In the context of near surface seismic imaging (a few hundreds of metres), we propose an alternative approach for inversion of surface waves in 2-D media with laterally varying velocities. It is based on Full Waveform Inversion (FWI) but using an alternative objective function formulated in the frequency–wavenumber f − k domain. The classical FWI objective function suffers from severe local minima problems in the presence of surface waves. It thus requires a very accurate initial model. The proposed objective function is similar to the one used in classical surface wave analysis. In this approach, the data are first split using sliding windows in the time–space t − x domain. For each window, the amplitude of the f − k spectrum is computed. The objective function measures the least-squares misfit between the amplitude of observed and modelled 2-D Fourier transformed data sets. We call this formulation the windowed-amplitude waveform inversion (w-AWI). The w-AWI objective function reduces some local minima problems as shown here through numerical examples. The global minimum basin is wider in the w-AWI approach than in FWI. Synthetic examples show that w-AWI may achieve convergence if the lowest data frequency content is twice higher than the one needed by FWI. For elastic inversion, w-AWI can be used to reconstruct a velocity model explaining surface waves. This surface wave inversion procedure can be used to retrieve near-surface model parameters in lateral-varying media