Titan, fractals, and filtering of Cassini altimeter data

Fractal behavior of one Titan profile acquired by the Cassini altimeter during its first flyby is demonstrated and quantitatively analyzed. The inadequacy of popular nonfractal models to represent scale-dependent behavior is also discussed. Our results lead to the conjecture that a proper geometrical model of the Titan surface is provided by the fractional Brownian motion stochastic process and that the particular acquired profile has a fractal dimension of about 2.4. In addition, use of the developed statistical model allows the design of model-based filters for a significant improvement of the measurement accuracy, at the expense of the horizontal resolution