Paleoseismic interevent times interpreted for an unsegmented earthquake rupture forecast

Forecasters want to consider an increasingly rich variety of earthquake ruptures. Past occurrence is captured in part by paloeseismic observations, which necessarily see three‐dimensional ruptures only at a point. This has not been a problem before, because forecasts have assumed that faults are segmented, and that repeated ruptures occur uniformly along them. A technique is now required to calculate paleo‐earthquake rates at points that may be affected by multiple recurrence processes, and that is consistent with an all‐possible‐ruptures forecast. Dating uncertainties are addressed by bootstrapping across event time windows, and the resulting distributions are transformed into log space as f (ln( T )) where T is interevent time. This takes advantage of a property of time‐dependent recurrence distributions in which their logarithms are normally distributed. Paleoseismic series necessarily have a finite number of observations such that the true long‐term mean interevent time ( μ ) is hard to estimate. However the mode (most frequent value) is easier to identify. Since the mode is equal to the mean of a normal distribution, μ can thus be found at the mode ( m ) of f (ln( T )) as μ = e m . The point μ − σ occurs where 32% of a folded (half) normal distribution is found in the interval between ln( T ) = 0 and m. The μ + σ value is identified by symmetry, which overcomes the difficulty of absent long intervals in the record. Tests are conducted with complex synthetic interevent distributions, and applications to real data from the Hayward and Garlock faults in California are shown.