How does the Earth's rotation affect predictions of gravitational wave strong lensing rates?

Understand

The next generation of ground-based gravitational wave (GW) detectors, e.g.

• the Einstein Telescope, is expected to observe a significant number of strongly lensed GW events as predicted in many previous papers.
• However, all these works ignored the impact of the Earth's rotation on this prediction.
• Multiple lensed images arrive at the Earth at different time, thus the ground-based detector has different responses to the lensed images due to different orientations of the detector relative to the GW source direction.