The main factors that affect ground motion include the earthquake source, the medium and path of seismic wave propagation and the local site condition. Although the spectral accelerations of ground motion have common characteristics in statistical sense, the specific shape of each spectral acceleration is unique, and some spectral accelerations have significant regular deviations from the statistical mean values. These deviations often appear in the form of a single-peak superimposed on the average spectral accelerations, which might be related to the earthquake parameters, such as earthquake magnitude and epicenter distance, and the site parameters, such as shear wave velocity and overburden thickness, and strong motion intensity.

In this paper, based on 85 976 strong earthquake records obtained by Japanese KiK-net network, the statistical relationship of the spectral accelerations normalized by peak ground acceleration （PGA） with magnitude and epicenter distance was obtained. Using predicted value plus 0.5 time of variances as the separatrix, the acceleration records were divided into two categories, that is, the records with or without regular deviations of spectral accelerations. By calculating the differences between the spectral accelerations of records with regular deviations and the predicted spectral accelerations without regular deviations, the regular deviations of the spectral accelerations were separated out, and the shapes of the regular deviations were verified to be highly consistent with the Gaussian curve. The regular deviations of spectral accelerations could be characterized by the central period, the relative height and the relative width of the fitted Gaussian curves.

Based on the statistical analyses of 25 229 acceleration records with regular deviations of spectral accelerations obtained by Japanese KiK-net network, the correlations between the characteristic parameters of regular deviations and earthquake parameters, local site conditions, and ground motion intensity were discussed. The results indicated that:

1） The central periods of regular deviations in logarithmic coordinates slightly increased with earthquake magnitudes in linear coordinates, slightly increased with epicenter distances in logarithmic coordinates, significantly increased with overburden thickness with shear wave velocity up to 1 km/s, and significantly decreased with 30 m average shear wave velocity v_S30, while their trend with strong motion intensity （i.e. PGA） was not obvious. It could be concluded that the central periods of regular deviations were mainly controlled by the local site conditions, and also affected by earthquake magnitudes and epicenter distances.

2） The relative heights of regular deviations in logarithmic coordinates significantly increased with v_S30, and slightly increased with overburden thickness with shear wave velocity up to 1 km/s, while their trend with earthquake magnitude, epicenter distances or PGA was not obvious. It could be concluded that the relative heights of regular deviations were mainly determined by the local site conditions, while the influences of earthquake magnitude, epicenter distance, and strong motion intensity were not significant.

3） The relative widths of regular deviations in logarithmic coordinate significantly increased with v_S30, and decreased with earthquake magnitude, epicenter distance, and overburden thickness with shear wave velocity up to 1 km/s, while the influences of strong motion intensity were not significant. It could be concluded that the relative widths of regular deviations were mainly influenced by the local site conditions and earthquake parameters.

Selecting average shear wave velocity, overburden thickness, earthquake magnitude, and epicenter distance as independent variables, empirical statistical relationships to predict the parameters of the regular deviations of spectral accelerations, including the central period, the relative height and the relative width, were given by the multiple linear regression methods, which could lead to the following prediction procedure of spectral accelerations considering regular deviations:

1） Considering the influence of earthquake magnitudes, epicenter distances and local site conditions, determine the site related spectral accelerations without regular deviations by the attenuation relationships （ground motion prediction equations） for spectral acceleration.

2） Considering the influence of average shear wave velocity, overburden thickness, earthquake magnitude, and epicenter distance, determine the central period, the relative height and the relative width of regular deviations by the empirical statistical relationships given in this paper.

3） Determine the regular deviation curve of spectral accelerations by the Gaussian function using independent variables including the central period, the relative height and the relative width.

4） Superimpose the regular deviation curves of spectral accelerations on the site-related spectral accelerations without regular deviations, and then obtain the site-related spectral accelerations with regular deviations.

The comparison between the observed spectral accelerations and their predicted values of typical acceleration records with regular deviations showed that the proposed procedure gave a more accurate prediction of spectral accelerations, which could reflect the unique single-peak regular deviations from the statistical mean values of spectral accelerations. Even though, further research was needed on how to determine the criteria for discriminating the strong motion records with/without regular deviations of spectral accelerations based on the parameters of earthquake, local site condition and strong motion field.