有限范围的重力层间改正算法

doi:10.11947/j.AGCS.2017.20160173

测绘学报 ›› 2017, Vol. 46 ›› Issue (1): 26-33.doi: 10.11947/j.AGCS.2017.20160173

有限范围的重力层间改正算法

马健^1,2, 魏子卿^2,3, 武丽丽⁴, 杨正辉⁵

1. 信息工程大学地理空间信息学院, 河南郑州 450052;
2. 地理信息工程国家重点实验室, 陕西西安 710054;
3. 西安测绘研究所, 陕西西安 710054;
4. 信息工程大学导航与空天目标工程学院, 河南郑州 450052;
5. 长安大学地质工程与测绘学院, 陕西西安 710054

收稿日期:2016-04-19 修回日期:2016-12-29 出版日期:2017-01-20 发布日期:2017-02-06
作者简介:马健(1988-),女,博士生,研究方向为物理大地测量。E-mail:majian_19881006@163.com
基金资助:
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）

The Bouguer Correction Algorithm for Gravity with Limited Range

MA Jian^1,2, WEI Ziqing^2,3, WU Lili⁴, YANG Zhenghui⁵

1. Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450052, China;
2. State Key Laboratory of Geo-information Engineering, Xi'an 710054, China;
3. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China;
4. College of Navigation and Aerospace Engineering, Information Engineering University, Zhengzhou 450052, China;
5. School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, China

Received:2016-04-19 Revised:2016-12-29 Online:2017-01-20 Published:2017-02-06
Supported by:
The National Natural Science Foundation of China (Nos.41674025;41674082);The Open Research Foundation of State Key Laboratory of Geo-information Engineering (No.SKLGIE2016-M-1-5)

摘要/Abstract

摘要： 层间改正是重力归算的一项重要内容，传统的平面层层间改正、球面层层间改正与地形改正的范围不一致，因此均存在远区虚拟地形引入的近似误差，且计算点高度越高，此误差越大。本文提出使用有限范围的层间改正进行重力归算的方法，使其区域范围与地形改正的范围一致。然后给出了有限范围层间改正的简便计算方法，该算法与通过地形改正严密积分法演化来的算法具有较好的一致性。内插试验说明当计算点地形高于1000 m时，内插应使用基于有限范围层间改正的重力归算方法。

关键词: 传统层间改正, 有限范围层间改正, 简便公式, 地形改正严密积分演化公式

Abstract: The Bouguer correction is an important item in gravity reduction, while the traditional Bouguer correction, whether the plane Bouguer correction or the spherical Bouguer correction, exists approximation error because of far-zone virtual terrain. The error grows as the calculation point gets higher. Therefore gravity reduction using the Bouguer correction with limited range, which was in accordance with the scope of the topographic correction, was researched in this paper. After that, a simplified formula to calculate the Bouguer correction with limited range was proposed. The algorithm, which is innovative and has the value of mathematical theory to some extent, shows consistency with the equation evolved from the strict integral algorithm for topographic correction. The interpolation experiment shows that gravity reduction based on the Bouguer correction with limited range is prior to unlimited range when the calculation point is taller than 1000 m.

Key words: the traditional Bouguer correction, the Bouguer correction with limited range, simplified formula, evolution equation from the strict integral algorithm for topographic correction

中图分类号:

P223

马健, 魏子卿, 武丽丽, 杨正辉. 有限范围的重力层间改正算法[J]. 测绘学报, 2017, 46(1): 26-33.

MA Jian, WEI Ziqing, WU Lili, YANG Zhenghui. The Bouguer Correction Algorithm for Gravity with Limited Range[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(1): 26-33.

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有限范围的重力层间改正算法

The Bouguer Correction Algorithm for Gravity with Limited Range

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