全月球撞击坑的空间分布模式

以基于嫦娥探月工程公开数据识别的全月球直径大于500 m的106 016个撞击坑为研究对象，划分月海、月陆、经向、纬向研究区域，采用核密度估计与Ripley's K函数的规格化函数-L函数相结合的GIS点模式分析方法，研究全月球撞击坑的空间模式。研究结果表明，全月球撞击坑分布形成了三个聚集中心，南北两极核密度低，东半球核密度高，西半球核密度低，北半球核密度高，南半球核密度低；月陆地区的核密度大于月海地区的核密度，在撞击坑直径范围1~500 km范围内，月陆地区的撞击坑数量是月海地区平均水平的5倍；全月球撞击坑的L（d）曲线随距离变化的过程中在总体上呈现先增后减的态势，经向、纬向研究区位在不同空间尺度上的聚集程度存在差异。

The Spatial Pattern of Lunar Craters on a Global Scale

Impact craters over the lunar surface are often arranged in alignments and clusters, which are related to the results of mass wasting, mantling, and structural modifications effected by micrometerorite and meteorite bombardment, volcanic processes and crustal vibrations. High-resolution optical images and DEM returned from Chang'E mission provide a new chance for estimation of spatial variation in the crater density. We used Kernel density and L(d) function coming from Ripley's K to explore the spatial pattern of lunar craters in the mare, highland, latitudinal zones from 28°N to 42°N and longitudinal zones from 40°W to 60°W on the Moon, which included 106 016 impact craters with diameters bigger than 500 m. Spatial distribution pattern analysis suggests a clustered distribution of craters on the Moon, and GIS-based spatial Kernel density identified three main clusters of craters within highlands (the biggest one located in the northeastern high latitude). The observed ratio of the crater density in highland to that in mare region is about 5 within the diameter ranged from 1km to 500 km. It also showed that the average density of craters on the eastern hemisphere was substantially higher than that on the western hemisphere, which was consistent with the proposal that western mare units are generally younger than eastern mare units. L(d) function value of the craters, which provided information on the degree of clustering, suggested the craters generally gathered together first then separated with the distance increasing. An amount of 31 study areas brought out the symmetric variations existed in latitudinal and longitudinal study areas on the local scale, which pointed to the craters density are in fluctuated decline from the equator to two poles and so are they from longitude of central meridian to eastern or western side of the Moon with the distance rising.