Quantitative measurement method for impact basin characteristics based on localized spherical harmonics

Characteristics of impact basins are important fundamental knowledge for assessing basin forming impacts and their influence on surficial and interior structural evolutions for lunar and planetary bodies. To estimate impact basin characteristics based on spherical harmonic expressions of topographic figures, we propose a quantitative method that we apply it to actual lunar topographic data. The estimated basin locations (center) are almost coincident with those determined by visual inspection. However, the numbers of ring structures differ from previously reported ones. The relation between the ring height and the ring diameter coincides well with those reported previously. Some older basins show discrepancies in the height/diameter relation, which probably reflect the degree of degradation by subsequent small impacts. We recognize a power law relation between the diameters of a ring and a neighboring ring structure. That relation suggests that the formation, volume and modification of the melt-cavity control the formation and size of peak-ring and multi-ring structures. These relations, which are thought to reflect the mechanism of the collapse stage of basin formation impact, provide helpful constraints for elucidating the long-standing problem of how multi-ring impact basins are formed.