Attenuation and dispersion have a significant impact in full waveform inversion and are essential to achieving greater resolution and fidelity in the inversion. These properties are often modeled in full waveform inversion using empirical nearly constant Q models. Significantly, these models do not hold universally, especially when large ranges of frequencies are considered. In this numerical study, we demonstrate that discrepancies between the attenuation physics in the subsurface and those used in the inversion can have severely negative impacts on the results of the inversion. This problem can be alleviated by adopting an updating strategy in the inversion in which relatively small bands of frequencies are considered at each iteration, allowing for empirical attenuation models to be applied in full waveform inversion with greater confidence.