Depth-to-Diameter Ratio and Slopes in Small Lunar Highland Craters

Geomorphology of small lunar highland craters is quantified with digital elevation models (DEM) that cover 540 craters. From these new data we measured apparent depth (Ra), apparent diameter (Da) and wall slopes. While photogrammetric studies exist from Apollo era data [2,3], the lower end of the crater size spectrum is not well represented and the statistics for craters with diameters 150 meters or less is sparse. The slope of log-scale depth-vs.-diameter fit was ~0.9 (Figure 1). Previous studies [3] with both mare and highland craters (Da >330m) had slopes of ~1, so this result was somewhat expected, although the highland data density was poor in this size regime in the earlier works. However, it was found that a straight line represented the depth-vs.-diameter data better than a power law relation (goodness-of-fit 0.97 compared to 0.6) which is interesting since larger craters are found to change shape allometrically [4]. The median value of the depth-to-diameter ratio was ~0.13 which is also unexpected for small craters (usually ~0.2). Wall slopes were relatively shallow (median ~ 8°) with ~95% of the data at slopes less than 18°. Slopes decreased with crater size (Figure 2), with a sharp drop at diameters more than 35m after which the rate of change was small. Decrease in slope with size was observed earlier with Apollo data [2], but for larger craters (Da >1Km). References: [1] Robinson, M.S. et al (2010),Space Sci. Rev.,150,81-124;[2] Pike, R.J.(1977) Proceedings of the Symposium on Planetary Cratering Mechanics, Arizona, Pergamon Press.,489-509;[3] Pike, R.J.(1977) Lunar Science Conference,3, 3427-3436;[4] Pike, R.J(1967) J. Geophys. Res. 72, 8, 2099-2106