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APPLICATION OF THE WAVELET TRANSFORM MODULUS MAXIMA METHOD TO ANALYZE THE MULTIFRACTAL BEHAVIOR OF GEOMAGNETIC VARIATIONS
Abstract
The objective of this research is to analyze the multifractal behavior of geomagnetic field corresponding to the well-known 27-day variation (solar rotation period) and its harmonics and the 1-day (solar diurnal) periodicities. We discuss the multifractal behavior of geomagnetic variations recorded at the middle latitude stations, using wavelet transform modulus maxima (WTMM). The WTMM is capable of partitioning the time and scale domain of a signal into fractal dimension regions, and the method is sometimes referred to as a "mathematical microscope" due to its ability to inspect the multi-scale dimensional characteristics of a signal and possibly inform about the sources of these characteristics. WTMM provides an understanding of the multifractal scaling behavior of a signal using the multifractal singularity spectra and the generalized Hurst exponents as diagnostic tools. In this research it is established that the 1-day period exhibits monofractal behavior regardless of the solar activity. Results indicate that except for the 1-day period, the geomagnetic variations at all other periods shows a higher degree of multifractality during solar maximum compared to solar minimum.
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References15
Arneodo A., Grasseau G., Holschneider M. Wavelet transform of multifractals, Physical Review Letters, vol. 61, pp. 2281-2284, 1988.
Mallat S.G., Hwang W.L., Singularity detection and processing with wavelets, IEEE Transactions on Information Theory, vol. 38, pp. 617-643, 1992.
Consolini G., De Marco R., De Michelis P., Intermittency and multifractional Brownian character of geomagnetic time series, Nonlinear Processes in Geophysics, vol. 20, pp. 455-466, 2013.
Riabova S., Application of wavelet analysis to the analysis of geomagnetic field variations, Journal of Physics Conference Series, 1141, DOI: 10.1088/1742- 6596/1141/1/012146, 2018.
Thede L., Practical analog and digital filter design, Artech House, Inc., Norwood, MA, USA, 2004.
Muzy J.-F., Bacry E., Arneodo A., Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method, Physical Review E, American Physical Society (APS), vol. 47, no. 2, pp.875-884, 1992.
Meyer Y. Wavelets: Algorithms and applications, SIAM, Philadelphia, 1993.
Muzy J.F., Bacry E., Arneodo A., Wavelets and multifractal formalism for singular signals: Application to turbulence data. Physical Review Letters, vol. 67, pp. 3515-3518, 1991.
Ivanova V.S., Novikov V.U., Oksogoev A.A. Fractals, applied synergetics and structure design, Nova Science Pub Inc., Hauppauge, NY, USA, 2004.
Muzy J.-F., Bacry E., Arneodo A., The multifractal formalism revisited with wavelets, International Journal of Bifurcation and Chaos, vol. 4, no. 02, pp. 245- 302, 1994.
Arneodo A., Bacry E., Muzy J.-F., The thermodynamics of fractals revisited with wavelets, Physica A, Statistical Mechanics and its Applications, vol. 213, no. 1–2, pp. 232-275, 1995.
Schertzer D., Lovejoy S., Schmitt F., Chigirinskaya Y., Marsan D., Multifractal cascade dynamics and turbulent intermittency, Fractals, vol. 5, no. 03, pp. 427- 471, 1997.
Bacry E., Muzy J.-F., Arneodo A., Singularity spectrum of fractal signals from wavelet analysis: Exact results, Journal of Statistical Physics, Springer Verlag, vol. 70, no. 3-4, pp. 635-674, 1993.
Audit B., Bacry E., Muzy J.-F., Arneodo A., Wavelet-based estimators of scaling behavior, IEEE Transactions on Information Theory, vol. 48, pp. 2938-2954, 2002.
Riabova S.A., Spivak A.A., Geomagnetic variation peculiarities at middle latitudes of the East European Platform, Geomagnetism and Aeronomy, vol. 57, no. 2, pp. 199-206, 2017.
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