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Incorporating acceleration variability into seismic hazard analysis

U.S. GEOLOGICAL SURVEY, MAIL STOP 966, BOX 25046, DENVER FEDERAL CENTER, DENVER, COLORADO 80225

Abstract

Accelerations at a site resulting from earthquakes of a given magnitude and distance are commonly assumed to be lognormally distributed with standard deviation (where is independent of magnitude and distance. Significantly higher accelerations may be predicted for a given return period when acceleration variability is taken into account than when only median acceleration values are used in seismic hazard calculations. If the magnitude range is not restricted, the acceleration having a given return period increases from a_o, obtained using median values, to a_oexp(ß²/2c₂), when acceleration variability is included. This result assumes the attenuation function is of the form log_e(a) = c₁ + c₂m + f(R) [where f(R) is a function of distance only], and the magnitude-frequency relationship is log_e(N) = – ßm. In this case, the acceleration for a return period is best approximated by using, rather than the median value for each magnitude and distance, the acceleration that is a factor exp(k) greater than the median, where k = ß/2c₂.

For a restricted magnitude range, m_min m m_max, using only median values limits the calculated accelerations at a site to a range a_min a a_max. If variability is included, the acceleration range is no longer limited; the return period of an acceleration near a_min increases, while that of an acceleration near a_max decreases. If the distribution of accelerations is truncated at n, the maximum acceleration at a site will be a_maxexp(n). Half or more of the increase in the acceleration level for a return period obtained by including acceleration variability may result from accelerations that are greater than 1.5 to 2.0 above the median value. Including variability and using a finite maximum magnitude may give a higher acceleration for a fixed return period than the value calculated using median values and an infinite maximum magnitude.

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