At long periods on vertical component seismograms, incoherent wave trains appear in addition to direct Rayleigh waves propagating around the spherical Earth. On seismograms of earthquakes with Mw>7, these incoherent wave trains continue for more than a few tens of hours. Scattering by distributed heterogeneities is the most probable origin for the excitation of incoherent wave trains. Here we propose a simple method to synthesize the mean-square (MS) envelope of long-period seismogram based on the radiative transfer theory for Rayleigh wave scattering. The Earth's surface can be modeled as a spherical surface on which point-like isotropic scatterers are randomly distributed. A nonisotropically radiating source is put at the surface. Adding the energy density of surface waves singly scattered by distributed scatterers lying on isochronal curves for a given lapse time, we calculate the energy density corresponding to the MS seismogram envelope at a receiver. Spherical trigonometry is used in the calculation of travel time and geometrical spreading factor. The time trace of the resultant energy density becomes large at arrivals of direct Rayleigh waves propagating around the Earth and is concave between these repeated direct arrivals. These characteristics of the theoretical model qualitatively explain the observed MS envelopes. Applying the above model with the velocity dispersion to seismograms of the 1999 Turkey earthquake (Mw 7.4), we estimated the total scattering coefficient to be about 2¿10-6 km-1 at periods between 100 and 200 s, which is 4 orders of magnitude smaller than that of shear waves at frequencies 1~20 Hz in the lithosphere. ¿ 2001 American Geophysical Union