**GENERALIZED OMORI LAW FOR AFTERSHOCKS AND FORESHOCKS
FROM A SIMPLE DYNAMICS**
**SHAW BE**
**GEOPHYSICAL RESEARCH LETTERS**

20: (10) 907-910 MAY 21 1993

**Abstract:**

A theory of the time dependence of earthquake foreshocks
and aftershocks is presented. The theory involves the response to sudden
forcing of a dynamics of self-driven acceleration to failure. The empirically
observed Omori law, which says that the rate of aftershocks as a function
of time falls as a power law in time, is derived theoretically. The exponent
of the falloff in time is shown to generically give a value close to one,
for rapidly accelerating dynamics. To see if the theory is consistent with
other features of real data, foreshocks and aftershocks of small magnitude
mainshocks are analyzed in a catalogue of real earthquakes. Results show
that the spatial and temporal distribution of aftershocks is separable
into a dependence on space and a dependence on time, that the spatial distribution
of aftershocks is consistent with the hypothesis that stress changes from
the mainshock cause aftershocks, and that the number of foreshocks approaches
the number of aftershocks as the magnitude of the mainshock becomes smaller.