EMPIRICAL EARTHQUAKE PROBABILITIES FROM OBSERVED RECURRENCE INTERVALS

The probability p that a given fault segment will rupture within a spe cified 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 sp ecified time interval is the same for all rupture cycles on that segme nt. Suppose that m of the n observed recurrence intervals correspond t o cycles in which rupture occurred within the interval T following the preceding earthquake. The probability density that rupture in the cur rent cycle will also fall within the interval T following the most rec ent earthquake is then given by the beta distribution P(p\m, n) = {(n + 1)!/[m!(n - m)!]}p(m)(1 - p)(n - m). The best estimate of the desire d probability p is [p] = (m + 1)/(n + 2), and a measure of the breadth of the distribution is the standard deviation sigma = [[p] (I - [p])/ (n + 3)]1/2. Because it is unlikely that the number n of observed recu rrence intervals will be much greater than 10, the probability general ly will not be defined more closely than +/-0.2. Moreover, increasing n decreases the uncertainty only very slowly.