应用求解沿轨迹重力异常的垂线偏差法以及求解空间分辨率的交叉谱分析法,建立了高度计测距精度与沿轨迹重力异常反演精度以及空间分辨率的关联性模型.首先依据卫星测高原理,给出了沿轨迹重力异常的误差传播公式,然后以此为基础通过推导交叉谱分析中一致性系数与信噪比的数学表达式,建立了高度计测距精度与空间分辨率的解析关系.数值仿真结果表明:雷达高度计测距精度与沿轨迹重力异常反演精度成正比关系,与空间分辨率成幂函数关系,即高度计测距精度提高m倍,沿轨迹重力异常反演精度提高m倍,全球海域平均空间分辨率提高m0.4644倍.将数值仿真结果与相关文献中对实际测高数据的处理结果进行比较,验证了理论分析及模型的正确性.
A correlation model between along-track gravity anomaly accuracy, spatial resolution and altimeter accuracy is proposed. This new model is based on along-track gravity anomaly recovery and resolution estimation. Firstly, an error propagation formula of along-track gravity anomaly is derived from the principle of satellite altimetry. Then the mathematics between the SNR (signal to noise ratio) and cross spectral coherence is deduced. The analytical correlation between altimeter accuracy and spatial resolution is finally obtained from the results above. Numerical simulation results show that along-track gravity anomaly accuracy is proportional to altimeter accuracy, while spatial resolution has a power relation with altimeter accuracy. e.g., with altimeter accuracy improving m times, gravity anomaly accuracy improves m times while spatial resolution improves m0.4644 times. This model is verified by real-world data.
[1] GOPALAPILLAI S. Non-global Recovery of Gravity Anomalies from a Combination of Terrestrial and Satellite Altimetry Data [D]. Columbus: Ohio State University, 1974.
[2] RAPP R H. Gravity Anomaly Recovery from Satellite Altimetry Data Using Least Squares Collocation Techniques[D].Columbus: Ohio State University, 1974.
[3] 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.
[4] WANG Haiying, WANG Guangyun. Inversion of Gravity Anomalies from Along-track Vertical Deflections with Satellite Altimeter Data and Its Applications[J]. Acta Geodaetica et Cartographica Sinica, 2001, 30(1): 21-26. (王海英,王广运. 卫星测高数据的沿轨迹重力异常反演法及其应用[J]. 测绘学报,2001, 30(1): 21-26.)
[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(5):304-312.
[6] 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(5):179-184.(黄漠涛,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(5):179-184.)
[7] OLGIATI A, BALMINO G, SARRAILH M, et al. Gravity Anomalies from Satellite Altimetry: Comparison between Computation via Geoid Heights and via Deflections of the Vertical[J]. Bulletin Géodésique, 1995, 69(4): 252-260.
[8] SANDWELL D T, MCADOO D C. High-accuracy, High-resolution Gravity Profiles from 2 Years of the Geosat Exact Repeat Mission[J]. Journal of Geophysical Research, 1999,95(C3): 3049-3060.
[9] FU L L, CAZANAVE A. Satellite Altimetry and Earth Sciences [M]. San Diego:Academic Press, 2001.
[10] SANDWELL D T, YALE M M, SMITH W H F. Comparison of Along-track Resolution of Stacked Geosat, ERS-1 and TOPEX Satellite Altimeters [J]. Journal of Geophysical Research, 1995, 100(B8): 15117-15127.
[11] SANDWELL D T, SMITH W H F. Global Marine Gravity from Retracked Geosat and ERS-1 Altimetry: Ridge Segmentation Versus Spreading Rate [J]. Journal of Geophysical Research, 2009, DOI: 10.1029/2008JB006008.
[12] ZHAI Zhenhe, SUN Zhongmiao. Spherical Harmonic Analysis of Error Propagation between Mean Gravity Anomaly and Sea Surface Height Data [J]. Journal of Geodesy and Geodynamics, 2010, 30(2): 137-140. (翟振和,孙中苗. 海面高数据与平均重力异常误差传播的球谐分析[J]. 大地测量与地球动力学,2010, 30(2): 137-140.)
[13] PENG Fuqing, CHEN Shuangjun, JIN Qunfeng. Influence of Altimetry Errors on Marine Geopotential Recovery [J]. Journal of Geodesy and Geodynamics, 2014, 43(4): 337-340. (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.)
[14] SANDWELL D T, SMITH W H F, GILLE S, 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.[S.l.]: CEOAS, 2001.
[15] BAO L, XU H, LI Z. Towards a 1 mGal Accuracy and 1 min Resolution Altimetry Gravity Field[J]. Journal of Geodesy, 2013, 87(10-12): 961-969.
[16] SANDWELL D, GARCIA E, SOOFI K, et al. Toward 1-mGal Accuracy in Global Marine Gravity from CryoSat-2, Envisat, and Jason-1[J]. The Leading Edge, 2013, 32(8): 892-899.
[17] TURCOTTE D L. A Fractal Interpretation of Topography and Geoid Spectra on the Earth, Moon, Venus, and Mars[J].Journal of Geophysical Research, 1987, 92(B4): 597-601.
[18] MAUS S, DIMRI V. Depth Estimation from the Scaling Power Spectrum of Potential Fields[J].Geophysical Journal International, 1996, 124(1): 113-120.
[19] JEKELI C. Omission Error, Data Requirements, and the Fractal Dimension of the Geoid[C]//VII Hotine-Marussi Symposium on Mathematical Geodesy. Berlin: Springer, 2012: 181-187.
[20] LILLIBRIDGE J, CHENEY R. The Geosat Altimeter JGM-3 GDRs on CD-ROM[R]. Silver Spring: National Oceanographic Data Center,1997.
[21] NING Jingsheng, LIU Jingnan, CHEN Junyong, et al. Theory and Technology of Modern Geodesy[M]. Wuhan: Wuhan University Press, 2006.(宁津生,刘经南,陈俊勇,等. 现代大地测量理论与技术[M]. 武汉:武汉大学出版社,2006.)
