As we all know, the LIGO collaboration published a paper recently on the first direct observation of a binary merging black hole system. From the observed signal, they were able to infer the black holes' masses and their distance from Earth. However, the fact that they can estimate masses and distance is completely non-intuitive to me. To my mind, the same signal could have been produced by two black holes that are much closer to us but have smaller masses. What is it that singles out the particular black hole configuration they reported? Does anyone have any intuition on that?