| 近区地形直接与间接影响的棱柱模型算法 |
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| 引用本文： | 马健,魏子卿.近区地形直接与间接影响的棱柱模型算法[J].测绘学报,2018,47(11):1429-1436. |
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| 作者姓名： | 马健 魏子卿 |
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| 作者单位： | 1. 地理信息工程国家重点实验室, 陕西 西安 710054;2. 信息工程大学地理空间信息学院, 河南 郑州 450001;3. 西安测绘研究所, 陕西 西安 710054 |
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| 基金项目： | 国家自然科学基金（41674025；41674082）；地理信息工程国家重点实验室开放研究基金（SKLGIE2016-M-1-5；SKLGIE2016-M-3-2） |
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| 摘 要： | 基于Helmert第二压缩法进行边值解算时需要计算地形压缩对重力的直接影响和对（似）大地水准面的间接影响。计算近区直接、间接影响的传统积分算法仍是二重积分形式。该算法以网格中心点处的积分核作为网格积分核的平均值的计算模式在一定程度上引入了近似误差。另外，直接、间接影响的传统积分算法在中央区存在奇异性，需单独计算中央网格地形影响，因而增加了计算的复杂性。为此，本文推导了近区地形直接、间接影响的棱柱模型公式，一方面提高了地形影响的计算精度；另一方面中央区不存在奇异性，从而简化了计算过程。为避免棱柱模型存在的平面近似误差，可使用顾及地球曲率的棱柱模型算法计算地形影响。最后通过试验得出结论，在（似）大地水准面精度要求较高的应用中，应尽量使用顾及地球曲率的棱柱模型算法计算地形影响。
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| 关 键 词： | 近区直接影响 近区间接影响 Helmert第二压缩法 中央奇异性 棱柱模型算法 顾及地球曲率 |
| 收稿时间： | 2017-06-29 |
| 修稿时间： | 2018-02-01 |
Prism Algorithms for the Near-zone Direct and Indirect Topographic Effects |
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| MA Jian,WEI Ziqing.Prism Algorithms for the Near-zone Direct and Indirect Topographic Effects[J].Acta Geodaetica et Cartographica Sinica,2018,47(11):1429-1436. |
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| Authors: | MA Jian WEI Ziqing |
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| Institution: | 1. State Key Laboratory of Geo-information Engineering, Xi'an 710054, China;2. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China;3. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China |
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| Abstract: | It is necessary to calculate the direct effect on gravity and the indirect effects on the geoid and quasi-geoid when reducing the topography based on Helmert's second condensation method for solving boundary value problems. The traditional integration algorithms for the near-zone direct and indirect topographic effects arein the double integral form and give some approximate errors when taking the integral kernel at the center of the grid as the average of the grid integral kernel. Furthermore, the traditional integral algorithms for the direct and indirect effects have singularity in the innermost area, which increases the computational complexity. In this paper, the prism formulae of the near-zone direct and indirect effects are deduced, which improves the calculation accuracy on the one hand and simplifies the computation process by removing the singularity in the innermost area on the other hand. To overcome the planar approximation error of the prism models, the curvature of the earth can be taken into account. Finally, experimental results show that the prism algorithm for the topographic effect considering the earth's curvature is recommended when a high-accuracy geoid/quasi-geoid is required. |
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