In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for groundbased detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year (∼ 1 yr −1 ) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as ∼ 80 yr −1 . These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be ∼ 30 per cent for the aLIGO survey and ∼ 6 per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems (∼ 90 per cent) will have time delays less than ∼ 1 month, which will be far shorter than survey durations.

Gravitational waves emitted from compact binary coalescence can be subject to wave diffraction if they are gravitationally lensed by an intervening mass clump whose Schwarzschild timescale matches the wave period. Waves in the ground-based frequency band f ∼ 10-10 3 Hz are sensitive to clumps with masses ME ∼ 10 2 -10 3 M enclosed within the impact parameter. These can be the central parts of low mass ML ∼ 10 3 -10 6 M dark matter halos, which are predicted in Cold Dark Matter scenarios but are challenging to observe. Neglecting finely-tuned impact parameters, we focus on lenses aligned generally on the Einstein scale for which multiple lensed images may not form in the case of an extended lens. In this case, diffraction induces amplitude and phase modulations whose sizes ∼ 10%-20% are small enough so that standard matched filtering with unlensed waveforms do not degrade, but are still detectable for events with high signal-to-noise ratio. We develop and test an agnostic detection method based on dynamic programming, which does not require a detailed model of the lensed waveforms. For pseudo-Jaffe lenses aligned up to the Einstein radius, we demonstrate that a pair of fully upgraded aLIGO/Virgo detectors can extract diffraction imprints from binary black hole mergers out to zs ∼ 0.2-0.3. The prospect will improve dramatically for a third-generation detector for which binary black hole mergers out to zs ∼ 2-4 will all become valuable sources.