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。
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.
[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.
