Xu, S., Chen, F., Lambaré, G. and Zhang, Y., 2013. Full waveform inversion of reflected seismic data. Journal of Seismic Exploration, 22: 449-462. Full waveform inversion has been widely used to build shallow high resolution velocity models. Successful inversion requires seismic data with reliable refracted waves and low frequencies. In this paper, we revisit full waveform inversion theory and highlight a method to relax the dependence of inversion on low frequency reflections. The method can update the long wavelength components of the velocity model by using the reflected arrivals, even when the low frequency components of seismic data are absent in the input. Our approach involves a non-linear iterative relaxation approach where short and long wavelength components of the velocity model are updated alternatively. The approach still targets at matching observed data with simulated data, except the later are computed through a demigration process using the migrated images as reflectivity model. The overall workflow for the inversion in this paper is similar to the algorithm of migration based travel time waveform inversion proposed by Chavent et al. (1994) (the short wave length components of the velocity models are just replaced by a reflectivity distribution). We derive the inversion equations using Born’s approximation and numerically analyze the Fréchet derivatives of the inversion. As a result we propose an efficient methodology taken advantage of the know how about preserved amplitude migration. At the end, we present a preliminary 2D application to a Gulf of Mexico conventional streamer dataset.