We compute seismograms of the fundamental Rayleigh waves propagating through a slab structure, with either a lateral variation in seismic velocities, or in attenuation. At periods of 100 sec, we show that the phase delay is strongly reduced by the surface waves Fresnel zone, and that coupling must be considered far along the dispersion branch, up to at least ¿25. Limiting the coupling to fewer modes produces a signal associated to a ghost structure at the antipode of the slab. We also show that the amplitude perturbations produced by the diffraction and the attenuation of the slab are comparable in size. Future waveform studies, especially those associated to global waveform inversions, must then carefully consider these effects.¿ 1997 American Geophysical Union