Testing time-predictable earthquake recurrence by direct measurement of strain accumulation and release

Probabilistic estimates of earthquake hazard use various models for the temporal distribution of earthquakes, including the 'time-predictable' recurrence model formulated by Shimazaki and Nakata (which incorporates the concept of elastic rebound described as early as 1910 by H. F. Reid). This model states that an earthquake occurs when the fault recovers the stress relieved in the most recent earthquake. Unlike time-independent models (for example, Poisson probability), the time-predictable model is thought to encompass some of the physics behind the earthquake cycle, in that earthquake probability increases with time. The time-predictable model is therefore often preferred when adequate data are available, and it is incorporated in hazard predictions for many earthquake-prone regions, including northern California, southern California, New Zealand and Japan. Here we show that the model fails in what should be an ideal locale for its application -- Parkfield, California. We estimate rigorous bounds on the predicted recurrence time of the magnitude approximately 6 1966 Parkfield earthquake through inversion of geodetic measurements and we show that, according to the time-predictable model, another earthquake should have occurred by 1987. The model's poor performance in a relatively simple tectonic setting does not bode well for its successful application to the many areas of the world characterized by complex fault interactions.