Analytical approach to calculation of response spectra from seismological models of ground motion

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Abstract
An analytical approach to calculate response spectra from seismological models of ground motion is presented. Seismological models have three major advantages over empirical models: (1) they help in an understanding of the physics of earthquake mechanisms, (2) they can be used to predict ground motions for future earthquakes and (3) they can be extrapolated to cases where there are no data available. As shown with this study, these models also present a convenient form for the calculation of response spectra, by using the methods of random vibration theory, for a given magnitude and site conditions. The first part of the paper reviews the past models for ground motion description, and introduces the available seismological models. Then, the random vibration equations for the spectral response are presented. The non‐stationarity, spectral bandwidth and the correlation of the peaks are considered in the calculation of the peak response. The accuracy of the model is found to be satisfactory after comparing the calculated spectra with the empirical spectrum of Joyner and Boore,51which was developed by using records from 12 shallow earthquakes in western North America. The last part of the paper presents some numerical examples that show the variation of response spectra and peak factors (i.e. peak response/RMS response) for different magnitudes and distances.

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