Characterizing Complexity in Solar Magnetogram Data Using a Wavelet-based Segmentation Method

Abstract

The multifractal nature of solar photospheric magnetic structures is studied using the two-dimensional 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 an average Hölder exponent ~-0.75, with observed multifractal properties due to the supergranular structure. On the other hand, active region multifractal spectra exhibit an average Hölder exponent ~0.38, similar to those found when studying experimental data from turbulent flows.