基于球谐函数的重力异常和垂线偏差误差匹配关系

doi:10.11947/j.AGCS.2017.20160414

测绘学报 ›› 2017, Vol. 46 ›› Issue (6): 706-713.doi: 10.11947/j.AGCS.2017.20160414

基于球谐函数的重力异常和垂线偏差误差匹配关系

万晓云¹, 张润宁², 李洋³, 刘波¹, 眭晓虹^1,3

1. 钱学森空间技术实验室, 北京 100094;
2. 北京空间飞行器总体设计部, 北京 100094;
3. 航天东方红卫星有限公司, 北京 100094

收稿日期:2016-08-22 修回日期:2017-05-18 出版日期:2017-06-20 发布日期:2017-06-28
通讯作者: 张润宁 E-mail:13661051645@139.com
作者简介:万晓云(1985—),男,博士,高级工程师,研究方向为卫星重力测量的理论与方法。E-mail:wxy191954@126.com
基金资助:
国家自然科学基金（41404019；41674026）；中国科学院太空应用重点实验室开放基金（CSU-WX-A-KJ-2016-044）

Matching Relationship between Precisions of Gravity Anomaly and Vertical Deflections in terms of Spherical Harmonic Function

WAN Xiaoyun¹, ZHANG Running², LI Yang³, LIU Bo¹, SUI Xiaohong^1,3

1. Qian Xuesen Laboratory of Space Technology, Beijing 100094, China;
2. Beijing Institute of Spacecraft System Engineering, Beijing 100094, China;
3. DFH Satellite Co.Ltd., Beijing 100094, China

Received:2016-08-22 Revised:2017-05-18 Online:2017-06-20 Published:2017-06-28
Supported by:
The National Natural Science Foundation of China (Nos. 41404019;41674026);The Open Fund of Key Laboratory of Space Utilization, Chinese Academy of Sciences (No.CSU-WX-A-KJ-2016-044)

摘要/Abstract

摘要： 重力异常和垂线偏差是测高卫星非常重要的产品。二者的精度指标对于未来的测高卫星方案设计至关重要。本文利用球谐函数来对重力异常和垂线偏差的精度指标进行讨论，首先从理论上推导了重力异常和垂线偏差误差的近似匹配关系，然后通过6个超高阶重力场模型验证了有关结论的正确性。数值试验表明：垂线偏差误差和重力异常误差满足近似的比例关系，即若垂线偏差各方位向等精度测量，且假定精度均为1 μ rad，则所对应的重力异常精度约为1.4 mGal；反之，若重力异常的精度为1 mGal，则所对应的垂线偏差的精度约为0.7 μ rad。

关键词: 重力异常, 垂线偏差, 精度, 匹配关系

Abstract: Gravity anomalies and vertical deflections are important products of altimetry satellites. The precision indexes of them are essential for the design of future altimetry satellites. In this paper, the spherical harmonic function is used to discuss the precisions of gravity anomaly and vertical deflections. Firstly, the approximate matching relationship between gravity anomaly and vertical deflection error is deduced theoretically. Then, six ultra-high degree gravity field models are used to verify the correctness of the conclusions. The results of numerical experiments show that the errors of vertical defections and gravity anomaly satisfy the approximate proportional relation, that is, if the precision of vertical deflection is 1 μ rad, the precision of gravity anomaly is about 1.4 mGal. Conversely, if the precision of the gravity anomaly is 1 mGal, the precision of the corresponding vertical deflection is about 0.7 μ rad.

Key words: gravity anomaly, vertical deflections, precision, matching relationship

中图分类号:

P228

万晓云, 张润宁, 李洋, 刘波, 眭晓虹. 基于球谐函数的重力异常和垂线偏差误差匹配关系[J]. 测绘学报, 2017, 46(6): 706-713.

WAN Xiaoyun, ZHANG Running, LI Yang, LIU Bo, SUI Xiaohong. Matching Relationship between Precisions of Gravity Anomaly and Vertical Deflections in terms of Spherical Harmonic Function[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(6): 706-713.

参考文献

[1] 许厚泽, 王海瑛, 陆洋, 等. 利用卫星测高数据推求中国近海及邻域大地水准面起伏和重力异常研究[J]. 地球物理学报, 1999, 42(4): 465-471. XU Houze, WANG Haiying, LU Yang, et al. Geoid Undulations and Gravity Anomalies from T/P and ERS-1 Altimeter Data in the China Sea and Vicinity[J]. Chinese Journal of Geophysics, 1999, 42(4): 465-471.
[2] 翟国君, 黄谟涛, 谢锡君, 等. 卫星测高数据处理的理论与方法[M]. 北京: 测绘出版社, 2000. ZHAI Guojun, HUANG Motao, XIE Xijun, et al. The Theory and Method of Satellite Altimeter Data Processing[M]. Beijing: Surveying and Mapping Press, 2000.
[3] 黄谟涛, 翟国君, 管铮, 等. 海洋重力场测定及其应用[M]. 北京: 测绘出版社, 2005. HUANG Motao, ZHAI Guojun, GUAN Zheng, et al. Marine Gravity Field Measurement and Its Application[M]. Beijing: Surveying and Mapping Press, 2005.
[4] 王海瑛, 许厚泽, 王广运. 中国近海海域Geosat卫星测高海平面和海面地形研究[J]. 科学通报, 1997, 42(8): 852-855. WANG Haiying, XU Houze, WANG Guangyun. Research of Mean Sea Surface and Sea Surface Topography of the Seas Adjacent to China from Geosat Mission[J]. Chinese Science Bulletin, 1997, 42(8): 852-855.
[5] 李建成, 金涛勇. 卫星测高技术及应用若干进展[J]. 测绘地理信息, 2013, 38(4): 1-8. LI Jiancheng, JIN Taoyong. On the Main Progress of Satellite Altimetry and Its Applications[J]. Journal of Geomatics, 2013, 38(4): 1-8.
[6] BAO Lifeng, GAO Peng, PENG Hailong, et al. First Accuracy Assessment of the HY-2A Altimeter Sea Surface Height Observations: Cross-calibration Results[J]. Advances in Space Research, 2015, 55(1): 90-105.
[7] BAO Lifeng, XU Houze, LI Zhicai. Towards A 1 mGal Accuracy and 1 Min Resolution Altimetry Gravity Field[J]. Journal of Geodesy, 2013, 87(10-12): 961-969.
[8] SOLTANPOUR A, NAHAVANDCHI H, GHAZAVI K. Recovery of Marine Gravity Anomalies from ERS1, ERS2 and ENVISAT Satellite Altimetry Data for Geoid Computations over Norway[J]. Studia Geophysica et Geodaetica, 2007, 51(3): 369-389.
[9] 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(5): 304-312.
[10] 黄谟涛, 翟国君, 管铮, 等. 利用卫星测高数据反演海洋重力异常研究[J]. 测绘学报, 2001, 30(2): 179-184. HUANG Motao, ZHAI Guojun, GUAN Zheng, et al. On the Recovery of Gravity Anomalies from Altimeter Data[J]. Acta Geodaetica et Cartographica Sinica, 2001, 30(2): 179-184.
[11] 彭富清, 陈双军, 金群峰. 卫星测高误差对海洋重力场反演的影响[J]. 测绘学报, 2014, 43(4): 337-340. DOI: 10.13485/j.cnki.11-2089.2014.0050. PENG Fuqing,CHEN Shuangjun, JIN Qunfeng. Influence of Altimetry Errors on Marine Geopotential Recovery[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(4): 337-340. DOI: 10.13485/j.cnki.11-2089.2014.0050.
[12] SANDWELL D T, SMITH W H, SARAH G, et al. Bathymetry from Space: White Paper in Support of A High-resolution, Ocean Altimeter Mission[C]//Proceedings of High-resolution Ocean Topography Science Working Group Meeting. Version 1.5. [S.l.]: CEOAS, 2001.
[13] 陈俊勇. 高程异常的推估及精度[J]. 测绘通报, 1993(4): 3-8, 22. CHEN Junyong. Estimation and Its Precision of Height Anomaly[J]. Bulletin of Surveying and Mapping, 1993(4): 3-8, 22.
[14] TSCHERNING C C, RAPP R H. Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations and Deflections of the Vertical Implied By Anomaly Degree Variance Models[R]. Reports of the Department of Geodetic Science. No. 208. Columbus, OH: The Ohio State University, 1974.
[15] XU Peiliang. Error Estimates of Velocities and Displacements from Accelerographs[J].Geophysical Journal International, 2012, 188(3): 1061-1064.
[16] 海斯卡涅W A, 莫里兹H. 物理大地测量学[M]. 卢福康, 胡国理, 译. 北京: 测绘出版社, 1979. HEISKANEN W, MORITZ H. Physical Geodesy[M]. LU Fukang, HU Guoli, trans. Beijing: Surveying and Mapping Press, 1979.
[17] 赫尔默特·莫里兹. 高等物理大地测量学[M]. 宁津生, 管泽霖, 译. 北京: 测绘出版社, 1984. MORITZ H. Advanced Physical Geodesy[M]. NING Jinsheng, GUAN Zelin, trans. Beijing: Chinese Surveying Mapping Press, 1984.
[18] FANTINO E, CASOTTO S. Methods of Harmonic Synthesis for Global Geopotential Models and Their First-, Second-and Third-order Gradients[J]. Journal of Geodesy, 2009, 83(7): 595-619.
[19] 万晓云, 于锦海. 极地空白对GOCE引力场恢复的影响[J]. 测绘学报, 2013, 42(3): 317-322. WAN Xiaoyun, YU Jinhai. Influence of Polar Gaps on Gravity Field Recovery Using GOCE Data[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(3): 317-322.
[20] 武汉大学测绘学院测量平差学科组. 误差理论与测量平差基础[M]. 3版. 武汉: 武汉大学出版社, 2014. Survey Adjustment Department of SGG WHU. Error Theory and Foundation of Surveying Adjustment[M]. 3rd ed. Wuhan: Wuhan University Press, 2014.
[21] 万晓云. 引力场梯度张量的非奇异公式推导[J]. 武汉大学学报(信息科学版), 2011, 36(12): 1486-1489. WAN Xiaoyun. New Derivation of Nonsingular Expression for Gravitational Gradients Calculation[J]. Geomatics and Information Science of Wuhan University, 2011, 36(12): 1486-1489.
[22] 于锦海, 万晓云. 计算Legendre函数导数的非奇异方法[J]. 测绘科学技术学报, 2010, 27(1): 1-3, 8. YU Jinhai, WAN Xiaoyun. Non-singular Formula for Computing Derivatives of Legendre Functions[J]. Journal of Geomatics Science and Technology, 2010, 27(1): 1-3, 8.
[23] 刘晓刚, 吴晓平, 赵东明, 等. 扰动重力梯度的非奇异表示[J]. 测绘学报, 2010, 39(5): 450-457. LIU Xiaogang, WU Xiaoping, ZHAO Dongming, et al. Non-singular Expression of the Disturbing Gravity Gradients[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(5): 450-457.
[24] 党诵诗. 物理大地测量的数学基础[M]. 北京: 测绘出版社, 1988. DANG Songshi. Mathematical Foundation of Physical Geodesy[M]. Beijing: Surveying and Mapping Press, 1988.
[25] 魏子卿. 完全正常化缔合勒让德函数及其导数与积分的递推关系[J]. 武汉大学学报(信息科学版), 2016, 41(1): 27-36. WEI Ziqing. Recurrence Relations for Fully Normalized Associated Legendre Functions and Their Derivatives and Integrals[J]. Geomatics and Information Science of Wuhan University, 2016, 41(1): 27-36.
[26] 维纳·K英格尔, 约翰·G·普罗克斯. 数字信号处理(MATLAB版)[M]. 刘树棠, 译. 西安: 西安交通大学出版社, 2009. INGLE V K, PROAKIS J G. Digital Signal Processing Using MATLAB[M]. Liu Shutang, trans. Xi'an: Xi'an Jiaotong University Press, 2009.
[27] 宁津生, 邱卫根, 陶本藻. 地球重力场模型理论[M]. 武汉: 武汉测绘科技大学出版社, 1990. NING Jinsheng, QIU Weigen, TAO Benzao. Theory of Earth Gravity Field Model[M]. Wuhan: Wuhan Surveying and Mapping Science and Technology University Press, 1990.

基于球谐函数的重力异常和垂线偏差误差匹配关系

Matching Relationship between Precisions of Gravity Anomaly and Vertical Deflections in terms of Spherical Harmonic Function

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	郭金运, 金鑫, 边少锋, 常晓涛. 垂线偏差测量的固体潮和海潮改正[J]. 测绘学报, 2022, 51(7): 1215-1224.
[2]	魏子卿. 第二大地边值问题引论[J]. 测绘学报, 2022, 51(6): 797-803.
[3]	王任享, 王建荣. 我国卫星摄影测量发展及其进步[J]. 测绘学报, 2022, 51(6): 804-810.
[4]	黄谟涛, 邓凯亮, 吴太旗, 欧阳永忠, 陈欣, 刘敏, 王许. 重力异常向上延拓严密改化模型及向下延拓应用[J]. 测绘学报, 2022, 51(1): 41-52.
[5]	董杰, 张泽宇, 文汉江, 孙文科. 超导重力数据检测到的2011年日本东北大地震(M_w 9.0)震前重力异常及同震重力变化[J]. 测绘学报, 2022, 51(1): 63-70.
[6]	谢俊峰, 刘仁. 全波形星载激光测距误差抑制的滑动窗口高斯拟合算法[J]. 测绘学报, 2021, 50(9): 1240-1250.
[7]	王乐洋, 李志强. 非线性模型精度评定的Bootstrap方法及其加权采样改进方法[J]. 测绘学报, 2021, 50(7): 863-878.
[8]	李涛, 唐新明, 高小明, 陈乾福, 张祥. SAR卫星业务化地形测绘能力分析与展望[J]. 测绘学报, 2021, 50(7): 891-904.
[9]	范雕, 李姗姗, 欧阳永忠, 孟书宇, 陈成, 邢志斌, 张驰. 顾及海底地形非线性项的最小二乘配置反演方法[J]. 测绘学报, 2021, 50(7): 953-971.
[10]	王乐洋, 陈涛, 邹传义. 病态乘性误差模型的加权最小二乘正则化迭代解法及精度评定[J]. 测绘学报, 2021, 50(5): 589-599.
[11]	袁运斌, 李敏, 霍星亮, 李子申, 王宁波. 北斗三号全球导航卫星系统全球广播电离层延迟修正模型(BDGIM)应用性能评估[J]. 测绘学报, 2021, 50(4): 436-447.
[12]	马小辉, 孙中苗, 张志斌, 张阿丽, 袁野, 孙正雄, 王宏. 利用射电天线轴线信息测定VLBI站点垂线偏差[J]. 测绘学报, 2021, 50(3): 315-323.
[13]	唐新明, 谢俊峰, 莫凡, 窦显辉, 李新, 李少宁, 李松, 黄庚华, 付兴科, 刘仁, 朱广彬, 欧阳斯达, 唐洪钊, 陈辉. 高分七号卫星双波束激光测高仪在轨几何检校与试验验证[J]. 测绘学报, 2021, 50(3): 384-395.
[14]	巩秀强, 袁俊军, 胡小工, 王彬, 陈俊平, 周善石. 北斗广播电文钟差模型精度评估及改善策略[J]. 测绘学报, 2021, 50(2): 181-188.
[15]	李国元, 唐新明, 陈继溢, 么嘉棋, 刘诏, 高小明, 左志强, 周晓青. 高分七号卫星激光测高数据处理与精度初步验证[J]. 测绘学报, 2021, 50(10): 1338-1348.