中国大陆厘米级大地水准面的地形影响分析

Analysis of Terrain Effects in cm-order Geoid Computations in Chinese Mainland

在分析现有地形影响处理方法的基础上,着重对以下3方面问题进行讨论:其一,在传统平面参考面的地形改正计算方法基础上,基于国际通用的GRS80椭球采用Tesseroid单元体积分法计算地形改正,以适用于山区和地形变化复杂地区的地形改正计算,推导了基于Tesseroid单元体的地形改正算法的泰勒级数展开公式,并验证该方法较传统方法的优越性。其二,目前,大地水准面计算中通常只考虑Molodensky一阶项影响,然而已有结果表明在山区二阶项的影响可达到分米级。针对目前厘米级大地水准面任务,基于Molodensky一阶项算法,给出了二阶项和三阶项对高程异常贡献的严密级数展开式。其三,本文详细讨论了利用地形改正值代替Molodensky级数解计算重力大地水准面的误差影响。

Based on conventional algorithm of terrain effect, three issues are discussed in this paper. Firstly, based on the most common method of dealing with terrain effects related to the planar refer- ence surface, the traditional implementation of ellipsoidal terrain correction based on the GRS80 ellip- soid using tesseroid modeling is proposed for geoid determination in mountainous areas or far zones, and the formulae for the attraction components of potential derivatives is applied. Secondly, usually we only consider the Molodensky＇s first term for geoid computation. Earlier studies however have shown that the effects of Molodensky＇s high-degree terms may be essential in more mountainous areas. On the basis of the demand for a cm-order precision geoid, a suit of simple and applicable formulas to deal with the terrain effects using Molodensky＇s first to three order terms for height anomaly are de- rived based on the algorithm of first-order term. Furthermore, approximation error in cm-order hight anomalies using the terrain correction instead of the Molodensky solution for geoid computation is dis-cussed.