Characterising Complexity in Solar Magnetogram Data using a Wavelet-based Segmentation Method

Abstract

The multifractal nature of solar photospheric magnetic structures are studied using the 2D wavelet transform modulus maxima (WTMM) method. This relies on computing partition functions from the wavelet transform skeleton defined by the WTMM method. This skeleton provides an adaptive space-scale partition of the fractal distribution under study, from which one can extract the multifractal singularity spectrum. We describe the implementation of a multiscale image processing segmentation procedure based on the partitioning of the WT skeleton which allows the disentangling of the information concerning the multifractal properties of active regions from the surrounding quiet-Sun field. The quiet Sun exhibits a average Hölder exponent $\sim -0.75$, with observed multifractal properties due to the supergranular structure. On the other hand, active region multifractal spectra exhibit an average Hölder exponent $\sim 0.38$ similar to those found when studying experimental data from turbulent flows.

accepted for publication in ApJ

References in corpus (9)

• Multifractality in Human Heartbeat Dynamics
• The multifractal nature of turbulent energy dissipation
• Causal cascade in the stock market from the ``infrared'' to the ``ultraviolet''
• A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data
• Generalizing the wavelet-based multifractal formalism to vector-valued random fields: application to turbulent velocity and vorticity 3D numerical data
• Turbulence, Complexity, and Solar Flares
• Turbulence in the Solar Atmosphere: Manifestations and Diagnostics via Solar Image Processing
• Multiresolution analysis of active region magnetic structure and its correlation with the Mt. Wilson classification and flaring activity
• Complex base numeral systems

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