﻿ 似大地水准面与大地水准面转换分析
 文章快速检索 高级检索
 大地测量与地球动力学  2024, Vol. 44 Issue (8): 853-856  DOI: 10.14075/j.jgg.2023.11.116

### 引用本文

ZHAO Hui, WANG Bin, WANG Wenchao, et al. Analysis of Geoid-Quasigeoid Separation[J]. Journal of Geodesy and Geodynamics, 2024, 44(8): 853-856.

### Foundation support

Science and Technology Innovation Project of Shaanxi Bureau of Surveying, Mapping and Geoinformation, No. SCK2022-03.

### Corresponding author

WANG Wenchao, engineer, majors in geodetic data processing, E-mail: wangwenchao.sd@qq.com.

### About the first author

ZHAO Hui, senior engineer, majors in geodetic data processing, E-mail: zhaohuiln@163.com.

### 文章历史

1. 自然资源部大地测量数据处理中心，西安市友谊东路334号，710054

1 转换方法

 $N-\zeta=\frac{\bar{g}-\bar{\gamma}}{\bar{\gamma}} h$ (1)

 $N-\zeta \approx \frac{\Delta g_{\mathrm{B}}}{\bar{\gamma}} h$ (2)

 $N-\zeta \approx \frac{\Delta g_{\mathrm{B}}}{\bar{\gamma}} h+\frac{V_0^{\mathrm{t}}-V^{\mathrm{t}}}{\bar{\gamma}}-\frac{h^2}{2 \bar{\gamma}} \frac{\partial \Delta g_{\mathrm{B}}}{\partial h}$ (3)

 $\Delta {g_{\rm{B}}} = \Delta g - 2{\rm{\pi }}G{\rho _0}h + {\rm{d}}{g_{tc}}$ (4)

 $\left(\frac{\Delta g_{\mathrm{B}}}{\partial h}\right)_P \approx \frac{R^2}{2 \pi} \iint \frac{\Delta g_{\mathrm{B}}-\left(\Delta g_{\mathrm{B}}\right)_P}{l_0^3} \mathrm{~d} \sigma-\frac{2}{R}\left(\Delta g_{\mathrm{B}}\right)_P$ (5)

2 数值实验与分析

 图 1 实验区地形高程 Fig. 1 Topographic height of the experimental area

 图 2 仅考虑重力改正的计算结果 Fig. 2 Calculation results only considering gravity correction

 图 3 顾及重力改正和地形位差改正的计算结果 Fig. 3 Calculation results considering gravity correction and terrain correction

 图 4 顾及3种改正的计算结果 Fig. 4 Calculation results considering three corrections

 图 5 高程分区严密计算转换统计 Fig. 5 Height zoning statistics according to strict formula

 图 6 地形与转换改正东西方向剖面 Fig. 6 Terrain and correction profile in the east-west direction

 图 7 地形与转换改正南北方向剖面 Fig. 7 Terrain and correction profile in the north-south direction

3 结语

 [1] 党亚民, 蒋涛, 陈俊勇. 全球高程基准研究进展[J]. 武汉大学学报: 信息科学版, 2022, 47(10): 1 576-1 586 (Dang Yamin, Jiang Tao, Chen Junyong. Review on Research Progress of the Global Height Datum[J]. Geomatics and Information Science of Wuhan University, 2022, 47(10): 1 576-1 586) (0) [2] Heiskanen W A, Moritz H. Physical Geodesy[M]. San Francisco: Freeman and Company, 1967 (0) [3] 张赤军. 论(N-ζ)公式的内涵及推求N的精度[J]. 武汉大学学报: 信息科学版, 2005, 30(6): 471-473 (Zhang Chijun. Content and Precision Determining of Difference between Geoid and Quasigeoid[J]. Geomatics and Information Science of Wuhan University, 2005, 30(6): 471-473) (0) [4] 李建成, 陈俊勇, 宁津生, 等. 地球重力场逼近理论与中国2000似大地水准面的确定[M]. 武汉: 武汉大学出版社, 2003 (Li Jiancheng, Chen Junyong, Ning Jinsheng, et al. Earth Gravity Field Approximation Theory and Determination of the Chinese 2000 Qusigeoid[M]. Wuhan: Wuhan University Press, 2003) (0) [5] 徐新强, 赵德军, 楼楠. 顾及高程二次项的大地水准面与似大地水准面之差距[J]. 大地测量与地球动力学, 2013, 33(5): 75-78 (Xu Xinqiang, Zhao Dejun, Lou Nan. A Geoid to Quasigeoid Separation Considering Second Order Height Terms[J]. Journal of Geodesy and Geodynamics, 2013, 33(5): 75-78) (0) [6] Tenzer R, Vaní Ač ek P, Santos M, et al. The Rigorous Determination of Orthometric Heights[J]. Journal of Geodesy, 2005, 79(1): 82-92 (0) [7] Flury J, Rummel R. On the Geoid-Quasigeoid Separation in Mountain Areas[J]. Journal of Geodesy, 2009, 83(9): 829-847 DOI:10.1007/s00190-009-0302-9 (0) [8] Sjöberg L E. A Strict Formula for Geoid-to-Quasigeoid Separation[J]. Journal of Geodesy, 2010, 84(11): 699-702 DOI:10.1007/s00190-010-0407-1 (0) [9] Wang Y M, Veronneau M, Huang J L, et al. Accurate Computation of Geoid-Quasigeoid Separation in Mountainous Region——A Case Study in Colorado with Full Extension to the Experimental Geoid Region[J]. Journal of Geodetic Science, 2023, 13(1) (0) [10] Sjöberg L E. The Geoid-to-Quasigeoid Difference Using an Arbitrary Gravity Reduction Model[J]. Studia Geophysica et Geodaetica, 2012, 56(4): 929-933 DOI:10.1007/s11200-011-9037-1 (0)
Analysis of Geoid-Quasigeoid Separation
ZHAO Hui1     WANG Bin1     WANG Wenchao1     WANG Xiali1     GENG Xiaoyan1
1. Geodetic Data Processing Center, MNR, 334 East-Youyi Road, Xi'an 710054, China
Abstract: The traditional method of geoid-quasigeoid separation is difficult to meet the accuracy requirements in mountainous regions with complex terrain. We use a strict formula to calculate the geoid-quasigeoid separation in the mount Qomolangma area and analyze spatial changes. The results show that the total correction using the strict formula varies from －3.270 m to －0.119 m, the potential correction reaches 1.272 m, and the gravity gradient correction reaches －0.138 m. The magnitude of these corrections is large enough and needs to be taken into account in mountainous areas. The strict method and the approximate method both have a certain correlation with height, and the former produces smoother results than the latter. Under the influence of Bouguer gravity anomaly and terrain changes, some local features of strict method are negatively correlated with height.
Key words: quasigeoid; geoid; Bouguer gravity anomaly; terrain potential correction; gravity gradient correction