Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks

Details Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks

2001-09-18

arxiv.org/abs/cond-mat/0109318v2

J. Geophys. Res. 107, NO. B10, 2237, doi:10.1029/2001JB001580 (2002)

Physics

Condensed Matter

Statistical Mechanics

Latex document of 41 pages + 6 eps figures + 1 table

Scientific paper

We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by a single mainshock decreases with the time from the mainshock according to the modified Omori law K/(t+c)^p with p=1+theta. A mainshock at time t=0 triggers aftershocks according to the local Omori law, that in turn trigger their own aftershocks and so on. The effective branching parameter n, defined as the mean aftershock number triggered per event, controls the transition between a sub-critical regime n<1 to a super-critical regime n>1. In the sub-critical regime, we recover and document the crossover from an Omori exponent 1-theta for t1 and theta>0, we find a novel transition from an Omori decay law with exponent 1-theta fot tt*. The case theta<0 yields an infinite n-value. In this case, we find another characteristic time tau controlling the crossover from an Omori law with exponent 1-theta for t

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