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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。
Crash pit is the most important geomorphology of the lunar surface. The related researches mostly use the ratio of crater depth and pit diameter as the research basis of the lunar topography. In fact, the shape of the impact crater is not a typical cone, but rather a truncated cone with a smaller size. According to the image of Chang’e-1 and the digital elevation model of the whole moon, the equivalent lip radius r1 of 1000 craters, the equivalent radius of pit bottom r2 and the depth h of craters were obtained, and then the r1, r2, h three parameters for statistical analysis and cluster analysis. The results show that: (1) The fractal dimension of the number of impact pits and r1 and r2 are respectively D1 = 1.88 and D2 = 1.51, which are both larger than the fractal dimension of the earth craters 1.16, indicating that the impact of lunar surface craters is more affected by the outside world The earth is low, and the complexity of the pit is higher than that of the pit; (2) there is a good linear positive correlation between r1-r2 and the clustering result is divided into three categories, the determining coefficients are R12 = 0.685, R22 = 0.886, R32 = 0.974; (3) Linearly fitting the three r1-r2-h coefficients to determine the coefficient R2 = 0.968, indicating that there is also a significant linear relationship between the three and the formation process and formation of lunar impact craters After all in a similar dynamic environment.