Fractal analysis of the martian landscape: A study of kilometre-scale topographic roughness

Abstract

Natural and engineered surfaces can be modelled as fractal objects described by a non-integer dimension (i.e., their fractal dimension). This approach has been used extensively to characterize surface complexity in terms of rugosity or roughness. In this paper, the local fractal dimension is proposed as a means of mapping the spatial variability of the surface roughness of the Martian landscape. The local fractal dimension complements measures of topographic roughness proposed by other authors and provides new images of the Martian surface texture at the kilometric scale that can be used to interpret geological events, geological processes and geological formations. It can also assist in geological mapping and in the detection and prioritisation of sites that merit further exploration. Mars Orbiter Laser Altimeter data were used to characterize the kilometre-scale terrain roughness of Mars. The procedure is general and can also be applied to digital elevation models with higher resolution (for example, digital elevation models generated by stereo-pair HiRISE images) to assess roughness at the metric scale. Sixteen test sites were selected and used to illustrate the patterns of the spatial variability of landscape roughness (local fractal dimension maps) at the kilometric scale. The results show that the mean of the local fractal dimension ranges from 2.036 in Argyre Planitia to 2.403 at the North Pole. The results also show that the mean roughness values of the Martian landscapes are less than those of the Earth's continents. Basically, the roughness of the Martian terrain at the kilometric scale depends, inter alia, on the number of kilometric-scale landforms present on the terrain. It is thus logical that the local fractal dimension is higher on Earth, a geologically active planet, than on Mars. Only the North Pole test site (an area larger than the North polar ice cap) shows a roughness histogram similar to those of terrestrial sites. The abundance of information embedded in the spatial variability patterns in the roughness maps provides a significant resource for planetary geology research.