Scaling equation between response spectrum and energy spectrum

In this paper, the scaling equation between the pseudo velocity response spectrum and the energy spectrum is proposed. Utilizing random vibration theory, the maximum response of SDOF is given as the function of power spectrum density of main part of earthquake motion. Whereas, energy spectrum is equal to Fourier amplitude spectrum smoothed by spectral window, which is clearly pointed out by Kuwamura, et al. Finally, the equation between response spectrum and energy spectrum is derived, by making connection between Fourier amplitude spectrum and power spectrum density considering the nonstationarity of earthquake motion. The proposed equation is verified not only using the artificial earthquake motions but also using the observed strong ground motions of both interplate earthquakes and inland crustal earthquakes. The equation between the peak ground acceleration/velocity and response spectrum is also proposed, which is the application of the method shown in this paper.