The multifractality of the internal geomagnetic field

Abstract

It is well established that the external geomagnetic field exhibits distinct multifractal behaviour with multiple characteristic timescales that are a manifest of the complex solar-driven dynamics of the magnetosphere or ionosphere. The internal magnetic field on the other hand is characterized by much longer timescales. Consequently, in order to observe any multifractal behaviour, there is needed a time series of magnetic dipolar moment spanning thousands or even millions of years of the past geomagnetic field of the core. Here, we analyse two series that describe the dipolar ingredient of the geomagnetic field for the last 4 and 2 million years, respectively. The first series is constructed from a continuous streak of sedimentary samples while the other series is a composite of a myriad of shorter time series contained within the 2 million years frame. We analysed the Generalized Hurst Exponent through the Multi Fractal-Detrended Fluctuation Analysis method and in each case, we observed typical multifractal structures. These results may be the manifestation of different phenomena evolving in the liquid outer core, possibly providing hints and insights into the details of the corresponding mechanisms. Analysis of the time evolution of the Generalized Hurst Exponent for each series displays a complicated behaviour. Typically the anti-persistent character of the series becomes more evident when close to e dipole reversal. Special efforts need to be dedicated in identifying connections between geomagnetic reversals and time dependence of the Generalized Hurst Exponent.