Analyzing horizontal component seismograms of small earthquakes with intermediate hypocentral distances in southeastern Honshu, Japan, we found that time widths of seismogram envelopes around direct S waves are much longer than source duration times estimated from their magnitudes. The time lags of the maximum amplitude of the half maximum after the peak were measured from the onset of the direct S wave arrival from band-pass-filtered seismograms from 2 to 32 Hz. Even though there is considerable scatter, both the time lags are found to increase with increasing hypocentral distance up to 305 km. We hypothesize that pulse shape broadens and the maximum amplitude is reduced after propagating through the random structure of the lithosphere. The parabolic approximation theoretically predicts that the long-wavelength component of velocity inhomogeneities compared with the wavelength of seismic waves produces diffraction fluctuations and makes seismogram envelopes broaden with increasing travel distance in the saturated regime. Supposing a Gaussian autocorrelation function for the randomness and an empirical frequency dependent attenuation, we propose a formula for the temporal change in the power spectral density of seismic waves. Applying this formula to the observed data, we statistically evaluated the scale of random inhomogeneities: the mean square fractional velocity fluctuation was estimated to be 10-3 times the correlation distance a in kilometers. ¿ American Geophysical Union 1989