全球及局部海洋扰动重力反演的快速解析方法

doi:10.11947/j.AGCS.2015.20140482

测绘学报 ›› 2015, Vol. 44 ›› Issue (8): 827-832.doi: 10.11947/j.AGCS.2015.20140482

• 大地测量学与导航 • 下一篇

全球及局部海洋扰动重力反演的快速解析方法

翟振和^1,2, 孙中苗², 王兴涛²

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

收稿日期:2014-09-15 修回日期:2014-12-15 出版日期:2015-09-20 发布日期:2015-09-02
作者简介:翟振和(1980-),男,博士生,研究方向为地球重力场及卫星测高。E-mail:zhaizhenhe1980@163.com
基金资助:
国家自然科学基金项目(41174017)

The Analytical and Quick Computation Method of Disturbing Gravity in Global and Local Ocean Area

ZHAI Zhenhe^1,2, SUN Zhongmiao², WANG Xingtao²

1. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450052, China;
2. Xi'an Institute of Surveying and Mapping, Xi'an 710054, China

Received:2014-09-15 Revised:2014-12-15 Online:2015-09-20 Published:2015-09-02
Supported by:
The National Natural Science Foundation of China(No. 41174017)

摘要/Abstract

摘要： 从经典边值问题理论及球谐函数理论出发,在空域推导获得了由大地水准面高以及垂线偏差计算扰动重力的解析计算公式,为利用卫星测高数据反演海洋扰动重力提供了理论基础。针对全球海洋区域和局部海洋区域的扰动重力反演,在前人已有工作基础上,提出了改进的基于一维FFT的精确快速算法,保证了计算结果与原解析方法完全一致,且计算速度提高约20倍。该算法在提高计算效率的同时避免了由于引入FFT而产生的混叠、边缘效应问题,而且对观测数据的序列长度没有硬性要求,使得应用更加灵活。利用EGM2008地球重力场模型分别生成了2.5'分辨率大地水准面高数据和垂线偏差数据,按照本文提出的改进方法(采用全球积分计算)分别反演获得了全球及局部海洋区域的扰动重力。经比较分析,由大地水准面和垂线偏差分别反演获得的扰动重力其差异在0.8×10^-5 m/s²以内,这说明两种反演方法是基本一致的,但在数据包含系统误差的情况下,由垂线偏差反演扰动重力具有一定优势。

关键词: 大地测量, 扰动重力, 大地水准面, 垂线偏差, 快速算法

Abstract: In order to solve the problem of deriving the disturbing gravity from satellite altimetry data, the analytical formula of disturbing gravity computed from geoid and vertical deflection are derived. The analytical formula can be used to get global ocean disturbing gravity by using altimetry data. Considering the existing achievements, the two improved quick computation methods which are respectively according to the global and local area are also get based on the one dimensional FFT algorithm. The quick computation methods can get the same results as the analytical computation and improve the computation speed of 20 times. The precise, quick computation methods can avoid the problem of aliasing and edge effects and have the flexible application. The 2.5' resolution of geoid and vertical deflection derived from EGM2008 model are used to compute the global and local ocean disturbing gravity. The results show that the difference between two method is about 0.8×10^-5 m/s², so the disturbing gravity respectively derived from geoid and vertical deflection are consistent. Considering the actual situation, the disturbing gravity derived from vertical deflection still has some advantages.

Key words: geodesy, disturbing gravity, geoid, vertical deflection, quick algorithm

中图分类号:

P223

翟振和, 孙中苗, 王兴涛. 全球及局部海洋扰动重力反演的快速解析方法[J]. 测绘学报, 2015, 44(8): 827-832.

ZHAI Zhenhe, SUN Zhongmiao, WANG Xingtao. The Analytical and Quick Computation Method of Disturbing Gravity in Global and Local Ocean Area[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(8): 827-832.

参考文献

[1] GUAN Zelin,GUAN Zheng,HUANG Motao,et al. Local Gravity Field Approximation Theory and Method[M]. Beijing: Surveying and Mapping Press,1997. (管泽霖,管铮,黄谟涛,等. 局部重力场逼近理论和方法[M]. 北京: 测绘出版社,1997.)
[2] VANÍČEK P,ZHANG Changyou,SJÖBERG L E. A Comparison of Stokes and Hotine's Approaches to Geoid Computation[J]. Manuscripta Geodaetica,1992,17: 29-35.
[3] CLAESSENS S. Solutions to the Ellipsoidal Boundary Value Problems for Gravity Field Modelling[D]. Curtin: Curtin University of Technology,2006.
[4] WU Xiaoping,LI Shanshan,ZHANG Chuanding. Problem of the Boundary Value of Disturbing Gravity and Practical Data Processing[J]. Geomatics and Information Science of Wuhan University,2003,28(S): 73-76. (吴晓平,李姗姗,张传定. 扰动重力边值问题与实际数据处理的研究[J]. 武汉大学学报: 信息科学版,2003,28(特刊): 73-76.)
[5] LI Fei,CHEN Wu,YUE Jianli. Physical Geodesy with GPS[J]. Acta Geodaetica et Cartographica Sinica,2003,32(3): 198-203. (李斐,陈武,岳建利. GPS在物理大地测量中的应用及GPS 边值问题[J]. 测绘学报,2003,32(3): 198-203.)
[6] SANDWELL D T,SMITH W H F. Marine Gravity Anomaly from Geosat and Ers 1 Satellite Altimetry[J]. Journal of Geophysical Research,1997,102(B5): 10039-10054.
[7] 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.
[8] COLOMBO O L. Numerical Methods for Harmonic Analysis on the Sphere[R]. Ohio: The Ohio State University, 1981.
[9] FORSBERG R,SIDERIS M G. Geoid Computations by the Multi-banding Spherical FFT Approach[J]. Manuscripta Geodaetica,1993,18(2): 82-90.
[10] HAAGMANS R,DE MIN E,GELDEREN M V. Fast Evaluation of Convolution Integrals on the Sphere Using 1D FFT,and a Comparison with Existing Methods for Stokes' Integral[J]. Manuscripta Geodaetica,1993,18(5): 227-241.
[11] SCHWARZ K P,SIDERIS M G,FORSBERG R. The Use of FFT Techniques in Physical Geodesy[J]. Geophysical Journal International,1990,100(3): 485-514.
[12] LI Jiancheng,CHEN Junyong,Ning Jinsheng,et al. The Earth's Gravitational Field Approximation Theory and the Determination of China 2000 Quasi-geoid[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.)
[13] 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): 179-183. (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): 179-183.)
[14] LI Jiancheng,NING Jinsheng,CHAO Dingbo,et al. The Applications and Progress of Satellite Altimetry in Geodesy[J]. Science of Surveying and Mapping,2006,31(6): 19-21. (李建成,宁津生,晁定波,等. 卫星测高在大地测量学中的应用及进展[J]. 测绘科学,2006,31(6): 19-21.)
[15] HUANG Motao,ZHAI Guojun,GUAN Zheng,et al. Marine Gravity Field Measurement and Its Applications[M]. Beijing: Surveying and Mapping Press,2005. (黄谟涛,翟国军,管铮,等. 海洋重力场测定及其应用[M]. 北京: 测绘出版社,2005.)
[16] WANG Bing,SHEN Weichang,TIAN Laike,et al. A Study on the Problem of Add Zero in the Algorithm of Cooley-Tukey Fast Fourier Transform[J]. Journal of Northwest University: Natural Science Edition,2004,34(1): 31-33. (王冰,申卫昌,田来科,等. 快速傅里叶变换Cooley-Tukey算法补零问题[J]. 西北大学学报: 自然科学版,2004,34(1): 31-33.)
[17] PAVLIS N K,HOLMES S A,KENYON S C,et al. An Earth Gravitational Model to Degree 2160: EGM2008[C]. Vienna,Austria: EGU General Assembly 2008,2008.
[18] HOFMANN-WELLENHOF B,MORITZ H. Physical Geodesy[M]. New York: Springer Wien,2006.

全球及局部海洋扰动重力反演的快速解析方法

The Analytical and Quick Computation Method of Disturbing Gravity in Global and Local Ocean Area

PDF

可视化

被引次数

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]	姜卫平, 李昭, 魏娜, 刘经南. 大地测量坐标框架建立的进展与思考[J]. 测绘学报, 2022, 51(7): 1259-1270.
[3]	魏子卿. 第二大地边值问题引论[J]. 测绘学报, 2022, 51(6): 797-803.
[4]	党亚民, 郭春喜, 蒋涛, 张庆涛, 陈斌, 蒋光伟. 2020珠峰测量与高程确定[J]. 测绘学报, 2021, 50(4): 556-561.
[5]	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.
[6]	张胜军, 李建成, 孔祥雪. 基于Laplace方程的垂线偏差法反演全球海域重力异常[J]. 测绘学报, 2020, 49(4): 452-460.
[7]	姚宜斌, 杨元喜, 孙和平, 李建成. 大地测量学科发展现状与趋势[J]. 测绘学报, 2020, 49(10): 1243-1251.
[8]	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.
[9]	邢志斌, 李姗姗. 我国陆海统一似大地水准面构建的三维重力矢量法[J]. 测绘学报, 2018, 47(5): 575-583.
[10]	王虎彪, 王勇, 柴华, 鲍李峰. 中国西太平洋海域1'×1'垂线偏差模型及精度评估[J]. 测绘学报, 2017, 46(9): 1073-1079.
[11]	许厚泽. 全球高程系统的统一问题[J]. 测绘学报, 2017, 46(8): 939-944.
[12]	刘磊, 郑为民, 张娟, 舒逢春, 童锋贤, 童力. 中国VLBI网软件相关处理机测地应用精度分析[J]. 测绘学报, 2017, 46(7): 805-814.
[13]	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.
[14]	王燚, 姜效典. 扰动重力梯度的球冠谐分析建模[J]. 测绘学报, 2017, 46(11): 1802-1811.
[15]	张勤, 黄观文, 杨成生. 地质灾害监测预警中的精密空间对地观测技术[J]. 测绘学报, 2017, 46(10): 1300-1307.