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1.
Topographic–isostatic masses represent an important source of gravity field information, especially in the high-frequency
band, even if the detailed mass-density distribution inside the topographic masses is unknown. If this information is used
within a remove-restore procedure, then the instability problems in downward continuation of gravity observations from aircraft
or satellite altitudes can be reduced. In this article, integral formulae are derived for determination of gravitational effects
of topographic–isostatic masses on the first- and second-order derivatives of the gravitational potential for three topographic–isostatic
models. The application of these formulas is useful for airborne gravimetry/gradiometry and satellite gravity gradiometry.
The formulas are presented in spherical approximation by separating the 3D integration in an analytical integration in the
radial direction and 2D integration over the mean sphere. Therefore, spherical volume elements can be considered as being
approximated by mass-lines located at the centre of the discretization compartments (the mass of the tesseroid is condensed
mathematically along its vertical axis). The errors of this approximation are investigated for the second-order derivatives
of the topographic–isostatic gravitational potential in the vicinity of the Earth’s surface. The formulas are then applied
to various scenarios of airborne gravimetry/gradiometry and satellite gradiometry. The components of the gravitational vector
at aircraft altitudes of 4 and 10 km have been determined, as well as the gravitational tensor components at a satellite altitude
of 250 km envisaged for the forthcoming GOCE (gravity field and steady-state ocean-circulation explorer) mission. The numerical
computations are based on digital elevation models with a 5-arc-minute resolution for satellite gravity gradiometry and 1-arc-minute
resolution for airborne gravity/gradiometry. 相似文献
2.
不同于当前广泛使用的空域法、时域法、直接解法,本文尝试采用Torus方法处理GOCE实测数据,利用71 d的GOCE卫星引力梯度数据反演了200阶次GOCE地球重力场模型,实现了对参考模型的精化。首先,采用Butterworth零相移滤波方法加移去—恢复技术,处理引力梯度观测值中的有色噪声,并利用泰勒级数展开和Kriging方法对GOCE卫星引力梯度数据进行归算和格网化,计算得到了名义轨道上格网点处的引力梯度数据。然后,利用2D-FFT技术和块对角最小二乘方法处理名义轨道上数据,获得了200阶次的GOCE地球重力场模型GOCE_Torus。利用中国和美国的GPS/水准数据进行外部检核结果说明,GOCE_Torus与ESA发布的同期模型的精度相当;GOCE_Torus模型与200阶次的EGM2008模型相比,在美国区域精度相当,但在中国区域精度提高了4.6 cm,这充分体现了GOCE卫星观测数据对地面重力稀疏区的贡献。Torus方法拥有快速高精度反演卫星重力场模型的优势,可以在重力梯度卫星的设计、误差分析及在轨快速评估等方面得到充分应用。 相似文献
3.
国际卫星重力梯度测量计划研究进展 总被引：12，自引：2，他引：10
本文首先阐述了重力梯度测量原理、从20世纪初到21世纪初重力梯度仪的研究历程、卫星重力梯度仪(静电悬浮重力梯度仪、超导重力梯度仪和量子重力梯度仪)的技术特征以及卫星重力梯度测量的特点;其次,介绍了基于卫星重力梯度技术恢复250阶GOCE地球重力场以及论证首先开展一维径向重力梯度仪的研制进而恢复高精度和高空间解析度中高频地球重力场可行性方面的研究进展;最后,建议我国尽早开展基于时空域混合法解算中高频地球重力场和卫星重力梯度测量系统误差分析的预先研究。 相似文献
4.
Biao Lu Zhicai Luo Bo Zhong Hao Zhou Frank Flechtner Christoph Förste Franz Barthelmes Rui Zhou 《Journal of Geodesy》2018,92(5):561-572
Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on the gravity field and steady-state ocean circulation explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model’s spherical harmonic coefficients. The linearized observation equations for the least squares method are obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent gravitational gradients (GGs), but the components \(V_{xy}\) and \(V_{yz}\) of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore, we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The spherical cap regularization approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE’s inclination of \(96.7^{\circ }\). With the techniques described above, a degree/order 240 gravity field model called IGGT_R1 is computed. Since the synthetic components of \(V_{xy}\) and \(V_{yz}\) are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore, this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT_R1’s accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/leveling data. 相似文献
5.
Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach 总被引：1，自引：0，他引：1
Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters. 相似文献
6.
应用张量不变理论对利用卫星重力梯度数据确定地球重力场的方法进行了研究,对张量不变观测方程的线性化处理、非全张量观测值的数据处理策略以及采用白噪声特性下的梯度观测值恢复地球重力场的精度等进行了数值分析.结果表明,张量不变解实现了不同观测值的联合求解,基于先验重力场模型的线性化方法在实现张量不变观测模型线性化处理的同时,提... 相似文献
7.
Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition 总被引：3，自引：0，他引：3
We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach
is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm
for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and
block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure.
Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the
algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation
of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime
results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming
satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month
of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations
and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion
strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development
stage, the LSQR method appears ready to deal with real-data applications. 相似文献
8.
利用GOCE模拟观测反演重力场的Torus法 总被引：1，自引：1，他引：0
在介绍Torus方法反演地球重力场模型的基本原理和方法的基础上,基于圆环面上均匀分布的卫星引力梯度模拟观测值解算了200阶次的地球重力场模型,在无误差情况下,Torus方法解算模型的阶误差RMS小于10-16,验证了该方法的严密性。利用61dGOCE卫星轨道上无误差的模拟引力梯度观测值解算了200阶次的地球重力场模型,分析了格网化误差、极空白对解算精度的影响,迭代3次后,在不考虑低次系数情况下,模型的大地水准面阶误差和累积误差均较小,最大值仅为0.022mm和0.099mm。在沿轨卫星引力梯度模拟数据中加入5mE/Hz1/2的白噪声,基于Torus方法和空域最小二乘法解算了200阶次的地球重力场模型,Torus方法的精度略低于空域最小二乘法的精度,在不考虑低次项的情况下,两种方法解算模型的大地水准面阶误差最大值分别为1.58cm和1.45cm,累积误差最大值分别为6.37cm和5.55cm。但由于采用了二维快速傅里叶技术和块对角最小二乘法,极大地提高了计算效率。本文数值结果说明Torus方法是一种独立有效的方法,可用于GOCE任务海量卫星引力梯度观测值反演重力场的快速解算。 相似文献
9.
重力梯度卫星GOCE通过搭载静电式重力梯度仪,将全球静态重力场恢复至200阶以上。目前GOCE卫星已结束寿命,亟须发展下一代更高分辨率的卫星重力梯度测量来完善200~360阶的全球静态重力场模型。原子干涉型的重力梯度测量在空间微重力环境下可获得较长的干涉时间,因此具有很高的星载测量精度,是下一代卫星重力梯度测量的候选技术之一。本文针对未来更高分辨率全球重力场测量的科学需求,提出了一种适用于空间微重力环境下的原子干涉重力梯度测量方案,其梯度测量噪声可低至0.85mE/Hz1/2。文中对不同类型的卫星重力梯度测量方案进行了重力场反演精度的对比评估,仿真结果表明,相比于现有静电式卫星重力梯度测量,原子干涉型的卫星重力梯度测量有望将重力场的恢复阶数提升至252~290阶,对应的累积大地水准面误差7~8cm,累积重力异常误差3×10-5 m/s2。 相似文献
10.
Observable quantities in satellite gradiometry 总被引：1，自引：1，他引：0
Martin Vermeer 《Journal of Geodesy》1990,64(4):347-361
Deriving the observables for satellite gravity gradiometry, several workers have identified the invariants under spatial rotation of the gravitation gradient tensor for obtaining quantities insensitive to the precise (unrecoverable) attitude of the satellite. Extending this work we show:
- Considering that an approximate (not precise) attitude recovery for these, three-axes-stabilised, satellites is to be expected, one can identifythree independent invariants instead of two.
- Besides studying gradient tensor invariants for one observation time, one should also study (as withGPS observables) first and seconddifferences between successive tensor component values in time. Bias and trend patterns in the measured tensor components caused by satellite rotation uncertainty, and by attitude uncertainty in some cross components, are shown to cancel. Information thus obtained is exclusively high-frequency, however.
11.
本文论述了最小二乘过程中有色噪声的处理方法,提出使用AR模型对GOCE梯度观测值中的有色噪声进行时域滤波,数值模拟结果验证了该方法的有效性。利用数值模拟验证了直接求逆方法和PCCG法求解大型法方程的有效性,后者的效率远远高于前者。联合加入噪声（有色噪声和白噪声）的卫星重力梯度张量径向分量观测值Vzz和SST观测值,分别使用空域最小二乘法和SA方法恢复了180阶全球重力场模型,前者求解重力场模型的大地水准面和重力异常在180阶次的精度分别为3.01cm和0.75mGal,优于SA方法求解模型的精度。 相似文献
12.
GOCE gravitational gradients along the orbit 总被引：6，自引：3，他引：3
Johannes Bouman Sophie Fiorot Martin Fuchs Thomas Gruber Ernst Schrama Christian Tscherning Martin Veicherts Pieter Visser 《Journal of Geodesy》2011,85(11):791-805
GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is,
the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational
field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving
the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational
gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational
gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V
XX
, V
YY
, V
ZZ
and V
XZ
are much more accurate than V
XY
and V
YZ
, and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured
GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed.
We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared
their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity
field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is
below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10−3 level. Furthermore, we found that the error of V
XX
and V
YY
is approximately at the level of the requirement on the gravitational gradient trace, whereas the V
ZZ
error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated
GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived
from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially
in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients
is good and that with this type of data valuable new gravity field information is obtained. 相似文献
13.
卫星重力梯度数据解算位系数的最小二乘配置法 总被引：1，自引：0，他引：1
卫星重力梯度测量在恢复地球重力场的研究中已经得到了广泛应用。本文通过空间扰动位协方差函数特性,得出卫星重力梯度数据与引力位系数的相关协方差函数。利用最小二乘配置法,最终推导出由重力梯度数据直接解算引力位系数的函数表达式,并简要分析其实用性。 相似文献
14.
从球冠谐理论出发,详细推导了球冠坐标系下扰动重力梯度的无奇异性计算公式。基于Tikhonov正则化方法,利用GOCE卫星实际观测数据解算局部重力场球冠谐模型。数值计算表明,基于扰动重力梯度的球冠谐分析建模方法能够有效地恢复局部重力场中的短波信号,与GO_CONS_GCF_2_DIR_R5模型的差异在±0.3×10~(-5) m/s~2水平。 相似文献
15.
Large-scale least squares problems require tailored numerical techniques to overcome the computational burden. For these types
of problems, iterative strategies are suitable because of their flexibility and effectiveness. The only shortcoming of iterative
strategies in least squares estimation is that the inverse of the normal equation matrix as the carrier of the covariance
information is either unavailable or very expensive to compute. This paper presents algorithms based on Monte Carlo integration,
which can be incorporated very efficiently into iterative solvers and which are demonstrated to close the aforementioned gap.
Tailored strategies for different types of solution techniques with respect to normal equations, observation equations, and
combined models are treated. Finally, the paper presents new criteria to define confidence regions for the estimated covariance
matrix of the parameters, as well as for all additional derived quantities. In a case study these techniques are applied to
simulated GOCE data, where satellite gravity gradiometry and satellite-to-satellite tracking information are combined for
reconstructing the gravity field. The problem of deriving the covariance matrix of gravity fields with high spatial resolution
by combined iterative estimation processes, unsolved until now, is treated. 相似文献
16.
万晓云 《武汉大学学报(信息科学版)》2011,36(12):1486-1489
传统的引力场梯度计算公式在两极附近存在奇异性,需要换用其他的非奇异计算公式。从奇异性产生的原因入手,并结合勒让德函数的有关性质,推导了一组新的计算公式。实际计算验证了该公式的正确性和有效性。 相似文献
17.
Mission design,operation and exploitation of the gravity field and steady-state ocean circulation explorer mission 总被引：6，自引：3，他引：3
The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March
2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at
a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field
and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived
from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation
and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS)
heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density
inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry
a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of
world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter.
In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible
measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in
as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users. 相似文献
18.
Christian Siemes 《Journal of Geodesy》2018,92(1):33-45
The GOCE gravity gradiometer measured highly accurate gravity gradients along the orbit during GOCE’s mission lifetime from March 17, 2009, to November 11, 2013. These measurements contain unique information on the gravity field at a spatial resolution of 80 km half wavelength, which is not provided to the same accuracy level by any other satellite mission now and in the foreseeable future. Unfortunately, the gravity gradient in cross-track direction is heavily perturbed in the regions around the geomagnetic poles. We show in this paper that the perturbing effect can be modeled accurately as a quadratic function of the non-gravitational acceleration of the satellite in cross-track direction. Most importantly, we can remove the perturbation from the cross-track gravity gradient to a great extent, which significantly improves the accuracy of the latter and offers opportunities for better scientific exploitation of the GOCE gravity gradient data set. 相似文献
19.
2009年GOCE卫星升空以后,卫星重力梯度数据参与解算的GOCE系列重力场模型已有多家研究机构相继公布。本文分别采用青藏地区的GPS/水准和重力异常实测数据对GOCE重力场模型进行了外部测试,并在重力异常验证过程中引入了一种新的滤波方法,验证结果表明在青藏地区GOCE重力场模型相比其它系列模型的优势在于中波段。同时,探讨了GOCE重力场模型与其他系列模型在青藏地区主要差异值的空间分布以及首次利用统计分析方法找出模型之间主要差异值的阶次分布,得出如下结论：模型之间的较大差异值在空间水平方向上主要分布在喜马拉雅山脉、天山等地形起伏较大的区域,在垂直方向上主要集中在岩石圈。 相似文献
20.
F. Wild-Pfeiffer 《Journal of Geodesy》2008,82(10):637-653
Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist
in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour
of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic
reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different
mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed
and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential,
the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different
mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap
and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the
tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements
is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the
most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect
is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The
order of magnitude in the radial-radial component is about ± 8 E.U.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献