Seismic attenuation plays an important role in real Earth and contains valuable information about the subsurface. To recover spatial distributions of both velocity and quality factor Q, in this work we investigate the applicability of 2D viscoacoustic full waveform inversion (FWI) to synthetic marine reflection data. Viscoacoustic FWI is a multiparameter inverse problem, and suffers from the cross-talk between different parameter classes. Based on the 2D Marmousi model, we investigate the cross-talk using spatially correlated and uncorrelated models of velocity and attenuation. Our results show a good reconstruction of the velocity model and satisfactory recovery of Q only in the shallow areas. With increasing depth we observe a stronger footprint of the velocity model. Nevertheless, the fit of synthetic and recorded seismograms is excellent. This can be interpreted either as low sensitivity of the synthetic data to attenuation properties in deep parts or as cross-talk with explanation of attenuation-related data misfit by the velocity model. We find that the investigation of multiparameter inverse problems with (highly) spatially uncorrelated parameters has to be considered as a necessary step to verify the reliability of inversion strategies.