Self-affine behavior of Martian topography at kilometer scale from Mars Orbiter Laser Altimeter data : Geophysical detection of surface water on Mars

We used Mars Orbiter Laser Altimeter (MOLA) data from the current Mars Global Surveyor mission to characterize the topographic roughness of the Martian surface and to provide a mean to evaluate clutter at long (10-300 m) wavelengths. Such wavelengths are relevant for the MARSIS and SHARAD subsurface radars, which will be flown in future missions to Mars. The method of analysis is based on the assumption that topography can be described as a self-affine fractal: 30-km-long segments of MOLA altimetry profiles have thus been reduced to the topographic parameters RMS height, RMS slope, and Hurst exponent, this last related to the fractal dimension, which can be used as inputs to a near-nadir radar scattering model. The values of the Hurst exponent are greater than 0.5 for most of the surface, meaning a scaling behavior which is almost self-similar. Maps of RMS height and Hurst exponent show that these two parameters have very different spatial distributions: whereas the RMS height is patterned after the north-south dichotomy, the Hurst exponent follows a latitudinal trend. We make use of a multivariate method called G-mode to classify profiles in the three-dimensional parameter space: we find several roughness units, some of which have a strong correlation with certain geologic units, while others are bound by latitude. However, at scales between 300 m and 3 km, large stretches of the surface of Mars share common statistical properties of topography, independent from the north-south dichotomy.