Conventional least-squares based full waveform inversion (FWI) is not suitable to construct low-wavenumber back- ground model when recorded data is dominated by reflected energy. We present a new approach to address the challenge of building kinematically correct background model with FWI for reflection-dominant seismic data. The new approach de- composes a subsurface model into a smooth background, which is updated via minimizing a new objective function, and a rough reflectivity, which is computed through a migration or least-squares migration at current background. With such a model decomposition strategy and the Born modeling, we are able to directly compute the reflection-based low-wavenumber components of a conventional FWI gradient. To guarantee that these low-wavenumber components contribute to updating background model in correct directions, we developed a new optimization strategy, which consists of two essential compo- nents: first, computing an offset-dependent matching filter to match the predicted Born wavefield and observed reflections; second, measuring the incoherency of this offset-dependent fil- ter along offset and time, and then updating the background to minimize this incoherency.Real data demonstrate the success of the proposed algorithm in constructing kinematically correct models.


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