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 −β 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 β: 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 + β is larger (1.4 for M 0=3), but approaches unity for higher threshold magnitudes M 0. In longer time ranges the exponent assumes values near 1.55, however, with increasing statistical variation at higher M 0, 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.
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Bittner, H.R., Tosi, P., Braun, C. et al. Counting statistics of f −β fluctuations: a new method for analysis of earthquake data. Geol Rundsch 85, 110–115 (1996). https://doi.org/10.1007/BF00192068
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DOI: https://doi.org/10.1007/BF00192068