基于CE-1数据的数字月海分形刻画及其动力学意义

月海是月球表面的主要地理单元。对月海地貌特征的研究能够认识月表起伏及其动力学成因。依据CE-1影像图和全月球数字高程模型数据,提取了南北半球不同纬度地区、不同填充岩性的典型月海范围,运用盒维数法、立方体覆盖法和多重分形q-Dq语言对月海边界及其地形表面的地貌特征进行了线和面的描述和研究。结果表明:①分形方法可以有效地描述月球地貌的复杂程度。月海边界的分维值介于1.065~1.100之间,平均值为1.086,标准差为0.014,在双对数坐标下5个月海区边界复杂度拟合的直线都近似平行。②月海地形表面的分维值介于2.704~2.852之间,5个月海地形表面的分维值标准差为0.051,lnδ-lnN(δ)图也近似平行,但截距的离散程度相较于月海边界的高。③月海地貌多重分析的q-Dq曲线图总体呈现非递增趋势,Dq值在q=-10和q=0时基本达到饱和,但差异较小。④从线、面单分形以及多重分形可见,5个月海均具有分形特征,但彼此之间差异较小。其动力学意义在于它们在形成之后,内动力作用基本停止或很小,与分形特征基本一致;而外力主要由陨石撞击作用少量地改变着月表的面貌,导致在分形特征上表现出差异性。

The fractal and dynamic characterizations on digital mares based on CE-1 data

Since mare is one of the major geographic units of lunar surface, the landscape features of mares can provide a direct reflection of the ups and downs of lunar surface and its geodynamic mechanisms. This paper extracts the scopes of the typical mares with different fill lithology at different latitudes by manual vectorization based on the image of moon and the global lunar DEM model by Chang'E-1. The geomorphological features of mare borders and their terrain surfaces are estimated by using box-counting dimension method, cubic-covering method and q-Dq language of multi-fractal method. The results demonstrate that: (1) The complexity of lunar landscape can be described effectively by fractal methods. The values of fractal dimension of five mares' borders range from 1.065 to 1.100 while the average is 1.086, and the standard deviation is 0.014. The border lines fitted in the double logarithmic coordinates are approximately parallel. (2) The values of fractal dimension of mares' terrain surfaces range from 2.704 to 2.852, and the standard deviation is 0.051. The graph of lnδ-lnN(δ) also shows an approximately parallel pattern, but the dispersion degree is higher than that of the mare borders. (3) The q-Dq graph of multi-fractal analysis of mare landscape indicates an overall trend of non-increase. Although the Dq values reach saturation when q=-10 and q=0, the differences are small. (4) Analysis of the results of line and surface single fractal and multi-fractal dimensions shows that the five mares have their fractal features, while the differences among each other are little. In the view of dynamics, after the formation, the internal forces stopped or become feeble, which can be concluded that their fractal characteristics are almost the same. In addition, external impact of meteorites changed the lunar surface slightly, resulting in the differences on the fractal characteristics.