Universal multifractal Martian topography

F. Landais, F. Schmidt, S. Lovejoy
2015 Nonlinear Processes in Geophysics Discussions  
In the present study, we investigate the scaling properties of the topography of Mars. Planetary topographic fields are well known to roughly exhibit (mono)fractal behavior. Indeed, the fractal formalism is reproduces much of the variability observed in topography. Still, a single fractal dimension is not enough to explain the huge variability and intermittency. Previous studies have claimed that fractal dimensions might be different from one region to an other, excluding a general description
more » ... eneral description at the planetary scale. In this article, we are analyzing the Martian topographic data with a multifractal formalism to study the scaling intermittency. In the multifractal paradigm, the apparent local variation of the fractal dimension is interpreted as a statistical property of multifractal fields. We analyze the topography measured with the laser altimeter MOLA at 300 m horizontal resolution, 1 m vertical resolution. We adapted the Haar fluctuation method to the the irregularly sampled signal. The results suggest a multifractal behavior from planetary scale down to 10 km. From 10 km to 300 m, the topography seems to be simple monofractal. This transition indicates a significant change in the geological processes governing the Red Planet's surface.
doi:10.5194/npgd-2-1007-2015 fatcat:ihnerdnbxfgzvl6j7b5yzpeape