Inter-event time statistics of earthquakes as a gauge of volcano activity

The probability distribution of inter-event time (IET) between two consecutive earthquakes is a measure for the uncertainty in the occurrence time of earthquakes in a region of interest. It is well known that the IET distribution for regular earthquakes is commonly characterized by a power law with the exponent of 0.3. However, less is known about other classes of earthquakes, such as volcanic earthquakes, which do not manifest mainshock-aftershocks sequences. Since volcanic earthquakes are caused by the movement of magmas, their IET distribution may be closely related to the volcanic activities and therefore of particular interest. Nevertheless, the general form of IET distribution for volcanic earthquakes and its dependence on volcanic activity are still unknown. Here we show that the power-law exponent characterizing the IET distribution exhibits a few common values depending on the stage of volcanic activity. Volcanoes with steady seismicity exhibit the lowest exponent ranging from 0.6 to 0.7. During the burst period, when the earthquake rate is highest, the exponent reaches its peak at approximately 1.3. In the preburst phase, the exponent takes on the intermediate value of 1.0. These values are common to several different volcanoes. Since the preburst phase is characterized by the distinct exponent value, it may serve as an indicator of imminent volcanic activity that is accompanied by a surge in seismic events.