Surface waves are useful for near-surface seismic characterisation. Media containing high velocitycontrasts and irregular lateral variations still represent a challenge for local 1D approaches. As analternative, inversion methods based on waveform modelling can be considered. The choice of an initialvelocity model for classical full waveform inversion is difficult in the presence of surface waves. Here, wepropose a waveform inversion approach using two different objective functions. A modified objectivefunction is used before the classical full waveform inversion. The modified objective function consists ofthe least-squares misfit between the amplitude of a local 2D Fourier transform of observed and modelleddata considering a sliding window. The choice of an initial velocity model is easier in this approach than inclassical full waveform inversion. By using this approach, we can assess the contribution of back-scatteredwaves to the estimation of a highly contrasted velocity model. Scattered waves are useful information andresults are better when the late scattered arrivals are inverted after the direct events.