Multifractal topography of several planetary bodies in the solar system

Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamics of a planet. For that purpose, the statistics of height and slopes may be described by different tools, at local and global scale. We propose here to use the multi-fractalapproach to describe fields of topography. This theory encompasses height and slopes and other statistical moments of the field, taking into account the scale invariance. Contrary to the widely used fractalformalism, multifractals are able to describe the intermittency of the topography field. As we commonly observe a juxtaposition of rough and smooth topographies at a given scale, the multifractal framework seems to be appropriate for hypsometric studies. Here we analyze the data at global scale of the Earth, Mars, Mercury and the Moon and find that the statistics are in good agreement with the multifractaltheory for scale larger than similar to 10 km. Surprisingly, the analysis shows that all bodies have the same fractal behavior for scale smaller than similar to 10 km. We hypothesize that dynamic topography of the mantle may be the explanation at large scale, whereas the smaller scale behavior may be related to elastic thickness.