The analysis of the seismogram coda envelopes of local and regional earthquakes is one of the most effective strategies for investigating the heterogeneous lithospheric structure characterized by the seismic scattering and attenuation. In order to synthesize the coda envelope we introduce a numerical scheme called the direct simulation Monte Carlo method, which has been used in the field of the kinetic theory of gases. Because of the simplicity of the algorithm the method has several advantages over previous methods in terms of the flexibility of the numerical calculation to incorporate various factors required to construct realistic seismogram envelopes. On the basis of coda envelope simulations, including multiple scattering, we show that an increase of seismic velocity with depth severely affects the shape of the coda envelope. The effects of ray bending due to the velocity increase at the Moho and the reflection at the free surface are clearly found in the synthesized envelope for a shallow earthquake. Our simulation demonstrates that the amplitude of the envelope is magnified by stagnation of seismic energy at shallow depths due to the positive velocity gradient with depth. Because of this effect, for an a priori assumption of a homogeneous velocity model the measurement of the scattering coefficient by conventional methods may be overestimated. ¿ 2000 American Geophysical Union