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Volume 44 Issue 2
Feb.  2019
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LI Houpu, BIAN Shaofeng, JI Bing, CHEN Yongbing. Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 200-205. doi: 10.13203/j.whugis20150744
 Citation: LI Houpu, BIAN Shaofeng, JI Bing, CHEN Yongbing. Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 200-205.

# Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula

##### doi: 10.13203/j.whugis20150744
Funds:

The National Natural Science Foundation of China 41631072

The National Natural Science Foundation of China 41771487

The National Natural Science Foundation of China 41474061

• Author Bio:

LI Houpu, PhD, associate professor, specializes in the mathematical analysis of geodesy. E-mail: lihoupu1985@126.com

• Corresponding author: BIAN Shaofeng, PhD, professor. E-mail:sfbian@sina.com
• Publish Date: 2019-02-05
• In order to improve the precision of the innermost area effects in altimetry gravity computed by the inverse Vening-Meinesz formula, deflections of the vertical are expressed as bi-quadratic polynomials regarding the innermost area as a rectangular one, and the formulas to calculate gravity anomaly of this area are derived after the non-singular transformation is introduced. A practical calculation is done based on deflections of the vertical data with a resolution of in the low latitude area. The results indicate that the maximal difference between the contributions of the innermost area including four grids calculated by traditional formulas and this paper's formulas is greater than 1 mGal. The formulas derived in this paper can provide theoretical basis for the innermost area effects in altimetry gravity with high precision.
•  [1] 王泽民, 张保军, 姜卫平, 等.联合卫星测高、GRACE、海洋和气象资料研究南海海水质量变化[J].武汉大学学报·信息科学版, 2018, 43(4):571-577 http://ch.whu.edu.cn/CN/abstract/abstract6023.shtml Wang Zhemin, Zang Baomin, Jiang Weiping, et al. Ocean Mass Variations in the South China Sea Inferred from Satellite Altimetry, GRACE, Oceanographic and Meteorological Data[J]. Geomatics and Information Science of Wuhan University, 2018, 43(4):571-577 http://ch.whu.edu.cn/CN/abstract/abstract6023.shtml [2] 汪海洪, 罗北.计算测高卫星地面轨迹交叉点的快速数值算法[J].武汉大学学报·信息科学版, 2017, 42(3):293-298 http://ch.whu.edu.cn/CN/abstract/abstract5676.shtml Wang Haihong, Luo Bei. Fast Numerical Algorithm for the Calculation of Altimetric Crossovers from Satellite Ground Tracks[J]. Geomatics and Information Science of Wuhan University, 2017, 42(3):293-298 http://ch.whu.edu.cn/CN/abstract/abstract5676.shtml [3] 李大伟, 李建成, 金涛勇, 等.利用多代卫星测高资料监测1993-2011年全球海平面变化[J].武汉大学学报·信息科学版, 2012, 37(12):1421-1424 http://ch.whu.edu.cn/CN/abstract/abstract394.shtml Li Dawei, Li Jiancheng, Jin Taoyong, et al. Monitoring Global Sea Level Change from 1993 to 2011 Using TOPEX and Jason Altimeter Missions[J]. Geomatics and Information Science of Wuhan University, 2012, 37(12):1421-1424 http://ch.whu.edu.cn/CN/abstract/abstract394.shtml [4] 黄谟涛, 欧阳永忠, 刘敏, 等.海域航空重力测量数据向下延拓的实用方法[J].武汉大学学报·信息科学版, 2014, 39(10):1147-1152 http://ch.whu.edu.cn/CN/abstract/abstract3085.shtml Huang Motao, Ouyang Yongzhong, Liu Min, et al. Practical Methods for the Downward Continuation of Airborne Gravity Data in the Sea Area[J]. Geomatics and Information Science of Wuhan University, 2014, 39(10):1147-1152 http://ch.whu.edu.cn/CN/abstract/abstract3085.shtml [5] Hwang C. Inverse Vening Meinesz Formula and Deflection-Geoid Formula:Applications to the Predictions of Gravity and Geoid over the South China Sea[J]. Journal of Geodesy, 1998, 72:304-312 [6] 王瑞, 李厚朴.基于逆Stokes公式的测高重力反演中央区效应计算[J].武汉大学学报·信息科学版, 2010, 35(4):467-470 http://ch.whu.edu.cn/CN/abstract/abstract907.shtml Wang Rui, LI Houpu. Calculation of Innermost Area Effects in Altimetry Gravity Recovery Based on the Inverse Stokes Formula[J]. Geomatics and Information Science of Wuhan University, 2010, 35(4):467-470 http://ch.whu.edu.cn/CN/abstract/abstract907.shtml [7] 李厚朴, 边少锋.利用垂线偏差计算大地水准面中央区效应的改进方法[J].测绘学报, 2011, 40(6):730-735 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201104083041 Li Houpu, Bian Shaofeng. The Improved Method of Calculating the Geoid Innermost Area Effects Using Deflections of the Vertical[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(6):730-735 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201104083041 [8] 黄谟涛, 王瑞, 翟国君, 等.多代卫星测高数据联合平差及重力场反演[J].武汉大学学报·信息科学版, 2007, 32(11):988-993 http://ch.whu.edu.cn/CN/abstract/abstract2021.shtml Huang Motao, Wang Rui, Zhai Guojun, et al. Integrated Data Processing for Multi-satellite Missions and Recovery of Marine Gravity Field[J]. Geomatics and Information Science of Wuhan University, 2007, 32(11):988-993 http://ch.whu.edu.cn/CN/abstract/abstract2021.shtml [9] 常晓涛, 李建成, 章传银, 等.测高重力内区效应的推导与计算[J].地球物理学报, 2005, 48(6):1302-1307 Chang Xiaotao, Li Jiancheng, Zhang Chuanyin, et al. Deduction and Estimation of Innermost Zone Effects in Altimetry Gravity Algorithm[J]. Chinese Journal of Geophysics, 2005, 48(6):1302-1307 [10] 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. The Approximation Theory of the Earth's Gravity Field and Determination of the 2000 Quasi Geoid in China[M]. Wuhan:Wuhan University Press, 2003 [11] Bian S F, Sun H Q. The Expression of Common Singular Integrals in Physical Geodesy[J]. Manuscripta Geodaetica, 1994, 19:62-69 [12] 边少锋.大地测量边值问题数值解法与地球重力场逼近[D].武汉: 武汉测绘科技大学, 1992 Bian Shaofeng. Numerical Solution for Geodetic Boundary Value Problem and the Earth's Gravity Field Approximation[D]. Wuhan: Wuhan Technical University of Surveying and Mapping, 1992 [13] Bian Shaofeng. Some Cubature Formulas for Singular Integrals in Physical Geodesy[J]. Journal of Geodesy, 1997, 71:443-453 [14] 边少锋, 许江宁.计算机代数系统与大地测量数学分析[M].北京:国防工业出版社, 2004 Bian Shaofeng, Xu Jiangning. The Computer Algebra System and Mathematical Analysis in Geodesy[M]. Beijing:National Defense Industry Press, 2004 [15] 李厚朴, 边少锋, 钟斌.地理坐标系计算机代数精密分析理论[M].北京:国防工业出版社, 2015 Li Houpu, Bian Shaofeng, Zhong Bin. Precise Analysis Theory of Geographic Coordinate System by Computer Algebra[M]. Beijing:National Defense Industry Press, 2015
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

Figures(4)  / Tables(1)

## Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula

##### doi: 10.13203/j.whugis20150744
###### 1. Department of Navigation, Naval University of Engineering, Wuhan 430033, China
Funds:

The National Natural Science Foundation of China 41631072

The National Natural Science Foundation of China 41771487

The National Natural Science Foundation of China 41474061

• Author Bio:

• ###### Corresponding author:BIAN Shaofeng, PhD, professor. E-mail:sfbian@sina.com

Abstract: In order to improve the precision of the innermost area effects in altimetry gravity computed by the inverse Vening-Meinesz formula, deflections of the vertical are expressed as bi-quadratic polynomials regarding the innermost area as a rectangular one, and the formulas to calculate gravity anomaly of this area are derived after the non-singular transformation is introduced. A practical calculation is done based on deflections of the vertical data with a resolution of in the low latitude area. The results indicate that the maximal difference between the contributions of the innermost area including four grids calculated by traditional formulas and this paper's formulas is greater than 1 mGal. The formulas derived in this paper can provide theoretical basis for the innermost area effects in altimetry gravity with high precision.

LI Houpu, BIAN Shaofeng, JI Bing, CHEN Yongbing. Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 200-205. doi: 10.13203/j.whugis20150744
 Citation: LI Houpu, BIAN Shaofeng, JI Bing, CHEN Yongbing. Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula[J]. Geomatics and Information Science of Wuhan University, 2019, 44(2): 200-205.
• 20世纪70年代，卫星测高技术的出现以及多个卫星测高任务的顺利实施为人们获取全球海域高精度、高分辨率的海面高数据提供了极大的便利。利用卫星测高数据推求海域重力异常是卫星测高在大地测量研究中的主要应用，国内外许多学者对此进行了大量的研究，取得了丰富的研究成果[1-9]。其中，逆Vening-Meinesz公式法的输入量为垂线偏差，而垂线偏差是由测高观测值的一次差分求得，可以消除与地理位置相关的径向轨道误差和长波海面地形等类似系统误差，同时含有丰富的重力场高频成分，非常有利于高分辨率海洋重力场的恢复。因此，逆Vening-Meinesz公式在测高重力反演中的应用较为广泛[10]

在计算点本身及其附近区域计算重力异常时，积分区域包含计算点，导致逆Vening-Meinesz公式中的积分奇异，本文称该积分区域为中央区。Hwang[5]将中央区视为圆域，推导出了中央区重力异常的计算公式；常晓涛等[9]将中央区视为方形域，推导出了中央区效应的计算公式，指出中央区效应与奇异区内垂线偏差分量的梯度及奇异区面积的大小有关。由于实际数据通常为网格化分布，受子午线收敛的影响，中央区更接近于矩形域，因此，将中央区视为圆域和方形域的处理方法与数据真实分布情况并不相符，由此产生的误差在高精度重力反演中能否忽略值得深入研究。鉴于此，本文推导出了视中央区为矩形域时的重力异常计算公式，并对导出公式和圆域与方形域下传统公式的误差进行了分析比较。

Reference (15)

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