Counting statistics of f ?? fluctuations: a new method for analysis of earthquake data

Abstract

In a variety of biological and physical phenomena, temporal fluctuations are found, which are not explainable as consequences of statistically independent random events. If these fluctuations are characterized by a power spectrum density S(f) decaying as f -¢ at low frequencies, this behaviour is called 1/f noise.Counting statistics applied to earthquake activity data leads to three time scales with different characteristics, represented by the exponent/3: at interval lengths less than 1 h, the shocks are randomly distributed as in a Poisson process. For medium time intervals (1 day to 3 months), the exponent 1 +/3 is larger (1.4 for M0=3), but approaches unity for higher threshold magnitudes M0. In longer time ranges the exponent assumes values near 1.55, however, with increasing statistical variation at higher M0, due to lower counts.The temporal sequence is different from white noise; thus, it might be fruitful to apply neural network algorithms, because this method allows predictions in some other cases with similar characteristics.

Scale-invariance Properties in Seismicity of Southern Apennine Chain (Italy)

“…It can be demonstrated (BITTNER et al, 1996) that the temporal fluctuations of earthquake activity are characterized by a power spectrum density S( f ) decaying as f − i at low frequencies. It can be demonstrated (BITTNER et al, 1996) that the temporal fluctuations of earthquake activity are characterized by a power spectrum density S( f ) decaying as f − i at low frequencies.…”

“…The rationale of the method consists in the relationship between the second-time derivative of the variance-time curve (VTC), defined as the variance of the counts in the time interval Dt =(t 1 , t 2 ), and the autocovariance of the point process, describing the earthquake sequence (BITTNER et al, 1996).…”