Random vibration theory offers an elegant and efficient way of predicting peak motions from a knowledge of the spectra of radiated energy. One limitation to applications in seismology is the assumption of stationarity used in the derivation of standard random vibration theory. This note provides a scheme that allows the standard theory to be applied to the transient signals common in seismology. This scheme is particularly necessary for predictions of peak response of long-period oscillators driven by short-duration ground motions.

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