Long records often show large earthquakes occurring in supercycles, sequences of temporal clusters of seismicity, cumulative displacement, and cumulative strain release separated by less active intervals. Supercycles and associated earthquake clusters are only partly characterized via the traditionally used aperiodicity, which measures the extent that a sequence differs from perfectly periodic. Supercycles are not well described by commonly used models of earthquake recurrence. In the Poisson model, the probability of a large earthquake is constant with time, so the fault has no memory. In a seismic cycle/renewal model, the probability is quasi-periodic, dropping to zero after a large earthquake, then increasing with time, so the probability of a large earthquake depends only on the time since the past one, and the fault has only “short-term memory.” We describe supercycles with a Long-Term Fault Memory (LTFM) model, where the probability of a large earthquake reflects the accumulated strain rather than elapsed time. The probability increases with accumulated strain (and time) until an earthquake happens, after which it decreases, but not necessarily to zero. Hence, the probability of an earthquake can depend on the earthquake history over multiple prior cycles. We use LTFM to simulate paleoseismic records from plate boundaries and intraplate areas. Simulations suggest that over timescales corresponding to the duration of paleoseismic records, the distribution of earthquake recurrence times can appear strongly periodic, weakly periodic, Poissonian, or bursty. Thus, a given paleoseismic window may not capture long-term trends in seismicity. This effect is significant for earthquake hazard assessment because whether an earthquake history is assumed to contain clusters can be more important than the probability density function chosen to describe the recurrence times. In such cases, probability estimates of the next earthquake will depend crucially on whether the cluster is treated as ongoing or over.
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We thank Ryan Gold, Chris Goldfinger, John Adams, Ned Field, and Joshua Hoover for fruitful discussions. We thank Tim Dixon for a helpful review. This research was supported by Northwestern University's Institute for Policy Research, Buffet Center for International Studies, and Institute on Complex Systems (NICO). Liu acknowledges support of NSF grant 1519980.
We thank Ryan Gold, Chris Goldfinger, John Adams, Ned Field, and Joshua Hoover for fruitful discussions. We thank Tim Dixon for a helpful review. This research was supported by Northwestern University 's Institute for Policy Research, Buffet Center for International Studies, and Institute on Complex Systems (NICO). Liu acknowledges support of NSF grant 1519980 .
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