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基于物理大地测量边值问题的解,利用一阶边界算子定义,推导重力异常Δg、单层密度μ、大地水准面高N,垂线偏差ε、扰动重力δg等扰动场元的解。利用球谐函数的正交特性,通过对核函数的算子运算,可以得到上述扰动场元的有关逆变换公式。相对经典物理大地测量公式应用的边界面条件,笔者将含有因子r的对应扰动场元反演关系的公式称为广义积分公式。针对常用的重力异常Δg、大地水准面高N,垂线偏差ε、扰动重力δg计算,重点分析它们之间的变换关系,给出利用某个选定扰动场元计算其他扰动场元的广义积分公式。同时,通过对积分边界面的讨论,分析经典公式与广义积分公式的差异和联系。最后,给出所有外部扰动场元与核函数映射的关系表。 相似文献
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An evaluation of some systematic error sources affecting terrestrial gravity anomalies 总被引:1,自引:2,他引:1
B. Heck 《Journal of Geodesy》1990,64(1):88-108
Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination.
Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a
normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with
respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system.
These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like
e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data.
In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding
systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and
vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The
deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air
gravity anomalies of about −0.10 mgal which value is nearly constant over the continent 相似文献
4.
根据地球重力场参数的计算模型,借助全球地球重力场模型EGM2008,利用Microsoft Visual Studio 2010面向对象的功能,设计和开发了可以计算任意点重力异常、高程异常、垂线偏差分量的计算程序,以德国地学中心(GFZ)研制的相关软件对程序的正确性进行了验证,以吉林省各城市的经纬度数据计算了对应的重力异常、高程异常、垂线偏差分量。 相似文献
5.
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
6.
重力异常和垂线偏差是测高卫星非常重要的产品。二者的精度指标对于未来的测高卫星方案设计至关重要。本文利用球谐函数来对重力异常和垂线偏差的精度指标进行讨论,首先从理论上推导了重力异常和垂线偏差误差的近似匹配关系,然后通过6个超高阶重力场模型验证了有关结论的正确性。数值试验表明:垂线偏差误差和重力异常误差满足近似的比例关系,即若垂线偏差各方位向等精度测量,且假定精度均为1μrad,则所对应的重力异常精度约为1.4mGal;反之,若重力异常的精度为1mGal,则所对应的垂线偏差的精度约为0.7μrad。 相似文献
7.
Johannes Bouman 《Journal of Geodesy》2012,86(4):287-304
The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection
of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations
have found application in satellite altimetry with the implicit assumption that the neglected terms—using remove-restore—are
sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are
made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives
in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives
on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements
on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity
gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected
terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted
for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small
when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical
approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it
appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the
vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term
is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite
altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case
the curvilinear term is needed, which is not readily available. 相似文献
8.
孙腾科 《测绘与空间地理信息》2013,(12):25-27
利用EGM2008地球重力场模型可以将地球重力场解析化,由此我们可以十分方便快速地表示和计算重力异常、高程异常、垂线偏差等其它重力场参数。本文运用Surfer软件将EGM2008重力场模型可视化,获取了全球和局部地区重力场相关参数的等值线图、线框图、3D表面图、影像图。 相似文献
9.
基于重力场水平分量-垂线偏差对地形信息敏感的特点,根据边值理论由重力与地形数据确定格网垂线偏差模型,在此基础上,首先利用三维重力矢量-格网垂线偏差与格网重力异常,联合格网高程数据求得格网点间高程异常差,然后通过GPS/水准点的控制,构成紧密的几何条件,进行严密平差,从而获得高分辨率、高精度似大地水准面的数值模型。按照本文方法,利用我国6600多个GPS/水准点、1'×1'的格网垂线偏差、格网重力异常、格网高程数据,整体平差计算了我国陆海统一的似大地水准面模型,经GPS/水准点检核,全国似大地水准面的绝对精度达到了4 cm,相对精度优于7 cm。 相似文献
10.
H. Nahavandchi 《Journal of Geodesy》2002,76(6-7):345-352
It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might
be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient
model. A `direct' method of geoidal height determination from a global Earth gravity model coefficient alone and an `indirect'
approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In
both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and
indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which
are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield
better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such
improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the
application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is
also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction
terms used for the indirect determination of geoidal heights from height anomalies.
Received: 26 July 2001 / Accepted: 21 February 2002 相似文献