Micro-scale, mid-scale, and macro-scale in global seismicity identified by empirical mode decomposition and their multifractal characteristics.

The magnitude time-series of the global seismicity is analyzed by the empirical mode decomposition giving rise to 14 intrinsic mode functions (IMF) and a trend. Using Hurst analysis one can identify three different sums of these IMFs and the trend which exhibit distinct multifractal behaviour and correspond to micro-, mid- and macro-scales. Their multifractal detrended fluctuation analysis reveals that the micro-scale time-series exhibits anticorrelated behaviour in contrast to the mid-scale one which is long-range correlated. Concerning the mid-scale one, in the range of 30 to 300 consecutive events the maximum entropy method power spectra indicates that it exhibits an 1/f behaviour with α close to 1/3 which is compatible with the long-range correlations identified by detrended fluctuation analysis during periods of stationary seismicity. The results have been also verified to hold regionally for the earthquakes in Japan and shed light on the significance of the mid-scale of 30 to 300 events in the natural time analysis of global (and regional) seismicity. It is shown that when using the mid-scale time-series only, we can obtain results similar to those obtained by the natural time analysis of global seismicity when focusing on the prediction of earthquakes with M ≥ 8.4.