We study attenuation characteristics of peak ground motions and relative velocity response spectra of ground motions with predominant surface waves in a period range of about 2 to 20 sec. First, we point out that it is important to know how dispersion of surface waves is in order to understand attenuation relations of surface waves. Then, we calculate attenuation relations of theoretical seismograms due to a shallow point source buried in the velocity structure used in the study by Mamula, et al. (1984) on site amplification factors of many Meteorological observatories in a period range of 3 to 15 sec. As a result, we point out that the idea that attenuation of surface waves is much smaller than that of body waves, which is wide-spreaded in studies on attenuation relations of earthquake ground motions in Japan, is not always appropriate.
