A physically-motivated model for earthquake recurrence based on the Brownian relaxation oscillator is introduced. The renewal process defining this point process model can be described by the steady rise of a state variable from the ground state to failure threshold as modulated by Brownian motion. Failure times in this model follow the Brownian passage time (BPT) distribution, which is specified by the mean time to failure, μ, and the aperiodicity of the mean, α (equivalent to the familiar coefficient of variation). Analysis of 37 series of recurrent earthquakes, M -0.7 to 9.2, suggests a provisional generic value of α = 0.5. For this value of α, the hazard function (instantaneous failure rate of survivors) exceeds the mean rate for times > μ⁄2, and is ~ ~ 2 ⁄ μ for all times > μ. Application of this model to the next M 6 earthquake on the San Andreas fault at Parkfield, California suggests that the annual probability of the earthquake is between 1:10 and 1:13.
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A physically-based earthquake recurrence model for estimation of long-term earthquake probabilities