Application of wavelet analysis to the analysis of geomagnetic field variations

Wavelet analysis is becoming more popular in geophysics. It is used for numerous researches, including tropical convection, the El Nino-Southern Oscillation, atmospheric cold fronts, temperature variations, the dispersion of ocean waves, and coherent structures in turbulent flows, number of sunspots etc. In this paper we research how informative is the application of wavelet analysis to the analysis of geomagnetic field variations at the mid-latitude observatory "Mikhnevo" of Institute of Geosphere Dynamics of Russian Academy of Science. We review continuous wavelet transform by focusing attention on such aspects as choice of mother wavelet, choice of scales, cone of influence, visualization of results, reconstruction of time series from wavelet transform and its application to estimate the Holder exponents and singularity spectra. In our work we use Morlet wavelet with frequency parameter of 6. In so doing, the reconstruction of the time series from the wavelet transform has a mean square error of 3.4%. The application of wavelet analysis made it possible to distinguish pronounced periodicities of the geomagnetic field with periods of 27, 13.5, 9, 6 days. In solar quiet-day variations is dominated by the 24- 12-, 8-, and 6-hour period components. An analysis of the modulus of the wavelet transform coefficients qualitatively indicates a scaling (close to the monofractal) character of the variations of the geomagnetic field in the diurnal range. Moreover, the intensity of periodic variations of geomagnetic variation isn't constant in time. The application of the method of wavelet transform modulus maxima confirmed the monofractal character of the diurnal variation for any solar activity. In contrast to the 1-day variation, the 27-day variation and its harmonics show a higher degree of multifractality during a maximum of solar activity in comparison with the minimum of solar activity.

[1]  J. Mouel,et al.  Time Variations of the Earth's Magnetic Field: From Daily to Secular , 1988 .

[2]  E. Bacry,et al.  Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Aldo Drago,et al.  Use of the wavelet transform on hydro-meteorological data , 2002 .

[4]  Douglas L. Jones,et al.  Efficient approximation of continuous wavelet transforms , 1991 .

[5]  N. M. Astaf’eva.  Wavelet analysis: basic theory and some applications , 1996 .

[6]  B. Briggs.  The variability of ionospheric dynamo currents , 1984 .

[7]  Aslak Grinsted,et al.  Nonlinear Processes in Geophysics Application of the Cross Wavelet Transform and Wavelet Coherence to Geophysical Time Series , 2022 .

[8]  V. P. Dimri,et al.  Wavelet and rescaled range approach for the Hurst coefficient for short and long time series , 2007, Comput. Geosci..

[9]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Antony C. Fraser-Smith,et al.  Spectrum of the geomagnetic activity index Ap , 1972 .

[11]  N. Gamage,et al.  Comparative Analysis of Low-Level Cold Fronts: Wavelet, Fourier, and Empirical Orthogonal Function Decompositions , 1993 .

[12]  E. Bacry,et al.  The Multifractal Formalism Revisited with Wavelets , 1994 .

[13]  Klaus Genuit,et al.  Prediction of sound and vibration in a virtual automobile , 2001 .

[14]  Ka-Ming Lau,et al.  Wavelets, Period Doubling, and Time–Frequency Localization with Application to Organization of Convection over the Tropical Western Pacific , 1994 .

[15]  A. Spivak,et al.  Effects of lunar-solar tides in the variations of geophysical fields at the boundary between the Earth’s crust and the atmosphere , 2012, Izvestiya, Physics of the Solid Earth.

[16]  D. Mcintosh,et al.  On the annual variation of magnetic disturbance , 1959, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[17]  J. O'Brien,et al.  An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves , 1993 .

[18]  Gerald Kaiser,et al.  A Friendly Guide to Wavelets , 1994 .

[19]  Yan Wang,et al.  Temporal structure of the southern oscillation as revealed by waveform and wavelet analysis , 1996 .

[20]  F. Ward.  The variance (power) spectra of Ci, Kp , and Ap , 1960 .

[21]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[22]  E. Bacry,et al.  Singularity spectrum of fractal signals from wavelet analysis: Exact results , 1993 .

[23]  A. Spivak,et al.  Near-surface geophysics: Complex investigations of the lithosphere-atmosphere interactions , 2012, Izvestiya, Physics of the Solid Earth.

[24]  J. Bartels.  Terrestrial-magnetic activity and its relations to solar phenomena , 1932 .

[25]  A. Grossmann,et al.  Cycle-octave and related transforms in seismic signal analysis , 1984 .

[26]  M. Farge.  Wavelet Transforms and their Applications to Turbulence , 1992 .

[27]  J. D. Bohlin.  Extreme-ultraviolet observations of coronal holes , 1977 .

[28]  A. Cortie.  Sun-spots and terrestrial magnetic phenomena, 1898-1911 , 1912 .

[29]  Robert L. McPherron,et al.  Semiannual variation of geomagnetic activity , 1973 .

[30]  W. Soon,et al.  Time scales and trends in the central England temperature data (1659–1990): A wavelet analysis , 1997 .

[31]  P. Mayaud,et al.  Spectral analysis of the geomagnetic activity index aa over a 103‐year interval , 1975 .

[32]  R. Banks.  Geomagnetic Variations and the Electrical Conductivity of the Upper Mantle , 1969 .

[33]  R. Trigo,et al.  MATSUYAMA CITY RAINFALL DATA ANALYSIS USING WAVELET TRANSFORM , 2001 .

[34]  Praveen Kumar,et al.  Wavelet Analysis in Geophysics: An Introduction , 1994 .

[35]  Pierre Brémaud,et al.  Fourier Analysis and Stochastic Processes , 2014 .

[36]  Alain Arneodo,et al.  Detecting vorticity filaments using wavelet analysis: About the statistical contribution of vorticity filaments to intermittency in swirling turbulent flows , 1999 .

[37]  S. Jaffard.  Pointwise smoothness, two-microlocalization and wavelet coefficients , 1991 .

[38]  Emmanuel Bacry,et al.  THE THERMODYNAMICS OF FRACTALS REVISITED WITH WAVELETS , 1995 .

[39]  Pierre Gilles Lemarié,et al.  Les Ondelettes en 1989 , 1990 .

[40]  A. Maute,et al.  Sq and EEJ—A Review on the Daily Variation of the Geomagnetic Field Caused by Ionospheric Dynamo Currents , 2017 .

[41]  Gabor Korvin,et al.  Fractal models in the earth sciences , 1992 .

[42]  Jan Adamowski,et al.  Development of a new method of wavelet aided trend detection and estimation , 2009 .

[43]  E. Bacry,et al.  Wavelets and multifractal formalism for singular signals: Application to turbulence data. , 1991, Physical review letters.

[44]  H. Hauska,et al.  A search for periodic variations in geomagnetic activity and their solar cycle dependence. , 1973 .

[45]  F. Hibberd.  The geomagnetic Sqvariation—annual, semi-annual and solar cycle variations and ring current effects , 1985 .

[46]  A. Richmond.  Ionospheric Wind Dynamo Theory: A Review , 1979 .

[47]  Praveen Kumar,et al.  Wavelets in Geophysics , 1994 .

[48]  Alain Arneodo,et al.  Revisiting multifractality of high‐resolution temporal rainfall using a wavelet‐based formalism , 2005 .