@article{ShebalinNarteauHolschneideretal.2011,
  author    = {Shebalin, Peter and Narteau, Clement and Holschneider, Matthias and Schorlemmer, Danijel},
  title     = {Short-Term earthquake forecasting using early aftershock statistics},
  series = {Bulletin of the Seismological Society of America},
  volume    = {101},
  journal   = {Bulletin of the Seismological Society of America},
  number    = {1},
  publisher = {Seismological Society of America},
  address   = {El Cerrito},
  issn      = {0037-1106},
  doi       = {10.1785/0120100119},
  pages     = {297 -- 312},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@article{ShebalinNarteauHolschneider2012,
  author    = {Shebalin, Peter and Narteau, Clement and Holschneider, Matthias},
  title     = {From alarm-based to rate-based earthquake forecast models},
  series = {Bulletin of the Seismological Society of America},
  volume    = {102},
  journal   = {Bulletin of the Seismological Society of America},
  number    = {1},
  publisher = {Seismological Society of America},
  address   = {Albany},
  issn      = {0037-1106},
  doi       = {10.1785/0120110126},
  pages     = {64 -- 72},
  year      = {2012},
  abstract  = {We propose a conversion method from alarm-based to rate-based earthquake forecast models. A differential probability gain g(alarm)(ref) is the absolute value of the local slope of the Molchan trajectory that evaluates the performance of the alarm-based model with respect to the chosen reference model. We consider that this differential probability gain is constant over time. Its value at each point of the testing region depends only on the alarm function value. The rate-based model is the product of the event rate of the reference model at this point multiplied by the corresponding differential probability gain. Thus, we increase or decrease the initial rates of the reference model according to the additional amount of information contained in the alarm-based model. Here, we apply this method to the Early Aftershock STatistics (EAST) model, an alarm-based model in which early aftershocks are used to identify space-time regions with a higher level of stress and, consequently, a higher seismogenic potential. The resulting rate-based model shows similar performance to the original alarm-based model for all ranges of earthquake magnitude in both retrospective and prospective tests. This conversion method offers the opportunity to perform all the standard evaluation tests of the earthquake testing centers on alarm-based models. In addition, we infer that it can also be used to consecutively combine independent forecast models and, with small modifications, seismic hazard maps with short- and medium-term forecasts.},
  language  = {en}
}