Full-waveform inversion (FWI) requires either a good initial velocity model or low-frequency data to mitigate the cycleskipping issue. Reflection-waveform inversion (RWI) uses a migration/demigration process to retrieve a background model that can be used as a good initial velocity in FWI. The drawback of the conventional RWI is that it requires the use of a least-squares migration, which is often computationally expensive. Efficient wavefield inversion (EWI) is a recently developed method from wavefield reconstruction inversion (WRI). EWI uses a modified source function to introduce the multiscattering components in the reconstructed wavefield. However, when the initial velocity is far from the true one, the wavefield can not be accurately reconstructed. We incorporate the RWI formulation into EWI by inverting for the Born scattered wavefield instead of the wavefield itself. In this case, we use the perturbation related to secondary sources as a modified source function. As the sources in the reflection-based EWI (REWI) are located in the subsurface, we are able to update the background model along the reflection wave path. We calculate the background model perturbation by a deconvolution process in each frequency like what is done in the original EWI. We demonstrate the validity of the proposed approach using synthetic data generated for the Marmousi model.