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1.
Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt 总被引：1，自引：0，他引：1
C. C. Tscherning Awar Radwan A. A. Tealeb S. M. Mahmoud M. Abd El-Monum Ramdan Hassan I. El-Syaed K. Saker 《Journal of Geodesy》2001,75(7-8):343-348
The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and
the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity
data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not
using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with
gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general
gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan
Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using
only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was
in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used,
as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave
difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the
agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances
and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account
for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads.
Received: 14 August 2000 / Accepted: 28 February 2001 相似文献
2.
When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered
at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This
kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation
(LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT).
Results of a regional gravity field recovery in a 10o×20o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated
quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above
degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for
gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows
the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights. 相似文献
3.
4.
Inverse Vening Meinesz formula and deflection-geoid formula: applications to the predictions of gravity and geoid over the South China Sea 总被引：12，自引：0，他引：12
C. Hwang 《Journal of Geodesy》1998,72(5):304-312
Using the spherical harmonic representations of the earth's disturbing potential and its functionals, we derive the inverse
Vening Meinesz formula, which converts deflection of the vertical to gravity anomaly using the gradient of the H function. The deflection-geoid formula is also derived that converts deflection to geoidal undulation using the gradient
of the C function. The two formulae are implemented by the 1D FFT and the 2D FFT methods. The innermost zone effect is derived. The
inverse Vening Meinesz formula is employed to compute gravity anomalies and geoidal undulations over the South China Sea using
deflections from Seasat, Geosat, ERS-1 and TOPEX//POSEIDON satellite altimetry. The 1D FFT yields the best result of 9.9-mgal
rms difference with the shipborne gravity anomalies. Using the simulated deflections from EGM96, the deflection-geoid formula
yields a 4-cm rms difference with the EGM96-generated geoid. The predicted gravity anomalies and geoidal undulations can be
used to study the tectonic structure and the ocean circulations of the South China Sea.
Received: 7 April 1997 / Accepted: 7 January 1998 相似文献
5.
Lars E. Sjöberg 《Journal of Geodesy》1989,63(2):213-221
Integral formulas are derived for the determination of geopotential coefficients from gravity anomalies and gravity disturbances
over the surface of the Earth. First order topographic corrections to spherical formulas are presented. In addition new integral
formulas are derived for the determination of the external gravity field from surface gravity.
Taking advantage of modern satellite positioning techniques, it is suggested that, in general, the external gravity field
as well as individual coefficients are better determined from gravity disturbances than from gravity anomalies. 相似文献
6.
以反解 Stokes公式为数学模型 ,应用由 T/ P测高数据计算的大地水准面高反演了海域平均重力异常 ,并与船测平均重力异常和 OSU91A位模型计算的平均重力异常进行了比对分析 ,得出了一些有益的结论。 相似文献
7.
从经典边值问题理论及球谐函数理论出发,在空域推导获得了由大地水准面高以及垂线偏差计算扰动重力的解析计算公式,为利用卫星测高数据反演海洋扰动重力提供了理论基础。针对全球海洋区域和局部海洋区域的扰动重力反演,在前人已有工作基础上,提出了改进的基于一维FFT的精确快速算法,保证了计算结果与原解析方法完全一致,且计算速度提高约20倍。该算法在提高计算效率的同时避免了由于引入FFT而产生的混叠、边缘效应问题,而且对观测数据的序列长度没有硬性要求,使得应用更加灵活。利用EGM2008地球重力场模型分别生成了2.5'分辨率大地水准面高数据和垂线偏差数据,按照本文提出的改进方法(采用全球积分计算)分别反演获得了全球及局部海洋区域的扰动重力。经比较分析,由大地水准面和垂线偏差分别反演获得的扰动重力其差异在0.8×10-5 m/s2以内,这说明两种反演方法是基本一致的,但在数据包含系统误差的情况下,由垂线偏差反演扰动重力具有一定优势。 相似文献
8.
提出利用地面重力异常数据计算地面扰动位径向二阶梯度，将该梯度的积分表达式转换为卷积形式的谱表达式，便于应用ＦＦＴ／ＦＨＴ技术进行快速计算。这一将地面重力异常化为重力梯度的实用算法为将卫星重力梯度和航空重力梯度观测数据与地面重力数据的联合处理提供了一种有效途径。最后，以本文导出的数学模型为基础，给出了模型（ＷＤＭ９４）数据的试算结果并作了分析 相似文献
9.
飞机运动加速度的测量精度是制约航空重力测量技术发展的主要障碍之一。相较于传统动态差分GPS（differential GPS,DGPS）技术,所提方法采用单站测量模式,无需布设地面基准站。首先通过相位历元间差分解得高精度历元间位移序列,然后结合泰勒一阶中心差分获得载体加速度,重点分析了卫星轨道和卫星钟差对加速度估计的影响,结果表明,不同卫星轨道产品对加速度估计影响较小,而卫星钟差采样率对加速度估计的影响很大。结合中国陕西省境内的GT-2A航空重力测量系统飞行实测数据,利用单站法解算的加速度联合重力和姿态数据解算重力扰动结果与DGPS解算的重力扰动符合较好,当滤波长度为100 s时,两者互差优于1.0 mGal。重力扰动交叉点不符值网平差后,均方根（root mean square,RMS）为1.13 mGal。与地面重力实测值比较的结果表明,所提方法与DGPS方法在精度上基本一致,说明单站法标量航空重力测量是可行的。 相似文献
10.
Gravity anomalies from satellite altimetry: comparison between computation via geoid heights and via deflections of the vertical 总被引：3，自引：0，他引：3
The accumulation of good quality satellite altimetry missions allows us to have a precise geoid with fair resolution and to compute free air gravity anomalies easily by fast Fourier transform (FFT) techniques.In this study we are comparing two methods to get gravity anomalies. The first one is to establish a geoid grid and transform it into anomalies using inverse Stokes formula in the spectral domain via FFT. The second one computes deflection of the vertical grids and transforms them into anomalies.The comparison is made using different data sets: Geosat, ERS-1 and Topex-Poseidon exact repeat misions (ERMs) north of 30°S and Geosat geodetic mission (GM) south of 30°S. The second method which transforms the geoid gradients converted into deflection of the vertical values is much better and the results have been favourably evaluated by comparison with marine gravity data. 相似文献
11.
Estimation of dynamic ocean topography in the Gulf Stream area using the Hotine formula and altimetry data 总被引：3，自引：2，他引：1
Changyou Zhang 《Journal of Geodesy》1998,72(9):499-510
Two modifications of the Hotine formula using the truncation theory and marine gravity disturbances with altimetry data are
developed and used to compute a marine gravimetric geoid in the Gulf Stream area. The purpose of the geoid computation from
marine gravity information is to derive the absolute dynamic ocean topography based on the best estimate of the mean surface
height from recent altimetry missions such as Geosat, ERS-1, and Topex. This paper also tries to overcome difficulties of
using Fast Fourier Transformation (FFT) techniques to the geoid computation when the Hotine kernel is modified according to
the truncation theory. The derived absolute dynamic ocean topography is compared with that from global circulation models
such as POCM4B and POP96. The RMS difference between altimetry-derived and global circulation model dynamic ocean topography
is at the level of 25cm. The corresponding mean difference for POCM4B and POP96 is only a few centimeters. This study also
shows that the POP96 model is in slightly better agreement with the results derived from the Hotine formula and altimetry
data than POCM4B in the Gulf Stream area. In addition, Hotine formula with modification (II) gives the better agreement with
the results from the two global circulation models than the other techniques discussed in this paper.
Received: 10 October 1996 / Accepted: 16 January 1998 相似文献
12.
13.
Computation of spherical harmonic coefficients and their error estimates using least-squares collocation 总被引：4，自引：0，他引：4
C. C. Tscherning 《Journal of Geodesy》2001,75(1):12-18
Equations expressing the covariances between spherical harmonic coefficients and linear functionals applied on the anomalous
gravity potential, T, are derived. The functionals are the evaluation functionals, and those associated with first- and second-order derivatives
of T. These equations form the basis for the prediction of spherical harmonic coefficients using least-squares collocation (LSC).
The equations were implemented in the GRAVSOFT program GEOCOL. Initially, tests using EGM96 were performed using global and
regional sets of geoid heights, gravity anomalies and second-order vertical gravity gradients at ground level and at altitude.
The global tests confirm that coefficients may be estimated consistently using LSC while the error estimates are much too
large for the lower-order coefficients. The validity of an error estimate calculated using LSC with an isotropic covariance
function is based on a hypothesis that the coefficients of a specific degree all belong to the same normal distribution. However,
the coefficients of lower degree do not fulfil this, and this seems to be the reason for the too-pessimistic error estimates.
In order to test this the coefficients of EGM96 were perturbed, so that the pertubations for a specific degree all belonged
to a normal distribution with the variance equal to the mean error variance of the coefficients. The pertubations were used
to generate residual geoid heights, gravity anomalies and second-order vertical gravity gradients. These data were then used
to calculate estimates of the perturbed coefficients as well as error estimates of the quantities, which now have a very good
agreement with the errors computed from the simulated observed minus calculated coefficients. Tests with regionally distributed
data showed that long-wavelength information is lost, but also that it seems to be recovered for specific coefficients depending
on where the data are located.
Received: 3 February 2000 / Accepted: 23 October 2000 相似文献
14.
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
15.
Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earths gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjöberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjöberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area. 相似文献
16.
陈俊勇 《武汉大学学报(信息科学版)》2004,29(5):377-379
现代卫星重力测量主要利用星载GPS接收机、加速度计、星载测距仪等来确定重力卫星的轨道 ,削弱非保守力的干扰 ,由此根据卫星的位置、速度及其变率来确定地球重力场。而上述GPS等星载仪器所提供的数据 ,包括卫星轨道坐标及其速率、扰动加速度、星间距离及其变率 ,都是以三维直角坐标 (x ,y ,z)的形式表示的 ,因此 ,地球重力场、重力和重力梯度在三维直角坐标系中的表达式在卫星重力解算中具有实际意义 相似文献
17.
LUO Jia LI Jiancheng CHAO Dingbo 《地球空间信息科学学报》2003,6(1):19-23
1 ＩｎｔｒｏｄｕｃｔｉｏｎＴｏｄｅｖｅｌｏｐｔｈｅｏｃｅａｎｗｉｄｅｌｙａｎｄｄｅｅｐｌｙ ,ｗｅｎｅｅｄａｂｕｎｄａｎｔｏｃｅａｎｉｎｆｏｒｍａｔｉｏｎ .Ａｓａｎｅｓｓｅｎｔｉａｌｐａｒｔｏｆｓｕｃｈｉｎｆｏｒｍａｔｉｏｎ ,ｓｅａｆｌｏｏｒｔｏｐｏｇｒａｐｈｙｐｌａｙｓａｖｅｒｙｉｍｐｏｒｔａｎｔｒｏｌｅｉｎａｖａｒｉｅｔｙｏｆｍａｒｉｎｅａｃｔｉｖｉｔｉｅｓ .Ｈｏｗｅｖｅｒ,ｔｈｅｈｉｇｈｃｏｓｔｆｏｒｏｃｅａｎｂａｔｈｙｍｅｔｒｉｃｓｕｒｖｅｙｉｎｇｌｉｍｉｔｓｔｈｅａｐｐｌｉｃａｔｉｏｎｏ… 相似文献
18.
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
19.
A formula for computing the gravity disturbance from the second radial derivative of the disturbing potential 总被引：6，自引：0，他引：6
J. Li 《Journal of Geodesy》2002,76(4):226-231
A formula for computing the gravity disturbance and gravity anomaly from the second radial derivative of the disturbing potential
is derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified
Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted
to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the
corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation.
Received: 27 December 2000 / Accepted: 3 September 2001 相似文献
20.
现代低轨卫星对地球重力场探测的实践和进展 总被引：4，自引：4，他引：4
综述了现代低轨卫星对地球重力场测量的特点和近况，介绍了已经和即将发射的重力卫星CHAMP、GRACE、GOCE和新型测高卫星，讨论了作为现代重力卫星首次实践－－CHAMP卫星的进展和目前尚待解决的问题。 相似文献