Seismic Electric Signals and 1/f "noise" in natural time

Abstract

By making use of the concept of natural time, a simple model is proposed which exhibits the $1/f^a$ behavior with $a$ close to unity. The properties of the model are compared to those of the Seismic Electric Signals (SES) activities that have been found to obey the ubiquitous $1/f^a$ behavior with $a \approx 1$. This comparison, which is made by using the most recent SES data, reveals certain similarities, but the following important difference is found: The model suggests that the entropy $S_-$ under time reversal becomes larger compared to the entropy $S$ in forward time, thus disagreeing with the experimental SES results which show that $S$ may be either smaller or larger than $S_-$. This might be due to the fact that SES activities exhibit {\em critical} dynamics, while the model cannot capture all the characteristics of such dynamics.