Strong and weak lensing of Gravitational Waves: a semi-analytical
  approach
  In this paper we study gravitational lensing of gravitational wave events.
The main point of the present work is to introduce a semi-analytic approach so
that each ingredient can be varied and tested individually. Our analytic model
for the source population is motivated by a numerical study and we compare
semi-analytical and numerical results. We determine the expected magnification
for events seen at a given observed luminosity distance. We find that while the
probability of significant magnification of the observed LIGO-Virgo events is
very small, the probability distribution of the magnification has a significant
tail to high $\mu$ such that e.g. the variance of the magnification is very
large and even diverges in the geometric optics approximation. For the 10
binary black hole mergers observed by LIGO-Virgo in the O1+O2 observation
campaigns, the probability that one of them has been magnified with
magnification of 5 or bigger is $\mathcal{P}_{\text{obs}}(>5)\sim 0.01$ while
the probability of magnification by 50 or bigger is
$\mathcal{P}_{\text{obs}}(>50)\sim 0.005$.
