| Abstract: Gravitational waves (GWs) from the inspiral and merger of compact objects are now routinely detected by the LIGO–Virgo–KAGRA (LVK) collaboration. As they propagate through the Universe, they are deflected by intervening massive structures (eg. galaxies), potentially resulting in multiple “images” of the same source, a phenomenon called strong gravitational lensing.These images exhibit characteristic time delays and relative magnifications that encode information about the lens population, such as their structure and distribution. Although no strongly lensed GW events have yet been confirmed, such detections are expected in the near future with increasing detector sensitivity. In this work, we model lenses using three commonly employed mass profiles: point mass (PM), singular isothermal sphere (SIS), and Navarro–Frenk–White (NFW) halos. For each model, we compute the expected rate of strongly lensed GW events, along with the distributions of image time delays and relative magnifications, for future observing scenarios including LIGO-VIRGO-KAGRA (LVK) O5, O6, and next-generation (XG) detectors. We then develop a Bayesian framework that combines these observables to infer the underlying lens model at different observational epochs. Our results show that the total number of detected strongly lensed events is sufficient to distinguish a PM lens population from extended mass distributions. However, for more realistic lenses such as SIS and NFW halos, the lensed event rates by itself are insufficient and incorporating time-delay and magnification information becomes crucial for model discrimination.
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