月球表面粗糙度的分形表征  

Fractal Characterization of Lunar Surface Roughness

作　　者：程婧[1] 杨瑞琰[1,2] 黄定华[2] 余兵[1] 胡海艳[1] 向世民[2] 

机构地区：[1]中国地质大学数理学院,武汉430074 [2]中国地质大学空间科学技术研究中心,武汉430074

出　　处：《中国空间科学技术》2010年第2期9-14,共6页Chinese Space Science and Technology

基　　金：863重点课题:"火星探测科学目标深化研究"(2004AA735020)

摘　　要：文中采用"嫦娥一号"卫星探测器返回的激光高程计的数据,从研究月球表面的分形特征出发,选取月球表面的湿海区域进行研究,通过对激光高度计的原始数据进行处理,并利用SPSS统计软件对这两组数据进行拟合得到最佳的拟合模型。结果指出:1)分维可以作为一个独立的表征参量来表征粗糙表面的平缓程度。2)由拟合结果图可知,对于月球表面的湿海区域,分维与粗糙度存在单调递增关系,即分维值越大,区域表面越粗糙,表面起伏变化也越剧烈;并通过分析得出湿海区域的地形起伏较大。3)通过分维值D与粗糙度之间的关系式,对于某区域的任意一段轮廓,可以通过计算分维值D得出该轮廓的粗糙度值。同样的,对任一粗糙度值,可以求出相应的分维值以及该轮廓的具体纬度值位置。4)对于月球表面的其他区域,同样可以得出他们之间的相关性,从而达到研究月表地貌演化过程的目的。Researching the relativity between the lunar surface＇s dimension and roughness may contribute significantly to the stratigraphic study of the moon. The laser detector＇s data from Chang＇E1 satellite. The selected Mare Humorum region of the lunar, and the SPSS statistical software were used to determind the best fitting model about the lunar surface＇s dimension and roughness parameters. The results show that the fractal dimension can be characterized as an independent parameter to represent the degree of rough surface. For the Mare Humorum region, it exists increasing relationship between the fractal dimension and surface roughness, and the Mare H umorum s hypsography has great disparity. Through the relationship between the {ractal dimension and roughness, we can calculate any contour＇s roughness when we know the fractal dimension of the contour, vice versa. For the other regions of the moon, this method also can be used to study the relativity between the lunar surface＇s dimension and roughness so as to study the lunar＇s evolution process.

关 键 词：月球 分形维数 表面粗糙度 粗糙度参数 卫星 

分 类 号：P184.5[天文地球—天文学]