Generating Seismic Design Power Spectral Density Functions

The most widely used way to describe earthquake motions for purposes of design is the response spectrum, but it is often difficult to apply a response spectrum when dealing with multiple degrees of freedom or with complex representations of structural behavior. The power spectral density function, which is a more fundamental description of the frequency content of ground motion, has found increasing use and is essential in the most popular methods of developing artificial earthquake time histories. Although in theory the response spectrum and the power spectral density are closely related, in practice it has proven difficult to compute one from the other. Two integration schemes described in the literature have been implemented in an interactive micro-computer program SPEED and are found to give substantially identical results. When they are used to find a power spectral density function that corresponds to a standard design response spectrum, the results do not converge at frequencies above 10 Hz. Possible explanations for this lie in the shape of the prescribed standard response spectra, the methodology used to generate them, and the lack of statistical variation at high frequencies. When power spectral density functions are calculated for response spectra determined from a statistical evaluation of strong motion across the full range of frequencies, the calculations converge rapidly.