Europhys. Lett., 62 (6) , pp. 801-807 (2003)
Multifractal surfaces and terrestrial topographyJ.-S. Gagnon1, S. Lovejoy1 and D. Schertzer2
1 Physics Department, McGill University 3600 rue University, Montréal, Canada, H3A 2T8
2 L.M.M., Université Pierre et Marie Curie, BP 162 4 Place Jussieu, 75252 Paris Cedex 05, France
(Received 25 September 2002; accepted in final form 22 April 2003)
We analyze terrestrial topographic data from four Digital Elevation Models which collectively span the range 20000 to 50 . We use power spectra and trace moment analysis techniques to show that topography is multifractal from planetary scales down to around 40 , where the multiscaling is broken by trees. We show that over this range the topography is reasonably described by a global nonlinear moment scaling function, itself determined by three parameters. We argue that these isotropic analyses are insensitive to the anisotropies and are hence compatible with different geomorphologies.
05.45.Df - Fractals.
61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).
91.10.Jf - Topography; geometric observations.
© EDP Sciences 2003