Reflection-based waveform inversion is a set of strategies for updating the long-wavelength part of a velocity model through the use of reflection data in a full waveform inversion approach. Two analytical formulations of this type are proposed in this paper. A migrationbased version uses a migration as the model of seismic reflectivity and directly calculates the effect of velocity model changes on this reflectivity. This approach is computationally intensive, and may estimate reflectivity poorly. The second approach considers only vertical shifts to a fixed reflectivity model. This reduces cost and allows for a better initial reflectivity model, but has the drawback of simplifying the effects of velocity model changes on the reflectivity. Neither approach uses demigration, instead using a long-wavelength model parameterization to ensure that reflectivities are not directly modified in the inversion.
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