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