During propagation through heterogeneous lithosphere, S waves impulsively radiated from a source increase in duration and decrease in maximum amplitude with increasing travel distance. We term these phenomena envelope broadening and maximum-amplitude decay, respectively. The present study is the first attempt to make a unified explanation of the envelope broadening and the maximum-amplitude decay based on wave scattering in random media. S wave envelopes observed at the forearc side of the volcanic front in northeastern Honshu, Japan, have the following characteristics in the frequency range from 2 to 16 Hz in the distance range from 75 to 410 km: Envelope duration increases with increasing travel distance in proportion to the distance to the power 1.7 to 1.8, and maximum amplitude decreases with increasing travel distance in proportion to the distance to the power -3 to -2. These observations are modeled by considering small-angle wave scattering around the forward direction in the media having randomly fluctuating wave velocity with frequency-dependent attenuation. The joint analysis of envelope duration and maximum amplitude is superior in estimating medium inhomogeneity and attenuation over the analysis of envelope duration or maximum amplitude alone. Assuming the von K¿rm¿n--type random media, we estimate the power spectral density function of S wave velocity fluctuation as P(m) ≈ 0.004m-5.0--0.01m-4.0 km3 in the range between 0.5 < m < 50 km-1, where m is the wave number of the inhomogeneity. The theoretical envelope calculated from the estimated random inhomogeneity and attenuation successfully gives a unified explanation of the envelope broadening and the maximum-amplitude decay in northeastern Honshu, Japan.