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sufficient data to permit a real-time estimate of the occurrence of earthquakes, the probability <br /> of exceeding a given value can be modeled as an equivalent Poisson process in which a <br /> variable average recurrence rate is assumed. The occurrence of ground motions at the site <br /> in excess of a specified level also is a Poisson process, if: <br /> (1) the occurrence of earthquakes is a Poisson process, and <br /> (2) the probability that any one event will result in ground motions at the site in <br /> excess of a specified level is independent of the occurrence of other events. <br /> The probability that a ground motion parameter "Z" exceeds a specified value "z" in a time <br /> period "t" is given by: <br /> p(Z > z) = 1-e°(Z)" (1) <br /> where v(z) is the annual mean number (or rate) of events in which Z exceeds z. It should <br /> be noted that the assumption of a Poisson process for the number of events is not critical. <br /> This is because the mean number of events in time t, v(z)•t, can be shown to be a close <br /> upper bound on the probability p(Z > z) for small probabilities (less than 0.10) that <br /> generally are of interest for engineering applications. The annual mean number of events <br /> is obtained by summing the contributions from all sources, that is: <br /> v(z) = E va(z) (2) <br /> n <br /> where Po(z) is the annual mean number (or rate) of events on source n for which Z exceeds <br /> z at the site. The parameter vn(z) is given by the expression: <br /> vn(z) = E E B.(m) • p(R=r,i mi) ' p(Z>z 1 m;,r;) (3) <br /> ij <br /> where: <br /> B.(m) = annual mean rate of recurrence of earthquakes of magnitude <br /> increment m; on source n; <br /> H:\CONTRACT\TENMR,E\3 3 M0412951500 <br />