error estimation and gravity anomalies obtained from the direct measurements. On the other hand, for height anomalies such an improvement is not observed. The results are discussed in context of the other previously published studies. 相似文献
9.
Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global
geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area
mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method
for computation of area mean gravity anomalies in ellipsoidal approximation (‘ellipsoidal area means’) by applying a simple
ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM
quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of
gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal
vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal
area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated
in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid
heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based
geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available
as area mean values. 相似文献
10.
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
11.
The continuous efforts on establishment and modernization of the geodetic control in Turkey include a number of regional geoid
models that have been determined since 1976. The recently released gravimetric Geoid of Turkey, TG03, is used in geodetic
applications where GPS-heights need to be converted to the local vertical datum. To reach a regional geoid model with improved
accuracy, the selection of the appropriate global geopotential model is of primary importance. This study assesses the performance
of a number of recent satellite-only and combined global geopotential models (GGMs) derived from CHAMP and GRACE missions’
data in comparison to the older EGM96 model, which is the underlying reference model for TG03. In this respect, gravity anomalies
and geoid heights from the global geopotential models were compared with terrestrial gravity data and low-pass filtered GPS/levelling
data, respectively. Also, five new gravimetric geoid models, computed by the Fast Fourier Transform technique using terrestrial
gravity data and the geopotential models, were validated at the GPS/levelling benchmarks. The findings were also compared
with the validation results of the TG03 model.
The tests showed that as it was expected any of the high-degree combined models (EIGEN-CG03C, EIGEN-GL04C, EGM96) can be employed
for determining the gravity anomalies over Turkey. In the west of Turkey, EGM96 and EIGEN-CHAMP03S fit the GPS/levelling surface
better. However, all the tested GGMs revealed equal performance when they were employed in gravimetric geoid modelling after
de-trending the gravimetric geoid model with corrector surface fitting. The new geoid models have improved accuracy (after
fit) compared to TG03. 相似文献
12.
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
13.
Satellite gradiometry is an observation technique providing data that allow for evaluation of Stokes’ (geopotential) coefficients.
This technique is capable of determining higher degrees/orders of the geopotential coefficients than can be achieved by traditional
dynamic satellite geodesy. The satellite gradiometry data include topographic and atmospheric effects. By removing those effects,
the satellite data becomes smoother and harmonic outside sea level and therefore more suitable for downward continuation to
the Earth’s surface. For example, in this way one may determine a set of spherical harmonics of the gravity field that is
harmonic in the exterior to sea level.
This article deals with the above effects on the satellite gravity gradients in the local north-oriented frame. The conventional
expressions of the gradients in this frame have a rather complicated form, depending on the first-and second-order derivatives
of the associated Legendre functions, which contain singular factors when approaching the poles. On the contrary, we express
the harmonic series of atmospheric and topographic effects as non-singular expressions. The theory is applied to the regions
of Fennoscandia and Iran, where maps of such effects and their statistics are presented and discussed. 相似文献
14.
GOCE Data Processing: The Spherical Cap Regularization Approach 总被引：3，自引：0，他引：3
Due to the sun-synchronous orbit of the satellite gravity gradiometry mission GOCE, the measurements will not be globally
available. As a consequence, using a set of base functions with global support such as spherical harmonics, the matrix of
normal equations tends to be ill-conditioned, leading to weakly determined low-order spherical harmonic coefficients. The
corresponding geopotential strongly oscillates at the poles.
Considering the special configuration of the GOCE mission, in order to stabilize the normal equations matrix, the Spherical
Cap Regularization Approach (SCRA) has been developed. In this approach the geopotential function at the poles is predescribed
by an analytical continuous function, which is defined solely in the spatially restricted polar regions. This function could
either be based on an existing gravity field model or, alternatively, a low-degree gravity field solution which is adjusted
from GOCE observations. Consequently the inversion process is stabilized.
The feasibility of the SCRA is evaluated based on a numerical closed-loop simulation, using a realistic GOCE mission scenario.
Compared with standard methods such as Kaula and Tikhonov regularization, the SCRA shows a considerably improved performance. 相似文献
15.
RWI_TOPO_2015 is a new high-resolution spherical harmonic representation of the Earth’s topographic gravitational potential that is based on a refined Rock–Water–Ice (RWI) approach. This method is characterized by a three-layer decomposition of the Earth’s topography with respect to its rock, water, and ice masses. To allow a rigorous separate modeling of these masses with variable density values, gravity forward modeling is performed in the space domain using tesseroid mass bodies arranged on an ellipsoidal reference surface. While the predecessor model RWI_TOPO_2012 was based on the \(5'\times 5'\) global topographic database DTM2006.0 (Digital Topographic Model 2006.0), the new RWI model uses updated height information of the \(1'\times 1'\) Earth2014 topography suite. Moreover, in the case of RWI_TOPO_2015, the representation in spherical harmonics is extended to degree and order 2190 (formerly 1800). Beside a presentation of the used formalism, the processing for RWI_TOPO_2015 is described in detail, and the characteristics of the resulting spherical harmonic coefficients are analyzed in the space and frequency domain. Furthermore, this paper focuses on a comparison of the RWI approach to the conventionally used rock-equivalent method. For this purpose, a consistent rock-equivalent version REQ_TOPO_2015 is generated, in which the heights of water and ice masses are condensed to the constant rock density. When evaluated on the surface of the GRS80 ellipsoid (Geodetic Reference System 1980), the differences of RWI_TOPO_2015 and REQ_TOPO_2015 reach maximum amplitudes of about 1 m, 50 mGal, and 20 mE in terms of height anomaly, gravity disturbance, and the radial–radial gravity gradient, respectively. Although these differences are attenuated with increasing height above the ellipsoid, significant magnitudes can even be detected in the case of the satellite altitudes of current gravity field missions. In order to assess their performance, RWI_TOPO_2015, REQ_TOPO_2015, and RWI_TOPO_2012 are validated against independent gravity information of current global geopotential models, clearly demonstrating the attained improvements in the case of the new RWI model. 相似文献
16.
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
17.
Recent satellite missions (CHAMP, GRACE) are now returning data on the time variation of the gravity field with harmonic coefficients computed every 4 weeks. The promise is to achieve a sub-microgal accuracy that will define continental mass variations involving large-scale hydrology. With this in mind, we examine the time varying gravity field over central Europe using a limited number of high quality ground-based superconducting gravimeter stations within the Global Geodynamics Project (GGP). Our purpose is to see whether there are coherent signals between the individual stations and to compare the regional component with that predicted from models of continental hydrology. The results are encouraging. We have found, using empirical orthogonal eigenfunctions of the gravity data that a clear annual signal is present that is consistent in phase (low amplitudes in summer) and amplitude (1–3 microgal) with that determined from a large-scale model of land water in connection with global climate modeling. More work is required to define how the gravity field is related to large-scale soil moisture and other mass variations, and we have yet to compare our results to the latest satellite-derived data. 相似文献
18.
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
19.
The gravity field of the earth is a natural element of the Global Geodetic Observing System (GGOS). Gravity field quantities are like spatial geodetic observations of potential very high accuracy, with measurements, currently at part-per-billion (ppb) accuracy, but gravity field quantities are also unique as they can be globally represented by harmonic functions (long-wavelength geopotential model primarily from satellite gravity field missions), or based on point sampling (airborne and in situ absolute and superconducting gravimetry). From a GGOS global perspective, one of the main challenges is to ensure the consistency of the global and regional geopotential and geoid models, and the temporal changes of the gravity field at large spatial scales. The International Gravity Field Service, an umbrella “level-2” IAG service (incorporating the International Gravity Bureau, International Geoid Service, International Center for Earth Tides, International Center for Global Earth models, and other future new services for, e.g., digital terrain models), would be a natural key element contributing to GGOS. Major parts of the work of the services would, however, remain complementary to the GGOS contributions, which focus on the long-wavelength components of the geopotential and its temporal variations, the consistent procedures for regional data processing in a unified vertical datum and Terrestrial Reference Frame, and the ensuring validations of long-wavelength gravity field data products. 相似文献
20.
JIANG Tao LI JianCheng DANG YaMin ZHANG ChuanYin WANG ZhengTao KE BaoGui 《中国科学:地球科学(英文版)》2014,57(7):1637-1644
Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy,and can provide fundamental information for geophysics,geodynamics,seismology,and mineral exploration.Rectangular harmonic analysis(RHA)is proposed for regional gravity field modeling in this paper.By solving the Laplace’s equation of gravitational potential in local Cartesian coordinate system,the rectangular harmonic expansions of disturbing potential,gravity anomaly,gravity disturbance,geoid undulation and deflection of the vertical are derived,and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients(RHC).We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations.In order to reduce the edge effects caused by periodic continuation in RHA,we propose the strategy of extending the size of computation domain.The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal.The accuracy of the 2.5′×2.5′geoid undulations computed from ground and airborne gravity data is 1 and 1.4cm,respectively.The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 mGal.Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model,which may be a new option for the representation of the fine structure of regional gravity field. 相似文献