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We present an alarm-based earthquake forecast model that uses the early aftershock statistics (EAST). This model is based on the hypothesis that the time delay before the onset of the power-law aftershock decay rate decreases as the level of stress and the seismogenic potential increase. Here, we estimate this time delay from < t(g)>, the time constant of the Omori-Utsu law. To isolate space-time regions with a relative high level of stress, the single local variable of our forecast model is the E-a value, the ratio between the long-term and short-term estimations of < t(g)>. When and where the E-a value exceeds a given threshold (i.e., the c value is abnormally small), an alarm is issued, and an earthquake is expected to occur during the next time step. Retrospective tests show that the EAST model has better predictive power than a stationary reference model based on smoothed extrapolation of past seismicity. The official prospective test for California started on 1 July 2009 in the testing center of the Collaboratory for the Study of Earthquake Predictability (CSEP). During the first nine months, 44 M >= 4 earthquakes occurred in the testing area. For this time period, the EAST model has better predictive power than the reference model at a 1% level of significance. Because the EAST model has also a better predictive power than several time-varying clustering models tested in CSEP at a 1% level of significance, we suggest that our successful prospective results are not due only to the space-time clustering of aftershocks.
In order to examine variations in aftershock decay rate, we propose a Bayesian framework to estimate the {K, c, p}-values of the modified Omori law (MOL), lambda(t) = K(c + t)(-p). The Bayesian setting allows not only to produce a point estimator of these three parameters but also to assess their uncertainties and posterior dependencies with respect to the observed aftershock sequences. Using a new parametrization of the MOL, we identify the trade-off between the c and p-value estimates and discuss its dependence on the number of aftershocks. Then, we analyze the influence of the catalog completeness interval [t(start), t(stop)] on the various estimates. To test this Bayesian approach on natural aftershock sequences, we use two independent and non-overlapping aftershock catalogs of the same earthquakes in Japan. Taking into account the posterior uncertainties, we show that both the handpicked (short times) and the instrumental (long times) catalogs predict the same ranges of parameter values. We therefore conclude that the same MOL may be valid over short and long times.