Comparative study of the surface roughness of the Moon, Mars and Mercury

Abstract

We analyze and compare the surface roughness of the Moon, Mercury and Mars by characterizing the scale-dependence of the slope distribution. We calculate the absolute and differential slopes at baselines ranging between a few hundreds of meters and hundred kilometers depending on the spatial resolutions of the datasets. For each planetary body, we analyze two types of terrains: the rough and old heavily cratered “highlands” regions and smoother and younger “plains” terrains, Mare on the Moon, northern plains on Mercury and Mars. The resulting curves are discussed in terms of the geological processes that shape the surfaces of terrestrial planets. We concentrate in particular on the Median Differential Slope (MDS), a measure of roughness that has already proven its relevance for the analysis of Martian and Lunar topography. The comparison of the MDS vs. baseline curves for different types of terrains on each planet reveals interesting common trends as well as intriguing differences. The Lunar highlands display the highest values of MDS at baselines larger than 2km but Mercury highlands seem to be slightly rougher at shorter baselines. Mars southern plateaus appear much smoother at all scales. On each planet, younger terrains show lower roughness than old terrains at long baselines. However, because they display a strong negative slope of MDS vs. baseline, the contrast of roughness between young and old terrains is fainter at short baseline.