We discuss several difficulties related to the application of Full Waveform Inversion using surface wavesin the context of seismic data acquired on an ultra-shallow ground model (0 — 10 m depth). For instance,the choice of an accurate initial velocity model in the presence of very high velocity contrasts iscomplicated. The presence of surface waves increases local minima problems in the objective function,preventing from convergence towards the global minimum. For improving convergence, we propose to usean alternative functional, the windowed-Amplitude Waveform Inversion, which is similar to dispersioncurve analysis but without any picking step. The source wavelet is iteratively estimated during the velocitymodel inversion. If previous examples have shown that this methodology is applicable in synthetic datasets, it is less obvious in real data sets as discussed here.