Statistical physics models for aftershocks and induced seismicity

A standard approach to quantifying the seismic hazard is the relative intensity (RI) method. It is assumed that the rate of seismicity is constant in time and the rate of occurrence of small earthquakes is extrapolated to large earthquakes using GutenbergRichter scaling. We introduce nowcasting to extend RI forecasting to time-dependent seismicity, for example, during an aftershock sequence. Nowcasting uses natural time; in seismicity natural time is the event count of small earthquakes. The event count for small earthquakes is extrapolated to larger earthquakes using GutenbergRichter scaling. We first review the concepts of natural time and nowcasting and then illustrate seismic nowcasting with three examples. We first consider the aftershock sequence of the 2004 Parkfield earthquake on the San Andreas fault in California. Some earthquakes have higher rates of aftershock activity than other earthquakes of the same magnitude. Our approach allows the determination of the rate in real time during the afters...