In this paper, we provide a theoretical comparison between twomethods of velocity estimation:<br>full-waveform inversion based on the minimization between the recorded data and the reconstructed<br>data based on a reflectivity model and a velocity model, and stack energy maximization<br>methods where the energy of a one-way migration is maximized. We first analyze the process of<br>migration and least-squares migration, then show that minimizing the data misfit is equivalent<br>to first order to energy maximization of a migration, when an appropriated weighting matrix is<br>used. We then obtain, by using 1D migration, a first order approximation of this weighting matrix.<br>Synthetic examples illustrates this derivation. The influence of using one-way propagation<br>instead of two-way is then discussed.


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