Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a certain magnitude M in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time τ0. As a consequence, the conditional mean recurrence time τ(τ0) between two events increases monotonically with τ0. For τ0 well below the average recurrence time τ,τ(τ0) is smaller than τ, while for τ0>τ, τ(τ0) is greater than τ. Also, the mean residual time until the next earthquake does not depend only on the elapsed time, but also strongly on τ0. The larger τ0 is, the larger is the mean residual time. The above features should be taken into account in any earthquake prognosis.