The paper deals with development of reliable techniques of full waveform inversion which guarantee correct reconstruction of a macrovelocity model for reasonable acquisitions and frequency ranges. As reasonable we mean realistic offsets (about one-two depths of target objects) and temporal frequency above 5-7 Hz. The paper proposes the so-called Migration Based Travel Times (MBTT) formulation of the data misfit functional in time frequency domain. This approach relies on the decomposition of a velocity model onto two subspaces - smooth propagator and rough depth reflectors. On this base the modified data misfit functional is introduced and compared with standard least squares formulation. Numerical Singular Value Decomposition proves that these two formulations produce functionals which have almost orthogonal stable subspaces. As is well known the classical formulation leads to stable subspaces mainly made of fast oscillating functions (reflectors). At the same time we prove that MBTT modification ensures appearance of the propagator in these stable subspaces. Numerical experiments prove the feasibility of full inversion for reflected waves in this modified reformulation for the well known Marmoussi velocity model. We demonstrate Common Image Gathers for initial guess and reconstructed model to valdate good quality of reconstructed velocity.