撞击坑是月表最主要的地貌形态,相关研究多采用撞击坑深度和坑口直径比值作为月球形貌研究依据。事实上撞击坑的形状不是典型的圆锥,而是上大下小的截锥形。依据"嫦娥一号"影像图和全月球数字高程模型数据,获取了1000个撞击坑坑唇等效半径r₁、坑底等效半径r₂,撞击坑的深度h,进而对r₁、r₂、h三个参数进行了统计分析和聚类分析。结果表明:(1)撞击坑数目与r₁和r₂的分形维数分别为D₁=1.88、D₂=1.51,都大于地球撞击坑的分维数1.16,表明月表撞击坑复杂度受到外界的影响较地球低,且坑唇的复杂度比坑底高;(2)r₁-r₂之间具有很好的线性正相关关系,聚类结果将其分为三类,决定系数分别为R₁²=0.685、R₂²=0.886、R₃²=0.974;(3)对r₁-r₂-h三者进行线性拟合,决定系数R₂=0.968,表明三者之间同样具有显著线性关系,且月表撞击坑的形成过程以及形成之后都处于相似的动力环境下。

Impact craters are the main geomorphological type on lunar surface.They can provide a large amount of information,including the age of geological unit,the history and evolution of the moon impact.Due to the fact that the current automatic recognition methods for impact craters have deviations of extraction range and locations,simultaneously they can not extract the information of the buttom,thus the whole characters of the impact craters can not be researched deeply.The top and buttom edges of 1000 impact craters have been extracted by manual vectorization in the remote sensing images evenly in this study.The equivalent radius of the top and buttom edges,that is r₁(top) and r₂(buttom),are computed by the area of the range of the crater's lip and buttom.And h,the height(depth) of the impact craters,are derived from the digital elevation model of the whole moon.Then all the parameters,r₁,r₂ and h,are researched by fractal analysis,statistical analysis and cluster analysis.The results show that:(1) The fractal dimension of the impact craters' number with r₁ and r₂ is D₁=1.88 and D₂=1.51 respectively.They are both larger than the fractal dimension of the impact craters on the earth,indicating that the extraneous interference which decides the complexity of the impact craters on the moon surface is lower than that on the earth's,and the complexity of the top is higher than that of the buttom at the same time.(2) There is a good liner correlation between r₁ and r₂,and the clustering results will be divided into three categories,with the coefficients of determination being R₁²=0.685,R₂²=0.886,and R₃²=0.974,respectively.(3) The coefficient of determination R₂=0.968 is obtained by the liner fit of three parameters r₁-r₂-h,which shows that there is also a good liner correlation among r₁-r₂-h,and the formation of the lunar impact craters is found in the same dynamic environment,the same as the environment after the formation.