Physics
Scientific paper
Dec 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufmng21a0419g&link_type=abstract
American Geophysical Union, Fall Meeting 2001, abstract #NG21A-0419
Physics
3250 Fractals And Multifractals, 3379 Turbulence
Scientific paper
We analyse topographic transects from four different Digital Elevation Models (DEMs) which collectively span - with overlapping ranges - scales from 20,000km to 50cm and contain more than 2X108 pixels. We use power spectra and trace moments analysis techniques to show that the Earth's topography is accurately multiscaling from planetary scales down to roughly 40 m where a break in our highest resolution data set occured apparently due to the presence of trees. Over this large scaling range, we show that topography can be described statistically at all scales by a global nonlinear moment scaling function K(q) which characterizes the scaling for every moment q and which is close to the form predicted for universal multifractals. The two basic parameters a, C1 are estimated as a=1.8, C1=0.12, and are apparently the same for bathymetry and continental topography, while the third universal parameter H has respectively the values H= 0.46, 0.66 for bathymetry and continental topography. The bathymetry exponent is close to and is a mulitfractal generalization of the theoretical Turcotte - Oxburg's ocean floor spreading exponent (=1/2). This multiscaling implies that topography is better described by multifractals than by monofractals which would have a=0 whereas the observed value is close to the theoretical maximum (a=2). Finally, we show how to make the corresponding multifractal simulations.
Gagnon Justin
Lovejoy Shaun
Schertzer Daniel
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