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The conventional waveform inversion objective function is insufficient when the acoustic wave equation is used in inversion. The insufficiency mainly comes from the fact that non-acoustic physics tend to alter the amplitude and phase of existing events and add new events compared with acoustic data. A new weighted waveform inversion objective function is quite robust, despite the presence of non-acoustic physics in recorded data, and it can recover important velocity structure that can not be detected by conventional ray-based tomography. For the purpose of near-surface velocity estimation, phase information is much less sensitive than amplitude information to the presence of non-acoustic parameters, and extra events caused by non-acoustic physics are usually late arriving and can be masked out during waveform matching. The velocity estimation results from this objective function are more stable than conventional waveform inversion.