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.

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Strong motion records of 2007 Niigata-ken Chuetsu-oki earthquake were examined in order to evaluate ground motion characteristics of the earthquake. Ground motions observed at Kashiwazaki Kariwa Nuclear Power Plant site were significantly larger than the response spectra evaluated on the basis of Noda et al. (2002), and the level of the ground motion observed at Arahama area (unit 1-4 side) was approximately twice as large as that at Ominato area (unit 5-7 side). Observation records of the offshore events other than the eathquake were also larger than the response spectra based on Noda et al. (2002), whereas records of the inland events were smaller than those. In addition, these characteristics were also observed in the vicinity of the site through the analysis of the ground motion records obtained by KiK-net.

The relational equation of the inhomogeneity of the subsurface soil and the propagation distance of the ground motion with the spatial variation of the ground motion between adjacent points is constructed based on the scattering theory. By applying the relational equation to the response wave of the seismic simulation using the three-dimensional heterogeneous soil model and the observation records on the Chiba array, heterogeneous parameters of subsurface soil and the depth 𝐿𝐿 � which affects the spatial variation of the seismic motion were estimated.

Effects of magnitude, hypocenter distance and subsurface soil structure on the spatial variability of ground motions between adjacent sites are examined using observed records from the Chiba array and pairs of the K-NET and the KiK-net which are adjacent to each other. The statistical analysis of coherence and standard deviation of Fourier spectrum ratio of the ground motion show that the spatial variability of ground motion depends on magnitude, distance and subsurface soil structure. In particular, subsurface soil structure has the most significant influence on the variability. The decrease in S-wave velocity of subsurface soil causes a reduction of spatial coherence. And we also found that the longer the distance between observation sites, the deeper the soil properties effects to the spatial variability of ground motions.