Displacement spectra for long periods

Using selected sets of high quality digital strong motion data from different regions (Taiwan, Japan, Italy, and Greece), the salient features of displacement response spectra in the long period range are illustrated (up to 10 s period) as a function of magnitude, source distance, and site conditions. By means of simple analytical models of displacement waveforms, we have derived analytical expressions for the displacement spectra that provide satisfactory fits to the observations. These expressions also demonstrate that the moment magnitude and distance control the shape of the spectra consistently with the commonly accepted models of the seismic source. Furthermore, we derived from simple physical considerations an analytical expression of the variation of peak ground displacement with magnitude and distance, that reasonably fits the observations. The findings of this study are believed to be particularly useful in the formulation of design elastic displacement spectra for seismic codes, and in zoning studies of seismic hazard for long-period structures.