tidal force of the SMBH [@meiron17; @hoang19; @randall19; @fang19]. These signatures can help us identify the BBHs affected by the redshift effects.

Redshift is not the only factor in GW astronomy that could affect the measurement of mass. Gas, for example, can exert a frictional force on a binary and hence lead to a faster orbital decay [@ostriker99; @kim07; @kim08]. The resulting GW signal is expected to deffer from the real chirp signal due to GW radiation only. The impact on the mass measurement deserves further investigation since a large fraction of BBHs may form in gaseous environments. For example, BBHs can be produced by binary-star evolution, and in this case the mergers may happen inside a common envelope [@ivanova13; @macleod17; @ginat19] or the fallback material from the previous supernovae [@tagawa18]. Moreover, some BBHs may form in the accretion disks of active galactic nuclei [AGNs, @mckernan12; @bartos17; @stone17]. When these BBHs merge, it is likely that they are surrounded by dense gas. Furthermore, the dense cores of massive stars may also produce BBHs, and hence the mergers would also be accompanied by gas [@loeb16; @fedrow17; @dorazio18]. The density of the gas can reach $10^{8}-10^{14}\,{\rm cm^{-3}}$ in the case of AGN 