Time delay issue for a very long signal
Description
For long-duration GW signals, the response of each detector evolves with time due to Earth’s rotation and orbital motion. As a result, both the detector’s antenna pattern and its geometric position relative to the source change continuously. When the signal lasts several hours or more, different portions of the signal are recorded at slightly different times by spatially separated detectors. This effect cannot be captured by a constant inter-detector time shift, since the relative delay between detectors depends on the instantaneous projection of their positions onto the line of sight to the source. Therefore, a time-dependent time delay \tau_d(t) = \mathbf{n}\cdot\mathbf{r}_d(t)/c must be included in the signal model.
Example for time delay between E1 and H1
Time delay from Geocenter to Earth
Implementation
Relevant Literature
- Parameter estimation of gravitational-wave signals with frequency-dependent antenna responses and higher-modes
- Localization of binary neutron star mergers with a single cosmic explorer
- A fast frequency-domain expression for the time-dependent detector response of ground-based gravitational-wave detectors to compact binary signals