The <i>l</i><sup>1/2</sup> law and multifractal topography: theory and analysis - Archive ouverte HAL Access content directly
Journal Articles Nonlinear Processes in Geophysics Year : 1995

The l1/2 law and multifractal topography: theory and analysis

(1) , (2) , (3) , (4)
1
2
3
4

Abstract

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 (?h) vary with horizontal separation (l) as ?h ˜ lH. 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 l1/2 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.
Fichier principal
Vignette du fichier
npg-2-16-1995.pdf (539.82 Ko) Télécharger le fichier
Origin : Explicit agreement for this submission

Dates and versions

hal-00331032 , version 1 (01-01-1995)

Identifiers

  • HAL Id : hal-00331032 , version 1

Cite

S. Lovejoy, D. Lavallée, D Schertzer, P. Ladoy. The l1/2 law and multifractal topography: theory and analysis. Nonlinear Processes in Geophysics, 1995, 2 (1), pp.16-22. ⟨hal-00331032⟩
316 View
90 Download

Share

Gmail Facebook Twitter LinkedIn More