The probability p that a given fault segment will rupture within a specified time T following the preceding rupture is evaluated empirically from a sample of observed recurrence intervals for that fault segment. All that is assumed is that the probability of rupture within the specified time interval is the same for all rupture cycles on that segment. Suppose that m of the n observed recurrence intervals correspond to cycles in which rupture occurred within the interval T following the preceding earthquake. The probability density that rupture in the current cycle will also fall within the interval T following the most recent earthquake is then given by the beta distribution P(p|m, n) = {(n + 1)!/[m!(nm!]}pm(1 − p)nm. The best estimate of the desired probability pis 〈p〉 = (m + 1)/(n + 2), and a measure of the breadth of the distribution is the standard deviation σ = [〈p〉 (1 − 〈p〉)/(n + 3)]1/2. Because it is unlikely that the number n of observed recurrence intervals will be much greater than 10, the probability generally will not be defined more closely than ±0.2. Moreover, increasing n decreases the uncertainty only very slowly.

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