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   -> Volume 3, Issue 9

Preprint: Wavelet-Based Multifractal Analysis
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Anthony Davis (

PostPosted: Mon Dec 02, 2002 1:08 pm    
Subject: Preprint: Wavelet-Based Multifractal Analysis
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Preprint: Wavelet-Based Multifractal Analysis

Dear Waveleteers,

I have noticed in past issues of the WD many questions about time-series
analysis and some about multifractal approaches. In the following paper we
survey statistical scale-invariance, mostly in the analysis mode, from a
wavelet standpoint.

TITLE: Wavelet-Based Multifractal Analysis of Nonstationary and/or
Intermittent Geophysical Signals

AUTHORS: Anthony Davis, Alexander Marshak and Warren Wiscombe


We show how some of the most popular wavelet transforms can be used to
compute simple yet dynamically meaningful statistical properties of a
one-dimensional dataset representative of a geophysical field or
time-series. The observed properties of turbulent velocity fields and of
liquid water density in clouds are used throughout as examples along with
theoretical models drawn from the literature. We introduce a diagnostic
tool called the "mean multifractal plane," simpler than (but representative
of) the two well-known multifractal hierarchies of exponents H(p) and D(q),
associated with structure functions and singularity analysis respectively.
It is used to demonstrate the pressing need for a new class of stochastic
models having both additive/nonstationary and multiplicative/intermittent

The paper will published as a chapter of "Wavelets in Geophysics" (Eds. Efi
Foufoula-Georgiou and Praveen Kumar, 365 pp, Academic Press) to appear in
July 1994. For a preprint, please contact me at:

Anthony Davis,
NASA Goddard Space Flight Center,
Climate & Radiation Branch (code 913),
Greenbelt, MD 20771

Tel: (310) 731 9300; Fax: (310) 731 1180
All times are GMT + 1 Hour
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