Extended power-law scaling of self-affine signals exhibiting apparent multifractality

Alberto Guadagnini, Shlomo P Neuman

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Many earth and environmental variables appear to scale as multiplicative (multifractal) processes with spatial or temporal increments possessing Gaussian or heavy-tailed distributions. The behavior, characterized by power-law scaling, is typically limited to intermediate ranges of separation scales (lags) considered, in the case of fully developed turbulence, to be dominated by inertia. It has been established empirically that, in numerous cases (e.g. turbulence, diffusion-limited aggregates, natural images, kinetic surface roughening, fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel-bed mobility, barometric pressure, low-energy cosmic rays, cosmic microwave background radiation, metal-insulator transition, irregularities in human heartbeat time series, turbulence in edge magnetized plasma of fusion devices and turbulent boundary layers of the Earth's magnetosphere), this range of lags can be enlarged significantly, at both ends of the spectrum, via a procedure known as Extended Self-Similarity (ESS). We demonstrate numerically that a similar procedure extends the power-law scaling range over which additive (self-affine) signals exhibit apparent multifractality. We conclude that signals appearing to exhibit either standard or extended (such as those listed) multifractal scaling may potentially represent self-affine processes.

Original languageEnglish (US)
Article numberL13403
JournalGeophysical Research Letters
Volume38
Issue number13
DOIs
StatePublished - 2011

Fingerprint

scaling laws
power law
turbulence
time lag
sand wave
cosmic microwave background radiation
gravels
Earth magnetosphere
turbulent boundary layer
morphometry
transition element
irregularities
inertia
rivers
cosmic ray
sands
magnetosphere
low pressure
beds
cosmic rays

ASJC Scopus subject areas

  • Earth and Planetary Sciences(all)
  • Geophysics

Cite this

Extended power-law scaling of self-affine signals exhibiting apparent multifractality. / Guadagnini, Alberto; Neuman, Shlomo P.

In: Geophysical Research Letters, Vol. 38, No. 13, L13403, 2011.

Research output: Contribution to journalArticle

@article{5f7e67e627d2447891c5e96c0522aa09,
title = "Extended power-law scaling of self-affine signals exhibiting apparent multifractality",
abstract = "Many earth and environmental variables appear to scale as multiplicative (multifractal) processes with spatial or temporal increments possessing Gaussian or heavy-tailed distributions. The behavior, characterized by power-law scaling, is typically limited to intermediate ranges of separation scales (lags) considered, in the case of fully developed turbulence, to be dominated by inertia. It has been established empirically that, in numerous cases (e.g. turbulence, diffusion-limited aggregates, natural images, kinetic surface roughening, fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel-bed mobility, barometric pressure, low-energy cosmic rays, cosmic microwave background radiation, metal-insulator transition, irregularities in human heartbeat time series, turbulence in edge magnetized plasma of fusion devices and turbulent boundary layers of the Earth's magnetosphere), this range of lags can be enlarged significantly, at both ends of the spectrum, via a procedure known as Extended Self-Similarity (ESS). We demonstrate numerically that a similar procedure extends the power-law scaling range over which additive (self-affine) signals exhibit apparent multifractality. We conclude that signals appearing to exhibit either standard or extended (such as those listed) multifractal scaling may potentially represent self-affine processes.",
author = "Alberto Guadagnini and Neuman, {Shlomo P}",
year = "2011",
doi = "10.1029/2011GL047727",
language = "English (US)",
volume = "38",
journal = "Geophysical Research Letters",
issn = "0094-8276",
publisher = "American Geophysical Union",
number = "13",

}

TY - JOUR

T1 - Extended power-law scaling of self-affine signals exhibiting apparent multifractality

AU - Guadagnini, Alberto

AU - Neuman, Shlomo P

PY - 2011

Y1 - 2011

N2 - Many earth and environmental variables appear to scale as multiplicative (multifractal) processes with spatial or temporal increments possessing Gaussian or heavy-tailed distributions. The behavior, characterized by power-law scaling, is typically limited to intermediate ranges of separation scales (lags) considered, in the case of fully developed turbulence, to be dominated by inertia. It has been established empirically that, in numerous cases (e.g. turbulence, diffusion-limited aggregates, natural images, kinetic surface roughening, fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel-bed mobility, barometric pressure, low-energy cosmic rays, cosmic microwave background radiation, metal-insulator transition, irregularities in human heartbeat time series, turbulence in edge magnetized plasma of fusion devices and turbulent boundary layers of the Earth's magnetosphere), this range of lags can be enlarged significantly, at both ends of the spectrum, via a procedure known as Extended Self-Similarity (ESS). We demonstrate numerically that a similar procedure extends the power-law scaling range over which additive (self-affine) signals exhibit apparent multifractality. We conclude that signals appearing to exhibit either standard or extended (such as those listed) multifractal scaling may potentially represent self-affine processes.

AB - Many earth and environmental variables appear to scale as multiplicative (multifractal) processes with spatial or temporal increments possessing Gaussian or heavy-tailed distributions. The behavior, characterized by power-law scaling, is typically limited to intermediate ranges of separation scales (lags) considered, in the case of fully developed turbulence, to be dominated by inertia. It has been established empirically that, in numerous cases (e.g. turbulence, diffusion-limited aggregates, natural images, kinetic surface roughening, fluvial turbulence, sand wave dynamics, Martian topography, river morphometry, gravel-bed mobility, barometric pressure, low-energy cosmic rays, cosmic microwave background radiation, metal-insulator transition, irregularities in human heartbeat time series, turbulence in edge magnetized plasma of fusion devices and turbulent boundary layers of the Earth's magnetosphere), this range of lags can be enlarged significantly, at both ends of the spectrum, via a procedure known as Extended Self-Similarity (ESS). We demonstrate numerically that a similar procedure extends the power-law scaling range over which additive (self-affine) signals exhibit apparent multifractality. We conclude that signals appearing to exhibit either standard or extended (such as those listed) multifractal scaling may potentially represent self-affine processes.

UR - http://www.scopus.com/inward/record.url?scp=79959962203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959962203&partnerID=8YFLogxK

U2 - 10.1029/2011GL047727

DO - 10.1029/2011GL047727

M3 - Article

AN - SCOPUS:79959962203

VL - 38

JO - Geophysical Research Letters

JF - Geophysical Research Letters

SN - 0094-8276

IS - 13

M1 - L13403

ER -