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...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
Copernicus Publications
1995-01-01
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Series: | Nonlinear Processes in Geophysics |
Online Access: | http://www.nonlin-processes-geophys.net/2/16/1995/npg-2-16-1995.pdf |
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 "universal" 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. |
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ISSN: | 1023-5809 1607-7946 |