Detection of events in seismic time series by time-frequency methods

The detection of events in seismic time series has been a subject of great interest during the last 30 years. Most of the works in this area were based on detecting special patterns or clusters in seismic data. The authors present here a event detection method based on a time-frequency analysis through the Wigner distribution (WD). The proposed method consists on defining an appropriate entropic measure through a suitable time-frequency distribution, acting as probability distribution function. It is known from previous studies in the field that the information entailed by time-frequency representations (TFR) of time signals can be explored by means of different Re-nyi entropy measures. The non-positivity character of the WD implies that the classical Shannon entropy cannot be used, and therefore it has been replaced by a generalised measure such as the Re-nyi entropy. However, owing to the existence of multiple TFR normalizations, the so-called quantum normalisation has been empirically selected here for this particular application. This method is based on the identification of the events as those temporal clusters having the highest amount of information (entropy). The method is described and applied to different earthquake signals and volcanic tremors, using both real and synthetic data. The results are compared to other existing event detection methods.