Order parameter analysis of seismicity in natural time domain

The natural time χ is a new time domain introduced by Varotsos et al in 2001. Novel dynamical features of time series in complex systems can emerge upon self analysis in natural time, which conforms to the desire to extract useful signal information and reduce uncertainty effectively. In this study, we first introduce the natural time method and then select top 30 earthquakes from the catalogue of China Earthquake Networks Center from 1978 to 2014, after that calculate the variance κ₁ and the coefficient of variation β of the normalized energy released from each earthquake in natural time domain. Taking κ₁ as the order parameter, we qualitatively analyse κ₁ by making use of β, and further quantitatively analyse κ₁ on that basis afterwards. The results show that the order parameter κ₁ nearly equals to 0.07 from half an hour to months before the main shock and abruptly decreases toward zero when the main shock happenes. Furthermore, we simply discuss the way to select time window in quantitative analysis and some special cases in analysis results. Hence, it seems that the results have a guiding significance for earthquake events retrospective study and earthquake prediction study.