Space–time ETAS models and an improved extension

For sensitive detection of anomalous seismicity such as quiescence and activation in a given region, we need a suitable statistical reference model that represents a normal seismic activity in the region. The regional occurrence rate of the earthquakes is modeled as a function of previous activity, the specific form of which is based on empirical laws in time and space such as the modified Omori formula and the Utsu–Seki scaling law of aftershock area against magnitude, respectively. This manuscript summarizes the development of the epidemic type aftershock sequence (ETAS) model and proposes an extended version of the best fitted space–time model that was suggested in Ogata [Ogata, Y., 1998. Space–time point-process models for earthquake occurrences, Ann. Inst. Statist. Math., 50: 379–402.]. This model indicates significantly better fit to seismicity in various regions in and around Japan.