Europhys. Lett.
Volume 62, Number 6, June 2003
Page(s) 801 - 807
Section General
Published online 01 June 2003
DOI: 10.1209/epl/i2003-00443-7
Europhys. Lett., 62 (6) , pp. 801-807 (2003)

Multifractal surfaces and terrestrial topography

J.-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 $\un{km}$ to 50 $\un{cm}$. We use power spectra and trace moment analysis techniques to show that topography is multifractal from planetary scales down to around 40 $\un{m}$, 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