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[~ <br />1 <br />1 <br />LJ <br />u <br /> <br />I <br />~J <br /> <br />1 <br />sufficient data to permit areal-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 /> <br />' where v(z) is the annual mean number (or rate) of events in which Z exceeds :i. 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) ttlat generally <br />are of interest for engineering applications. The annual mean number of events. is obtained <br />by summing the contributions from all sources, that is: <br /> <br />1 <br />r <br />LJ <br /> <br /> <br />v(z) = E vn(z) (2) <br />n <br />where v(z) is the annual mean number (or rate) of events on source n for which Z exceeds <br />z at the site. The parameter v,(z) is given by the expression: <br />v(z) = E E B•(~) • P(R=rtl~) • P(Z>zltty,rt) (3) <br />tJ <br />where: <br />B•(m;) = annual mean rate of recurrence of earthquakes of magnitude <br />increment m; on source n; <br />H:\COMRACn23/561.DUP3 3 M0309951609 <br />