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Full Waveform Inversion (FWI) aims to estimate high resolution velocity models by minimizing the difference between observed and modelled seismic waveforms. Good low frequency data play an important role in the successful application of FWI. Variable-depth streamer acquisition delivers high signal-to-noise (S/N) seismic data over a significantly wider frequency bandwidth than standard streamer acquisition. We show that FWI adapts naturally to the variable-depth acquisition geometry and so benefits from the improved low frequencies recorded in this configuration. Application to data from the Central North Sea reveals detailed velocity features associated with shallow channels in the near surface geology. Migration with this updated velocity model improves the subsequent imaging.