Full waveform inversion (FWI) has the potential to recover detailed quantitative property models of the subsurface, but the process is computationally expensive. Currently available computer systems do not allow to use the full bandwidth of the acquired seismic data, which effectively reduces the resolution that can be obtained. In this paper, we propose a novel approach to obtain high resolution subsurface models from broad-band FWI. The method is based on localization of the inversion, while subsequently the interaction between local domains is estimated. A global field update is calculated which honours the non-linear relationship between the subsurface properties and the measured seismic data. By using this non-linearity, the spectral gap between the a priori background model and the seismic bandwidth will be closed and spatially broad-band properties can be estimated from a band-limited seismic signal.