Scale-free statistics of time interval between successive earthquakes

The statistical property of the calm times, i.e., time intervals between successive earthquakes with arbitrary values of magnitude, is studied by analyzing the seismic time series data in California and Japan. It is found that the calm times obey the Zipf-Mandelbrot power law, exhibiting a new scale-free nature of the earthquake phenomenon. Dependence of the exponent of the power-law distribution on threshold for magnitude is examined. As threshold increases, the tail of the distribution tends to become longer, showing difficulty in statistically estimating time intervals of earthquakes.