Stochastic modeling of nonstationary earthquake time series with long-term clustering effects

Abstract

Earthquake time series are widely used to characterize the main features of regional seismicity and to provide useful insights into earthquake dynamics. Properties such as intermittency and nonstationary clustering are common in earthquake time series, highlighting the complex nature of the earthquake generation process. In the present work we introduce a stochastic model with memory effects that reproduces the temporal scaling behavior observed in regional seismicity. For nonstationary earthquake activity, where the average seismic rate fluctuates, the solution of the stochastic model is the $q$-generalized gamma function that presents two power-law regimes for short and long waiting times, respectively, while for stationary activity it reduces to the standard gamma function. To validate the derived model, we study nonstationary earthquake time series from Southern California and Japan. The analysis shows that for various threshold magnitudes and spatial areas and after rescaling with the mean waiting time, the normalized probability density functions fall onto a unique curve, which is characterized by two power-law regimes for short and long waiting times, respectively, a scaling behavior that can exactly be recovered by the derived $q$-generalized gamma function. The results show the validity of the stochastic model and the derived scaling function, further signifying both short- and long-term clustering effects and memory in the evolution of seismicity.