Recent seismological studies suggest that the amplitude attenuation of S waves in the lithosphere may be primarily due to scattering by its random inhomogeneity. There is, however, a disturbing discrepancy between statistical scattering theory and observation with regard to the asymptotic frequency dependence of Q-1 in the high-frequency limit. Although the observed Q-1 decreases with frequency above 1 Hz, the usual mean wave formalism predicts Q-1 of media with random velocity fluctuation increases with frequency; we take a mean over waves with large travel time fluctuations that are caused by long-scale velocity fluctuations compared with the wavelength studied. We propose a new statistical averaging method; mean wave is defined after the correction of travel time fluctuations. The random media with a mean square fractional velocity fluctuation of 5.0¿10-3 and a correlation distance of 4.0 km will explain the observed and partially conjectured Q-1 for frequencies from 0.05 to 30 Hz.