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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 22, issue 6
Nonlin. Processes Geophys., 22, 713–722, 2015
https://doi.org/10.5194/npg-22-713-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 22, 713–722, 2015
https://doi.org/10.5194/npg-22-713-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 30 Nov 2015

Research article | 30 Nov 2015

Universal multifractal Martian topography

F. Landais1, F. Schmidt1, and S. Lovejoy2 F. Landais et al.
  • 1GEOPS, Univ. Paris-Sud, CNRS, Universite Paris-Saclay, Rue du Belvedere, Bat. 504–509, 91405 Orsay, France
  • 2Physics department, McGill University, 3600 University st., Montreal, Que. H3A 2T8, Canada

Abstract. 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 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 another, excluding a general description at the planetary scale. In this article, we analyze 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 Mars Orbiter Laser altimeter (MOLA) at 300 m horizontal resolution, 1 m vertical resolution. We adapted the Haar fluctuation method to the irregularly sampled signal. The results suggest a multifractal behavior from the planetary scale down to 10 km. From 10 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.

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In the present study, we investigate the scaling properties of the topography of Mars. Planetary topographic fields are well known to exhibit (mono)fractal behavior. Indeed, fractal formalism is efficient in reproducing the variability observed in topography. Our results suggest a multifractal behavior from the planetary scale down to 10 km. From 10 km to 300 m, the topography seems to be simple monofractal.
In the present study, we investigate the scaling properties of the topography of Mars. Planetary...
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