Estimating recurrence times and seismic hazard of large earthquakes on an individual fault

S U M M A R Y We present a strategy for estimating the recurrence times between large earthquakes and associated seismic hazard on a given fault section. The goal of the analysis is to address two fundamental problems. (1) The lack of sufficient direct earthquake data and (2) the existence of ‘subgrid’ processes that can not be accounted for in any model. We deal with the first problem by using long simulations (some 10 000 yr) of a physically motivated ‘coarsegrain’ model that reproduces the main statistical properties of seismicity on individual faults. We address the second problem by adding stochasticity to the macroscopic model parameters. A small number N of observational earthquake times (2 ≤ N ≤ 10) can be used to determine the values of model parameters which are most representative for the fault. As an application of the method, we consider a model set-up that produces the characteristic earthquake distribution, and where the stress drops are associated with some uncertainty. Using several model realizations with different values of stress drops, we generate a set of corresponding synthetic earthquake catalogues. The recurrence time distributions in the simulated catalogues are fitted approximately by a gamma distribution. A superposition of appropriately scaled gamma distributions is then used to construct a distribution of recurrence intervals that incorporates the assumed uncertainty of the stress drops. Combining such synthetic data with observed recurrence times between the observational ∼M6 earthquakes on the Parkfield segment of the San Andreas fault, allows us to constrain the distribution of recurrence intervals and to estimate the average stress drop of the events. Based on this procedure, we calculate for the Parkfield region the expected recurrence time distribution, the hazard function, and the mean waiting time to the next ∼M6 earthquake. Using five observational recurrence times from 1857 to 1966, the recurrence time distribution has a maximum at 22.2 yr and decays rapidly for higher intervals. The probability for the post 1966 large event to occur on or before 2004 September 28 is 94 per cent. The average stress drop of ∼M6 Parkfield earthquakes is in the range τ = (3.04 ± 0.27) MPa.