Computation of Earthquake Response via Fourier Amplitude Spectra

A theoretical relation is presented between the seismological Fourier amplitude spectrumand the mean squared value of the elastic response, which is defined by Gaussian distribution. Byshifting a general process to its mean value, spectrum of the mean squared value of the displacementis computed from the Fourier amplitude spectrum and the real part of the relative displacementtransfer function of the single-degree-of-freedom elastic oscillator. It is shown that the relationpresented in this work opens the door for a better understanding of the relationship between timeinvariantmean squared value of linear response of a single degree freedom system and seismologicalvariables, such as magnitude, focal distance, and path and soil conditions. For illustrating theproposed theoretical relation, the mean squared values of a drift have been calculated for earthquakeground motions with different magnitude, focal distance and soil.