Applying comparative fractal analysis to infer origin and process in channels on Earth and Mars

Recently there has been a large amount of interest in identifying the nature of channels on (extra terrestrial) bodies. These studies are closely linked to the search for water (and ultimately signs of life) and are unarguably important. Current efforts in this direction rely on identifying geomorphic characteristics of these channels through painstaking analysis of multiple high resolution images. Here we present a new and simple technique that shows significant potential in its ability to distinguish between lava and water channels. Channels formed by water or lava on earth (as depicted in map view) display sinuosity over a large scale of range. Their geometries often point to the fluid dynamics, channel gradient, type of sediments in the river channels and for lava channels, it has been suggested that they are indicative of the thermal characteristics of the flow. The degree of this sinuosity in geometry can be measured using the divider method, and represented by fractal dimension (D) values. The higher D value corresponds to higher degree of sinuosity and channel irregularity and vice versa. Here we apply this fractal analysis to compare channels on Earth and Mars using D values extracted from satellite images. The fractal dimensions computed in this work for terrestrial river channels range from 1.04 - 1.38, terrestrial lava channels range from 1.01-1.10 and Martian channels range from 1.01 - 1.18. For terrestrial channels, preliminary results from river networks attain a fractal dimension greater than or equal to 1.1 while lava channels have fractal dimension less than or equal to 1.1. This analysis demonstrates the higher degree of irregularity present in rivers as opposed to lava channels and ratifies the utility of using fractal dimension to identify the source of channels on earth, and by extension, extra terrestrial bodies. Initial estimates of the fractal dimension from Mars fall within the same ranges as the lava channels on Earth. Based on what has been observed on Earth, we hypothesize that the differences in the dynamics of lava and water flow will cause significant differences in the degrees of irregularity of their respective channels. Thus fractal analysis has the potential to be a simple, straight forward and easily available tool to provide first-order constraint on the origin and processes active in Martian channels.