Multifractals and their application to geospace data

Abstract

In this thesis I first introduce multifractal theory and mathematical concepts for multifractal analysis. Different methods for different uses are described, with focus on a differentiating between coarse and fine theory approaches. Methods for analysing time series are also described, more specificly a direct method based on the coarse theory analysis, the wavelet transform modulus maxima (WTMM) method and the multifractal detrended fluctuation analysis (MFDFA). The next part of this thesis contains a selection of examples of applications of multifractals in science. Multifractal analysis have become very useful to describe properties of many phenomena in a wide range of fields, for instance space physics, medicine and finance, in addition to geology where fractal theory was first introduced. Finally, I have analysed the three components of the interplanetary magnetic field strength at the Earth's bow shock nose, the AE index and the Dst index for solar cycle 23, lasting from 1996 to 2006 with a peak in 1999. Multifractality was found for the IMF data and the AE index, which may indicate that both the AE index and the interplanetary magnetic field have a intermittent and turbulent character. Multifractality for the D$_{st}$ index was not shown as clearly, which indicates that this index is only weakly intermittent or not intermittent at all.