Slepian函数在月球局部重力场分析中的适用性分析  

An Analysis of the Applicability of Slepian Function in Analyzing Lunar Local Gravity Field

作　　者：孙雪梅[1,2] 李斐[1,3] 鄢建国[1] 郝卫峰[3] 

机构地区：[1]武汉大学测绘遥感信息工程国家重点实验室,湖北武汉430079 [2]常州市测绘院,江苏常州213000 [3]武汉大学中国南极测绘研究中心,湖北武汉430079

出　　处：《测绘学报》2015年第3期264-273,共10页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41174019;41104006);湖北省自然科学基金重点创新群体项目(2012FFA041);中央高校基本科研业务费专项资金(2042014kf0051);山东省基础地理信息与数字化技术重点实验室开放基金(SD080705)~~

摘　　要：在分析Slepian函数数学性质的基础上,选取月球北极球冠区域为研究范围,结合CEGM02模型,研究Slepian函数在解算月球局部重力场和局部功率谱优缺点和适用范围。同时利用CEGM02、SGM150j、LP150Q、GRAIL660模型,分析不同模型的月球局部重力场-地形导纳及相关性。结果表明Slepian函数的局部正交特性在表达月球局部重力场方面有明显优势;由Slepian模型计算得到的局部重力场功率谱可信可靠带宽较大,但球冠边缘异常信号对谱分析结果高频部分带来较大不确定性;利用Slepian加窗的局部谱分析方法可以分析局部区域能量与全球的关系,但其谱分析结果可信可靠频段较窄,低阶段误差较大。4个重力场模型局部重力-地形导纳中低阶部分接近,高阶部分随阶次增大差距明显,可靠性降低。Based on a detailed analysis of the Slepian function ,the advantages and disadvantages of the application of the Slepian function in computing lunar local gravity model ,local power spectrum combined with the CEGM02 model and local admittance and correl ation based on CEGM02 ,SGM150j ,LP150Q and GRAIL660 were analyzed in this paper .It turns out that the local orthogonal Slepian function shows obvious advantages in modeling lunar local gravity field .In the application of power spectrum ,the method of Slepian model shows a much wider ,credible and reliable bandwidth but brings greater uncertainty in high degrees with the abnormal signal on the cap edge .On the contrary ,the local power spectrum curve of Slepian window reflects the relationship between local gravity and the whole moon ,but the spectral curve showsanarrowreliablebandwidthandsignificanterrorsinlowdegrees.Local admittanceandcorrelation of four gravity models shows small difference in low orders but obvious difference as the orders get higher .

关 键 词：Slepian函数 月球局部重力场 局部功率谱 加窗 

分 类 号：P228[天文地球—大地测量学与测量工程]