Effect of gravitational lensing on the distribution of gravitational
  waves from distant binary black hole mergers
  The detailed observation of the distribution of redshifts and chirp masses of
binary black hole mergers is expected to provide a clue to their origin. In
this paper, we develop a hybrid model of the probability distribution function
of gravitational lensing magnification taking account of both strong and weak
gravitational lensing, and use it to study the effect of gravitational lensing
magnification on the distribution of gravitational waves from distant binary
black hole mergers detected in ongoing and future gravitational wave
observations. We find that the effect of gravitational lensing magnification is
significant at high ends of observed chirp mass and redshift distributions.
While a high mass tail in the observed chirp mass distribution is produced by
highly magnified gravitational lensing events, we find that highly demagnified
images of strong lensing events produce a high redshift ($z_{\rm obs}> 15$)
tail in the observed redshift distribution, which can easily be observed in the
third-generation gravitational wave observatories. Such a demagnified,
apparently high redshift event is expected to be accompanied by a magnified
image that is observed typically $10-100$ days before the demagnified image.
For highly magnified events that produce apparently very high chirp masses, we
expect pairs of events with similar magnifications with time delays typically
less than a day. This work suggests the critical importance of gravitational
lensing (de-)magnification on the interpretation of apparently very high mass
or redshift gravitational wave events.
