In Time Dependent Model, the definition of foreshock, mainshock and aftershock is not necessary. In this model, every event is potentially triggered by all the previous events and every event can trigger subsequent events according to their relative time-space distance. What do you say about Stochastic models of earthquake clustering?
What are Stochastic models of earthquake clustering?.
Stochastic modeling allows the computation of the expected earthquakes rate density on a continuous space-time volume, suitable for the validation of a model with respect to others and for real time forecasts.
The significant steps made during the last decades in the physical modeling of earthquake clustering provide a tool for the refinement of these stochastic models.
Jointly with the improvement of the seismological observations, these steps appear as a progress towards the possible practical application for earthquake forecast.
In time dependent model:
The magnitude distribution is the same for all the earthquakes (Gutenberg-Richter law).
The occurrence rate density is the superposition of a time independent (poissonian) component and that of the triggered seismic activity.
The occurrence rate of triggered events depends exponentially on the magnitude of every preceding event.
The spatial distribution of triggered events is described by an isotropic function around the epicenter of every previous event.
The temporal behavior of triggered events is described by the Omori law starting from the occurrence time of every previous event.