Effects of the spherical terrain on gravity and the geoid
Effects of the spherical terrain on gravity and the geoid
复制标题
球形地形对重力和大地水准面的影响
DOI：
10.1007/s001900100201
复制
发表时间：
2001
影响因子：
4.4
通讯作者：
M. Véronneau
中科院分区：
文献类型：
--
作者：
Pavel Novák;P. Vaníček;Z. Martinec;M. Véronneau
摘要。重力大地水准面的确定是基于在地形表面观测到的重力大小，并应用于势理论的两个边值问题：Dirichlet问题（将重力异常从地形向下延拓到大地水准面）和Stokes问题（将重力异常转化为大地水准面扰动重力势）。由于这两个问题都要求相关函数在大地水准面外处处是调和的，因此必须适当地减小重力。这篇论文讨论了Stokes-Helmert方案中全球地形对重力和大地水准面的远区影响。利用全球地形的球面调和模型和molodenskij型谱方法推导出合适的计算公式。文中给出了加拿大落基山脉部分地区的数值结果，以说明这些影响在精确（即厘米）大地水准面计算中的重要性。它们的遗漏可能导致大地水准面出现长频率偏差，尤其是在山区。由于测试区域的地形粗糙，这些数值可以用作影响的最大全球估计（可能喜马拉雅山脉除外）。本研究是充分模拟地形对重力和大地水准面影响的努力的延续，特别是比较了平面地形板块和球形地形壳对重力和大地水准面影响的研究[Vaníček， Novák, Martinec (2001) J Geod 75: 210-215]。
Abstract. The determination of the gravimetric geoid is based on the magnitude of gravity observed at the topographical surface and applied in two boundary value problems of potential theory: the Dirichlet problem (for downward continuation of gravity anomalies from the topography to the geoid) and the Stokes problem (for transformation of gravity anomalies into the disturbing gravity potential at the geoid). Since both problems require involved functions to be harmonic everywhere outside the geoid, proper reduction of gravity must be applied. This contribution deals with far-zone effects of the global terrain on gravity and the geoid in the Stokes–Helmert scheme. A spherical harmonic model of the global topography and a Molodenskij-type spectral approach are used for a derivation of suitable computational formulae. Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the significance of these effects in precise (i.e. centimetre) geoid computations. Their omission can be responsible for a long-frequency bias in the geoid, especially over mountainous areas. Due to the rough topography of the testing area, these numerical values can be used as maximum global estimates of the effects (maybe with the exception of the Himalayas). This study is a continuation of efforts to model adequately the topographical effects on gravity and the geoid, especially of a comparing the effects of the planar topographical plate and the spherical topographical shell on gravity and the geoid [Vaníček, Novák, Martinec (2001) J Geod 75: 210–215].