Full waveform inversion offers a robust and automated way to estimate high resolution velocity models at the expense of a good initial model. This technique is classically applied on wide angle data, but more rarely on surface waves because of their dispersive nature. However, surface wave information is significantly useful for near surface imaging. We propose to use a modified approach, here named windowed amplitude waveform inversion, as an alternative to the classical full waveform inversion. We first window the input data, then apply a 2D Fourier transform and minimize the misfit between the absolute values. The windowed amplitude waveform inversion is less restrictive with respect to the initial model as shown in a synthetic example. Inversion results confirm that the proposed approach may converge when using initial models for which the classical formulation does not converge to the exact velocity model.