Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography
Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography
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基于地形球谐展开的不同地形补偿模型的远区效应
DOI：
10.1007/s00190-008-0214-0
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发表时间：
2007
影响因子：
4.4
通讯作者：
Makhloof
中科院分区：
文献类型：
--
作者：
Makhloof
重力大地水准面的确定是基于在地球表面或空中高度观测到的重力大小。为了在大地水准面应用斯托克斯或霍廷公式，大地水准面外部的势必须是谐波的，并且观测到的重力必须减少到大地水准面。因此，大地水准面外部的地形（和大气）质量必须在大地水准面内部“凝聚”或“转移”，以便干扰重力势在大地水准面之外的任何地方都满足拉普拉斯方程。地形补偿质量的重力效应还可用于从机载观测中减去这些高频重力信号并简化向下延续程序。地形补偿质量的影响可以通过基于数字地形模型的数值积分或通过球谐展开来表示地形质量来计算。为了减少前一种情况的计算时间，地球上的积分可以分为两部分：计算点周围的球冠，称为近区，以及世界的其他部分，称为远区。后一种也可以用全局球谐展开式来表示。这可以通过 Molodenskii 型光谱方法来执行。本文扩展了 Novák 等人提出的原始方法。 (J Geod 75(9–10):491–504, 2001)，仅限于确定赫尔默特第二种地面重力测量凝结方法的远区效应。这里提出了赫尔默特第一种凝结方法以及艾里-海斯卡宁模型的全球地形对重力和大地水准面高度的远区影响的公式，并给出了一些改进。此外，这种方法被推广用于确定飞机高度的远区效应。加拿大落基山脉部分地区的数值结果显示了这些影响的大小和分布。
The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potentialTfulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes. Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these effects.
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DOI：
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发表时间：
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期刊：
影响因子：
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作者：
F. R. Helmert
通讯作者：
F. R. Helmert
地形均衡质量对地球表面、机载和卫星高度的重力函数的影响
影响因子：
4.4
作者：
Makhloof
通讯作者：
Makhloof
DOI：
--
发表时间：
2005
期刊：
影响因子：
--
作者：
P. Novák;E. Grafarend
通讯作者：
E. Grafarend
Die Figur der erde。
DOI：
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发表时间：
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期刊：
影响因子：
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作者：
H. Bruns
通讯作者：
H. Bruns
球形地形对重力和大地水准面的影响
影响因子：
4.4
作者：
Pavel Novák;P. Vaníček;Z. Martinec;M. Véronneau
通讯作者：
M. Véronneau