确定似大地水准面的Hotine-Helmert边值解算模型

doi:10.11947/j.AGCS.2019.20170594

测绘学报 ›› 2019, Vol. 48 ›› Issue (2): 153-160.doi: 10.11947/j.AGCS.2019.20170594

确定似大地水准面的Hotine-Helmert边值解算模型

马健^1,2,3, 魏子卿^2,3, 任红飞^2,3

1. 信息工程大学地理空间信息学院, 河南郑州 450052;
2. 西安测绘研究所, 陕西西安 710054;
3. 地理信息工程国家重点实验室, 陕西西安 710054

收稿日期:2017-10-17 修回日期:2018-09-10 出版日期:2019-02-20 发布日期:2019-03-02
作者简介:马健(1988-),女,博士,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自主研究基金（SKLGIE2018-ZZ-10）

Hotine-Helmert boundary-value calculation model for quasi-geoid determination

MA Jian^1,2,3, WEI Ziqing^2,3, REN Hongfei^2,3

1. Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450052, China;
2. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China;
3. State Key Laboratory of Geo-information Engineering, Xi'an 710054, China

Received:2017-10-17 Revised:2018-09-10 Online:2019-02-20 Published:2019-03-02
Supported by:
The National Natural Science Foundation of China (Nos. 41674025;41674082);The Independent Research Foundation of State Key Laboratory of Geo-information Engineering (No. SKLGIE2018-ZZ-10)

摘要/Abstract

摘要：

空间大地测量技术的发展使大地高的观测成为可能，从而为第二大地边值问题的研究带来了新的机遇，本文对基于Helmert第二压缩法的第二边值问题（简称为Hotine-Helmert边值问题）展开研究。首先介绍了地形直接、间接影响的定义与算法，然后推导了Hotine-Helmert边值问题的解算模型。Hotine-Helmert边值理论无须计算地形压缩对重力的次要间接影响，因而较Stokes-Helmert边值理论更简单。此外，文中引入了一种低阶修正的Hotine截断核函数，该核函数较传统的截断核函数能有效地改善似大地水准面的解算精度。为了验证本文构建的Hotine-Helmert边值解算模型的有效性和实用性，本文将EIGEN-6C4模型的前360阶作为参考模型，利用Hotine-Helmert边值解算模型构建了我国中部地区6°×4°范围、1.5'×1.5'分辨率的重力似大地水准面，其精度达到±4.8 cm。

关键词: Hotine-Helmert边值解算模型, 地形直接、间接影响, 低阶修正的截断核函数, 似大地水准面

Abstract:

The development of the space geodesy techniques has made it possible to obtain the ellipsoidal height, thus bringing new opportunities for the research of the second geodetic boundary value problem. The Hotine-Helmert boundary value problem, i.e. the second boundary value problem based on the Helmert's second condensation method, is studied in this paper. The definitions and algorithms for the direct and indirect topographic effects are presented at first. Then a calculation model for the Hotine-Helmert boundary value problem is presented in this contribution. The secondary indirect topographic effect on the gravity caused by the terrain condensation is unnecessary in the Hotine-Helmert boundary-value model, making it easier than the Stokes-Helmert boundary-value model. Furthermore, a kind of spheroidal Hotine kernel function whose low degrees are modified is introduced, which can effectively improve the accuracy of the quasi-geoid compared with the traditional spheroidal kernel. In order to verify the validity and practicability of the Hotine-Helmert boundary-value calculation model, the gravimetric quasi-geoid in central China with the area of 6°×4° and the resolution of 1.5'×1.5' is solved according to the Hotine-Helmert boundary-value model, using the first 360 degrees of EIGEN-6C4 model as the reference model. The accuracy of the determined gravimetric quasi-geoid in the test area is ±4.8 cm.

Key words: Hotine-Helmert boundary-value calculation model, the direct and indirect topographic effects, the low-degree modified spheroidal Hotine kernel, quasi-geoid

中图分类号:

P223

马健, 魏子卿, 任红飞. 确定似大地水准面的Hotine-Helmert边值解算模型[J]. 测绘学报, 2019, 48(2): 153-160.

MA Jian, WEI Ziqing, REN Hongfei. Hotine-Helmert boundary-value calculation model for quasi-geoid determination[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(2): 153-160.

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确定似大地水准面的Hotine-Helmert边值解算模型

Hotine-Helmert boundary-value calculation model for quasi-geoid determination

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