Recurrence of Exceedence of Threshold Seismic Ground Motion from Earthquake Recurrence, Ground-Motion Attenuation, and Hypocentral-Depth Relations

Abstract

In evaluating potential sites of major engineered facilities for purposes of preliminary screening, feasibility, or conceptual design it is important to establish the recurrence interval (return period) of critical levels of seismically-induced ground motion. An essential element in estimating this parameter both in regions with and without known seismogenic faults, is the analysis of “random” earthquakes. A useful tool in performing this analysis is the well known earthquake size-to-recurrence equation, log 10 N = a – bM. This paper illustrates how this equation can be used with attenuation relations and hypocentral depths to estimate recurrence of exceedence of threshhold values of seismic ground-motion parameters. Intended for preliminary site screening, feasibility, and conceptual design studies in regions of “random” earthquakes, with or without seismogenic faults, the illustrated method of approach provides reasonable constraints to preliminary evaluation and site selection decisions when recurrence of threshhold ground motion is considered. In a first hypothetical example a site in a region where all earthquakes are “random” is assumed. Using a given threshold acceleration level and a suitable attenuation equation the areas within which epicenters of given-magnitude earthquakes must be located for the earthquakes to produce the threshold site acceleration are calculated. By means of a recurrence equation these areas are converted to an annual frequency and return period of epicenters of events capable of generating the specified ground motion. Finally, estimates of hypocentral depth are used to convert epicentral frequency to frequency of exceedence of the specified acceleration at the given site. In a second hypothetical example an active fault generating a given magnitude earthquake is assumed and a site acceleration derived. The recurrence of exceedence of this value by lower magnitude “random” earthquakes is then calculated and it is shown that recurrence of site acceleration generated by “random” events can be significant even in regions of known seismogenic structures.