Calibration of time history simulation methods

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Abstract
Ground-motion time histories for use in engineering analyses of structures in eastern North America are often simulated from seismological models, owing to the paucity of real recordings in the magnitude and distance ranges of interest. Two simulation methods have been widely used in recent years: the stochastic method and the ray-theory method. In the stochastic method, as implemented in this study, ground motion is treated as filtered Gaussian noise whose underlying spectrum is determined from an empirical region-specific seismological model of the source and propagation processes. In the ray-theory method, as implemented in this study, the ground motions are simulated by convolving an empirical source function with theoretical Green's functions for a specified crustal structure model. This article compares results of the two simulation methods for four well-recorded “calibration” events and assesses the applicability of the methods. The assessment is based on comparisons of ground-motion parameters from the simulated data with those of the actual recordings. Ground-motion parameters in the frequency range from 1 to 10 Hz are satisfactorily predicted by both methods. Averaged over the four events studied, the stochastic method underpredicts 1-Hz response spectra by 20 to 40% but accurately predicts response spectra for frequencies of greater than 2 Hz; it also accurately predicts peak ground acceleration and velocity. The wave-propagation method underpredicts 1-Hz response spectra by 10 to 40% but accurately predicts response spectra for higher frequencies; it overpredicts peak ground acceleration and velocity by 10 to 40%. Both methods are imprecise: the standard error of an estimate is a factor of about 2.2. The bias and standard error of an estimate for the wave-propagation method are generally slightly lower than for the stochastic method, if the focal depth of the event can be specified (i.e., as for a past earthquake). If the focal depth of the event is not known (i.e., as for a future earthquake) then the accuracy and precision of the two methods are about the same. The chief advantage of the wave-propagation method is its predictive power; since its attenuation function is derived from the focal depth and crustal structure it does not require knowledge of the empirical attenuation function. The chief advantage of the stochastic model is its economy and simplicity.

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