Nonlinear Structure of Geomagnetic Field Hourly Variations

Investigation of dynamics of geomagnetic field variation remains as one of the important problems of nowadays geophysics. In this regard using of modern nonlinear methods helps to understand qualitatively and to analyze quantitatively geomagnetic field variations at different time scales. From this point of view in present work the dynamics of temporal behavior of geomagnetic field was investigated based on time series of hourly values of the horizontal component, H, of total geomagnetic field from the Dusheti observatory (Georgia). Namely we have analyzed integral time series of measured hourly values for five consequent years (1989-1994). Separately were considered yearly and monthly time series of H values. In order to avoid common problems related with the lack of stationarity the data series were processed after removing slowly varying trend and normalization. Separately were analysed original time series too, taking into account possibility of distortion of inherent dynamics due to detrending, in fact, filtering procedure. It was shown that power spectrum of variation of horizontal component of geomagnetic field being extremely rich in bands of different frequencies are characterized by spectral indexes, typical for coloured type of noise for al considered time periods. Hurst exponent calculation (about 0.2-0.4) provides evidence for clear antipersistence in geomagnetic time series. Correlation dimension of integral as well as yearly time series though is not clearly high dimensional, statistically is near to low dimensionality threshold (commonly equal to 5). In order to analyse dynamics of geomagnetic field variability for shorter time periods we have used Lempel-Ziv complexity measure which being essentially nonlinear can be used for short time series. As it follows from our results complexity measure of geomagnetic field (H) values (0.4-0.6) for monthly time series is near to chaotic type of dynamics being quite different from random as well as randomized original time series (1.00-1.05). This result points to existence of nonlinear structure in considered time series. In order to further elucidate this question we have used surrogate time series testing based on correlation dimension as the discriminating metric. According to our results dynamics of geomagnetic fields horizontal component is characterised by metrics, which is significantly different from used two type of surrogates discriminating metrics i.e. they indeed have nonlinear structure. Results of present investigation provide evidence that variations of geomagnetic field at hourly time scale represent highdimensional not random process having clear nonlinear structure.