Multifractal topography of several planetary bodies in the Solar System

TL;DR

This study applies a multifractal approach to analyze planetary topography, revealing scale-invariant properties and similar behaviors across Earth, Mars, Mercury, and the Moon at scales larger than 10km, with implications for planetary dynamics.

Contribution

It introduces the use of multifractal analysis for planetary topography, capturing intermittency and scale invariance, and compares topographic statistics across multiple planetary bodies.

Findings

Topography exhibits multifractal behavior at scales larger than 10km.

All studied planetary bodies share similar fractal properties below 10km.

Different physical processes may explain topography at different scales.

Abstract

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 dynamic 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 multifractal approach to describe fields of topography. This theory both encompass height and slopes and other statistical moment of the field, tacking into account the scale invariance. Contrary to the widely used fractal formalism, multifractal is able to describe the intermittency of the topography field. As we commonly observe the juxtapostion of rough and smooth at 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 multifractal theory for scale larger than 10km. Surprisingly, the analysis shows that all bodies have the same fractal behavior for scale smaller than 10km. We hypothesized that dynamic topography of the mantle may be the explanation at large scale, whereas the smaller scales behavior may be related to elastic thickness.