Analysis of the time-scaling behaviour in the sequence of the aftershocks of the Bovec (Slovenia) April 12, 1998 earthquake

Analysis of the temporal fluctuations, described by a power spectral density S(f) decaying as 1/f(alpha) with exponent alpha > 0, in the sequence of aftershocks of the Bovec (Slovenia) earthquake of April 12, 1998 has been performed, using the Allan Factor (AF) method. The sequence of the occurrence times of the events with threshold magnitude M(th) greater than or equal to 2.0 is characterised by a scale-invariant behaviour from the time scale tau similar to 2.10(4) s with a scaling coefficient alpha similar to 0.9, evaluated by a least-square method. By gradually increasing the threshold magnitude up to M(th) = 2.9, the AF curves, associated, respectively with the processes of selected events with magnitude M greater than or equal to M(th) indicate a monotonic decrease of the value of the scaling exponent alpha, in the range of time scales stretching from 10(2) to 5.10(5) s. For all the thresholds considered, the AF curves increase monotonically with the counting time and are well fitted by an increasing power-law function for counting times greater than approximately 2.10(4) s. This monotonic power-law increase indicates the presence of fluctuations on many time scales and therefore of fractal clustering.