Wavelets for the space-time structure analysis of physical fields

P.G. Frick^a, b, D.D. Sokoloff^c, d, e, R.A. Stepanov^a, f
^aInstitute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, ul. akad. Koroleva 1, Perm, 614013, Russian Federation
^bPerm State National Research University, Bukireva st. 15, Perm', 614990, Russian Federation
^cLomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
^dPushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Kaluzhskoe shosse 4, Troitsk, Москва, 108840, Russian Federation
^eMoscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
^fPerm National Research Polytechnic University, Komsomol'skii prosp. 29, Perm, 614990, Russian Federation

Spectral analysis, based on the Fourier method, is a general tool in physics. Wavelets appeared as a natural generalization of classical spectral analysis to the case of complex nonstationary and spatially inhomogeneous systems, for which a comparison with an infinite sinusoid, which forms the basis of the Fourier method, has to be replaced by a comparison with a finite wave packet, which is known as a wavelet. In this review, the authors, based largely on their own experience of application wavelet analysis in astro- and geophysics, solar-terrestrial relations, as well as climatology, medical physics, and laboratory hydrodynamic experiments, demonstrate the possibilities and discuss the practical aspects of the application of the wavelet apparatus to the interpretation of signals and images of various physical natures.

Keywords: wavelets, spectral analysis, data processing for signals and images, solar and stellar activity, galactic magnetic fields, geophysics, medical physics
PACS: 47.27.er, 95.75.−z (all)
DOI: 10.3367/UFNe.2020.10.038859
URL: https://ufn.ru/en/articles/2022/1/d/
Web of Science

000788597000004
Scopus

2-s2.0-85128540479
ADS NASA

2022PhyU...65...62F
Citation: Frick P G, Sokoloff D D, Stepanov R A "Wavelets for the space-time structure analysis of physical fields" Phys. Usp. 65 62–89 (2022)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 8th, August 2020, revised: 20th, October 2020, accepted: 25th, October 2020

Оригинал: Фрик П Г, Соколов Д Д, Степанов Р А «Вейвлет-анализ пространственно-временной структуры физических полей» УФН 192 69–99 (2022); DOI: 10.3367/UFNr.2020.10.038859

References (113) Cited by (24) Similar articles (20) ↓

M.V. Kalashnik, M.V. Kurgansky, O.G. Chkhetiani “Baroclinic instability in geophysical fluid dynamics” Phys. Usp. 65 1039–1070 (2022)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” Phys. Usp. 49 1151–1178 (2006)
O.G. Onishchenko, O.A. Pokhotelov et al “Structure and dynamics of concentrated mesoscale vortices in planetary atmospheres” Phys. Usp. 63 683–697 (2020)
B.M. Smirnov “Electrical cycle in the Earth’s atmosphere” Phys. Usp. 57 1041–1062 (2014)
A.N. Vulfson, O.O. Borodin “The system of convective thermals as a generalized ensemble of Brownian particles” Phys. Usp. 59 109–120 (2016)
A.N. Pavlov, A.E. Hramov et al “Wavelet analysis in neurodynamics” Phys. Usp. 55 845–875 (2012)
O.G. Onishchenko, O.A. Pokhotelov, N.M. Astaf’eva “Generation of large-scale eddies and zonal winds in planetary atmospheres” Phys. Usp. 51 577–589 (2008)
V.M. Fedorov “Problems of parameterization of the radiation block in physical and mathematical climate models and the possibility of their solution” Phys. Usp. 66 914–930 (2023)
F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin “Stability and vortex structures of quasi-two-dimensional shear flows” Sov. Phys. Usp. 33 (7) 495–520 (1990)
L.Kh. Ingel, M.V. Kalashnik “Nontrivial features in the hydrodynamics of seawater and other stratified solutions” Phys. Usp. 55 356–381 (2012)
Yu.A. Stepanyants, A.L. Fabrikant “Propagation of waves in hydrodynamic shear flows” Sov. Phys. Usp. 32 783–805 (1989)
S.V. Bulanov, Ja.J. Wilkens et al “Laser ion acceleration for hadron therapy” Phys. Usp. 57 1149–1179 (2014)
V.M. Fedorov “Earth insolation variation and its incorporation into physical and mathematical climate models” Phys. Usp. 62 32–45 (2019)
O.G. Bakunin “Stochastic instability and turbulent transport. Characteristic scales, increments, diffusion coefficients” Phys. Usp. 58 252–285 (2015)
D.N. Razdoburdin, V.V. Zhuravlev “Transient dynamics of perturbations in astrophysical disks” Phys. Usp. 58 1031–1058 (2015)
A.A. Koronovskii, O.I. Moskalenko, A.E. Hramov “On the use of chaotic synchronization for secure communication” Phys. Usp. 52 1213–1238 (2009)
N.M. Astaf’eva “Wavelet analysis: basic theory and some applications” Phys. Usp. 39 1085–1108 (1996)
O.V. Verkhodanov “Cosmological results from the Planck space mission and their comparison with data from the WMAP and BICEP2 experiments” Phys. Usp. 59 3–41 (2016)
A.E. Hramov, N.S. Frolov et al “Functional networks of the brain: from connectivity restoration to dynamic integration” Phys. Usp. 64 584–616 (2021)
G.N. Makarov “Laser separation of boron isotopes: research results and options for technological implementation” Phys. Usp. 68 452–489 (2025)

The list is formed automatically.