Low frequencies play a crucial role in the convergence of full-waveform inversion to the correct model in most of its current implementations. However, the lower the frequencies, the bigger are the amplitudes of the surface waves, causing the inversion to be driven by the latter. If they are not blanked out or removed, this may lead to convergence problems. To analyze this situation, we consider the simplest case where surface waves are present: an acoustic layer over a halfspace. We earlier analyzed the contributions of various wave types to the wavenumber spectrum of a velocity perturbation above a reflecting halfspace, without a free surface. Here, we extend this spectral sensitivity analysis to the case with a free surface, which generates multiples and ghosts. In this setting, the surface guided P-waves can be considered as a superposition of free-surface multiples. Our analysis shows that the conditioning of the linearized inverse problem, which is solved at each iteration of full-waveform inversion, becomes worse when multiples are taken into account. At the same time the inclusion of multiples increases the sensitivity to some low wavenumbers in the model spectrum, which should be beneficial for full-waveform inversion once a suitable preconditioner has been found.


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