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SECT UTWO Seismic Hazard Analysis Methodology <br /> Several factors control the level and character of earthquake ground shaking. These factors are <br /> in general: (1) rupture dimensions, geometry, and orientation of the causative fault;(2)distance <br /> from the causative fault; (3) magnitude of the earthquake; (4) the rate of attenuation of the <br /> seismic waves along the propagation path from the source to site; and (5) site factors including <br /> the effects of near-surface geology particularly from soils and unconsolidated sediments. Other <br /> factors, which vary in their significance depending on specific conditions, include slip <br /> distribution along the fault, rupture process, footwall/hanging-wall effects, and the effects of <br /> crustal structure such as basin effects. <br /> 2.1 PSHA APPROACH <br /> The PSHA used in this study is based on the model developed principally by Cornell (1968). <br /> The occurrence of earthquakes on a fault is assumed to be a Poisson process. The Poisson model <br /> is widely used and is a reasonable assumption in regions where data are sufficient to provide <br /> only an estimate of average recurrence rate (Comell, 1968). When there are sufficient data to <br /> permit a real-time estimate of the occurrence of earthquakes,the probability of exceeding a given <br /> value can be modeled as an equivalent Poisson process in which a variable average recurrence <br /> rate is assumed. The occurrence of ground motions at a site in excess of a specified level also is <br /> a Poisson process, if (1) the occurrence of earthquakes is a Poisson process, and (2) the <br /> probability that any one event will result in ground motions at the site in excess of a specified <br /> 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 1z", (1) <br /> where v(z) is the annual mean number (or rate) of events in which Z exceeds z. It should be <br /> noted that the assumption of a Poisson process for the number of events is not critical. This is <br /> because the mean number of events in time t, v(z)•t can be shown to be a close upper bound on <br /> the probability p(Z> z) for small probabilities (less than 0.10)that generally are of interest for <br /> engineering applications. The annual mean number of events is obtained by summing the <br /> contributions from all sources,that is: <br /> V(Z)=E V„(Z) (2) <br /> n <br /> where V„(Z) is the annual mean number(or rate) of events on source n for which Z exceeds z at <br /> the site. The parameter v„(z)is given by the expression: <br /> v„(z)=EEBn(mi)•p(R=rjlm,)•p(Z>zlm,,ri) (3) <br /> ij <br /> where: <br /> Bn(m,) = annual mean rate of recurrence of earthquakes of magnitude increment m,on <br /> source n; <br /> p(R=rim,) = probability that given the occurrence of an earthquake of magnitude m, on <br /> source n, rj is the closest distance increment from the rupture surface to the <br /> site; <br /> UM 2 <br />