How does the Earth's rotation affect predictions of gravitational wave
  strong lensing rates?
  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. Therefore the amplitudes of
the GW signal from different images are modulated appropriately, in addition to
the lensing magnification. In order to assess this effect, we performed Monte
Carlo simulations to calculate the event rate of lensed GW signals. Our
conclusion is that the Earth's rotation has a non-negligible impact on the
event rate of lensed GW image. The updated event rates decrease by factors of
$\sim40\%, \sim20\%, \sim10\%$, for NS-NS, BH-NS, BH-BH systems respectively.
