基于逆Vening-Meinesz公式的测高重力中央区效应精密计算
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摘要
为提高利用逆Vening-Meinesz公式反演测高重力中央区效应的精度,视中央区为矩形域,将垂线偏差分量表示成双二次多项式插值形式,引入非奇异变换,推导出了重力异常的计算公式。以低纬度区域2′×2′的垂线偏差实际数据为背景场进行了计算,结果表明,当中央区包含4个网格时,传统公式与推导出的重力异常计算公式误差的最大值大于1 mGal。推导出的公式可为高精度测高重力中央区效应的计算提供理论依据。
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.
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.
引文
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[2] 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(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)
[3] 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): 1 421-1 424(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): 1 421-1 424)
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[6] 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 (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)
[7] 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(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)
[8] 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(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)
[9] 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): 1 302-1 307(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): 1 302-1 307)
[10] 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(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)
[11] Bian S F, Sun H Q. The Expression of Common Singular Integrals in Physical Geodesy[J]. Manuscripta Geodaetica, 1994, 19: 62-69
[12] 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(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)
[13] Bian Shaofeng . Some Cubature Formulas for Singular Integrals in Physical Geodesy[J]. Journal of Geodesy, 1997, 71: 443-453
[14] Bian Shaofeng, Xu Jiangning. The Computer Algebra System and Mathematical Analysis in Geodesy[M]. Beijing: National Defense Industry Press, 2004(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)
[15] Li Houpu, Bian Shaofeng, Zhong Bin. Precise Analysis Theory of Geographic Coordinate System by Computer Algebra[M]. Beijing: National Defense Industry Press, 2015(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)
[2] 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(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)
[3] 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): 1 421-1 424(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): 1 421-1 424)
[4] 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): 1 147-1 152(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): 1 147-1 152)
[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] 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 (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)
[7] 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(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)
[8] 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(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)
[9] 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): 1 302-1 307(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): 1 302-1 307)
[10] 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(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)
[11] Bian S F, Sun H Q. The Expression of Common Singular Integrals in Physical Geodesy[J]. Manuscripta Geodaetica, 1994, 19: 62-69
[12] 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(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)
[13] Bian Shaofeng . Some Cubature Formulas for Singular Integrals in Physical Geodesy[J]. Journal of Geodesy, 1997, 71: 443-453
[14] Bian Shaofeng, Xu Jiangning. The Computer Algebra System and Mathematical Analysis in Geodesy[M]. Beijing: National Defense Industry Press, 2004(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)
[15] Li Houpu, Bian Shaofeng, Zhong Bin. Precise Analysis Theory of Geographic Coordinate System by Computer Algebra[M]. Beijing: National Defense Industry Press, 2015(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)