The <i>l</i><sup>1/2</sup> law and multifractal topography: theory and analysis

Over wide ranges of scale, orographic processes have no obvious scale; this has provided the justification for both deterministic and monofractal scaling models of the earth's topography. These models predict that differences in altitude (Δh) vary with horizontal separation (<i>l</i&g...

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Bibliographic Details
Main Authors: S. Lovejoy, D. Lavallée, D. Schertzer, P. Ladoy
Format: Article
Language:English
Published: Copernicus Publications 1995-01-01
Series:Nonlinear Processes in Geophysics
Online Access:http://www.nonlin-processes-geophys.net/2/16/1995/npg-2-16-1995.pdf
Description
Summary:Over wide ranges of scale, orographic processes have no obvious scale; this has provided the justification for both deterministic and monofractal scaling models of the earth's topography. These models predict that differences in altitude (Δh) vary with horizontal separation (<i>l</i>) as Δh ≈ <i>l</i><sup>H</sup>. The scaling exponent has been estimated theoretically and empirically to have the value H=1/2. Scale invariant nonlinear processes are now known to generally give rise to multifractals and we have recently empirically shown that topography is indeed a special kind of theoretically predicted &quot;universal&quot; multifractal. In this paper we provide a multifractal generalization of the<i> l</i><sup>1/2</sup> law, and propose two distinct multifractal models, each leading via dimensional arguments to the exponent 1/2. The first, for ocean bathymetry assumes that the orographic dynamics are dominated by heat fluxes from the earth's mantle, whereas the second - for continental topography - is based on tectonic movement and gravity. We test these ideas empirically on digital elevation models of Deadman's Butte, Wyoming.
ISSN:1023-5809
1607-7946