Two stochastic models of the earthquake process are used to generate sequences featuring seismic gaps, foreshock and aftershock episodes, background seismicity, and other patterns which resemble those of observed sequences. The models are based on the following statistical assumptions.

  • The distribution of earthquake magnitude is exponential.

  • The distribution in time of earthquake occurrences (excluding aftershocks) is Poisson.

  • The distribution in space of earthquake occurrences (excluding aftershocks) is Poisson.

  • The probability of occurrence of aftershocks increases with main event magnitude and follows Omori's law.

  • The distribution of distances between main event and aftershocks is exponential, with mean proportional to 100.57M, where M is the magnitude of the main event.

  • The distribution of aftershock magnitudes is exponential and related to the main event magnitude by Båth's law.

One model generates sequences in time only; the other generates events in time and space.

The similarity between realizations of the stochastic models and observed earthquake sequences suggests that there may be no information in seismic gaps about the time of occurrence or the magnitude of the next large event in the region.

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