By the distance of the two LIGO detectors and the time delay for the same gravitational wave(GW) event, the speed of GW can be determined. Do you know where can I find related data?
2 Answers
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First of all: no, it can't in general. You can only determine the speed of propagation if you know where the source is. Without knowing that you can put an upper bound on the speed: for instance you know it is no more than $d/\Delta t$ where $d$ is the straight-line distance between the detectors and $\Delta t$ the difference in observation times (I'm making various naïve-Galilean-relativity assumptions here, but they're good approximations). But note that $\Delta t =0$ is perfectly possible, in which case the bound is not very good. I don't think you can get a lower bound using this approach.
With three detectors you can do better, but you still can have a case where $\Delta t_{ab} = 0$ for all pairs $a$ and $b$. With four non-coplanar detectors I think you can do considerably better.
Of course the actual analysis that LIGO do is a lot more sophisticated than this. I would suggest that their publications list is a good place to start, and probably the GW150914 detection paper in particular. Note that the event was detected about $7\,\mathrm{ms}$ apart by the two detectors, when the light travel time between the detectors is about $10\,\mathrm{ms}$.
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$\begingroup$ I realized your 1st point already. The directly measurement for speed of gravitational wave by LIGO will face the problem how to determine the position of the source accurately. Thanks for your suggestion. $\endgroup$ Oct 6, 2016 at 13:15
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The speed of gravitational waves can be bounded by gravitational-wave observations alone. There is a paper here1 that discusses an approach to doing so.
In essence, by combining multiple observations together you can bound the speed of gravitational waves by looking at the distribution of arrival times in each detector. For the Hanford-Livingston network for example, the time delay must be within $\pm 10\ {\rm ms}$. Sources should be isotropically distributed in the sky, so we can predict what the distribution of time delays ought to be for the standard speed of gravitation, and for a modified one. By comparing the observed distribution of time delays to the predicted one, bounds on the speed of gravity can be made.
1 N. Cornish, D. Blas, and G. Nardini, "Bounding the Speed of Gravity with Gravitational Wave Observations", Phys. Rev. Lett. 119, 161102 (2017).