To illustrate the idea, I show two examples of acoustic inversion of data generated with wave equations contain more complex physics than pure acoustics. The first example uses data generated by the visco-acoustic wave equation, which means there is attenuation in the subsurface that causes phase/amplitude change in the data. The second example uses data generated by the elastic wave equation. This not only changes the phase/amplitude of existing events relative to data generated by acoustic wave equation, but also add extra events which are converted modes. However in both cases, by carefully masking out non-acoustic events and focusing on the phase of "acoustic-equivalent" data, acoustic inversion can still produce a good estimate of near-surface velocity.
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