A semi-Markov model estimating the waiting times and magnitudes of large earthquakes is proposed. The model defines a discrete-time, discrete-state process in which successive state occupancies are governed by the transition probabilities of the Markov process. The stay in any state is described by an integer-valued random variable that depends on the presently occupied state and the state to which the next transition is made. Basic parameters of the model are the transition probabilities for successive states, the holding time distribution, and the initial conditions (the magnitude of the most recent earthquake and the time elapsed since then).
The model was tested by examining compatibility with historical seismicity data for large earthquakes in the circum-Pacific belt. The examination showed reasonable agreement between the calculated and actual waiting times and earthquake magnitudes. The proposed procedure provides a more consistent model of the physical process of gradual accumulation of strain and its intermittent, nonuniform release through large earthquakes and can be applied in the evaluation of seismic risk.
Although geological and geomorphic evidence strongly suggests that the Wasatch fault zone has generated large-magnitude earthquakes in late Quaternary time, the fault zone has not been associated with earthquakes greater than magnitude 512 in the past 133 yr. Therefore, realistic estimates of the likelihood of future damaging earthquakes must be based on more than historical seismicity data. The data base can be expanded by collecting site-specific geological information on earthquake recurrence and fault slip rates and by using this information in a model of the earthquake generation process. Uncertainties in both the physical basis for the model and in the geological parameters dictate a probabilistic approach. A semi-Markov model provides real-time probabilities of occurrence of at least one moderate to large (magnitude 612 or larger) earthquake at either of two sites for given elapsed times. Probabilities derived for the entire Wasatch fault zone are based on earthquake recurrence data on individual fault segments and are especially sensitive to elapsed times on individual segments.
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