gravity - How did LIGO verify that the gravitational waves originated 1.3 billion years ago from two specific black hole collision?

The original paper states the methodology used to determine the location of the gravity waves. The bottom line is that they were detected in two different locations. Using the difference in timing, one can estimate the location in the sky to an area of about 600 degrees squared where the origin of the wave could have been. The two signals had an offset of 7 ms. Pure speed of light differences would have been 10 ms. This can be used to effectively identify a circle in the sky where the merger might have happened. Of course, this doesn't reveal the distance.

The distance was figured by a number of things. First of all, the frequency pattern was used to estimate the mass of each black hole. Using these masses, one can find the estimated total power of the event. Using this estimate, and seeing the estimate of the amplitude from the signal, one can use the inverse squared law to estimate the distance to said event.