Realistic artificial seismograms may be computed by considering body waves as sums of normal or leaking modes of surface waves: the S wave and those arriving after S may be considered as sums of higher normal modes of Rayleigh waves (RiN) and Love waves (LiN); in this case the apparent velocity c < βn. Earlier arrivals are generally due to the first kind of leaking modes of Rayleigh waves (RiL1) for which βn < c < αn. Deep reflections in seismic prospecting are RiL2 for which c > αn. Synthetic seismograms can be computed by double Fourier transformation in those two last cases. Alternately the method of residues followed by a single Fourier (or Laplace) transformation may be used in all cases. Earth-stretching approximations should give excellent results for SH waves and may give satisfactory results for P and SV waves.