A study of histograms of wavelet coefficients of the Mars topography to determine its scaling properties

Recently, the scaling properties of Mars topography have been analyzed through the Wavelet Leaders Method. The signals studied have often a few values radically different from the rest of the signal, due to the presence of crater for example. These values can disrupt the fractal study of the signals and the interpretation of the results is thus more difficult.
Some new methods based on the use of histograms of wavelet coefficients allows to be more robust for the characterization of the fractal nature of signals. The main methods are the Wavelet Profile Method and the Leaders Profile Method. Moreover, a great advantage of these methods is to have a new criterion to differentiate the monofractal and the multifractal signals which is not based on the linearity of a inverse Legendre transform, as it is the case for the most of the methods of signal analysis.
In this work, we show that these methods applied on Mars Orbiter Laser Altimeter (MOLA) data allows to have additional information on the topography of Mars compared to the other methods.