Full waveform inversion (FWI) is a powerful tool to build high-resolution velocity models, from recorded seismic data. However, a major issue with FWI is that it fails at reconstructing the low-wavenumber components in the absence of low-frequency information in the data. Generally, for a limited-offset acquisition geometry, deep targets are only sampled by reﬂected waves with narrow scattering angles, which makes such failure inevitable. In this paper, we point out the limitation of conventional FWI when applied to reﬂection data, and review an alternative approach to overcome this limitation. The new waveform inversion formalism relies on decomposing the subsurface model into a background part that we seek to resolve, and a reﬂectivity part that we assume to be known. We show that separating the decoupled velocity model into long-wavelength and shortwavelength components permit us to extract the contribution of the reﬂected data to the background part of the velocity model.
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