The reflectivity method of seismogram synthesis is extended to compute near-field seismograms due to a propagating fault. The complete representation of a point dislocation wave-field is made using Fuchs matrices and SH propagator matrices. The inversion of Fourier-Bessel transforms and fault surface integration are carried out numerically with the complex frequency technique and some time-reducing devices. Numerical examples which demonstrate the validity of our extension are also made. One of them shows that body waves are amplified by the sediment layers inferred from refraction experiments compared to those predicted using homogeneous crustal models. This amplification suggests that the effects of sediment layers should be included in the interpretations of near-field seismograms.