A STUDY OF MAGNETIC COMPLEXITY USING HURST'S RESCALED RANGE ANALYSIS

A fractal analysis using the classical Hurst method has been applied to artificial data, simulated sunspot magnetic field data, and to data acquired with NASA/Marshall Space Flight Center's vector magnetograph. The main goals of this study are to quantify the complexity of an active region and to determine if significant changes in complexity are associated with flare activity. We tested the analysis using three basic types of two-dimensional synthetic data: (1) data composed of gaussians with various types of superimposed features, (2) random data, and (3) synthetic sunspots created from a basic, simple configuration on which are placed increasingly smaller structures. Our results confirm that the Hurst method of analysis is sensitive to the presence of large-scale structures within a two-dimensional image. When the large-scale structure has been removed, the value of the Hurst exponent is inversely proportional to increasing complexity in the image. The Hurst exponent of magnetograph data with the large-scale structure of the sunspot removed, shows a tantalizing variation in the shear parameter five minutes prior to a flare.