Gravitational wave redshifts and LIGO When I heard about the LIGO gravitational wave detection, I wondered if the distance to the event was determined by the inverse square law of radiation and/or by measured red shifts. Which is/are the case? A previous answer to the nature of the redshifts of gravitational waves implies that the original frequency is unknown and therefore the red shift is also unknown. I further wonder how the computations of the masses of the two stars can be so precise, but the gravitational waves' frequencies not be.  
I am an amateur astronomer, and past planetarium director, and not versed in relativistic gravity theory. I have hunted for an answer since February, even e mailing Kip Thorne, whose book "Gravitation" I own.
Regarding critique as a duplicate:  I am  accustomed to asking the distance to an object, by asking the redshift, esp. for distances too far for Cephiad variables to be visible. Perhaps the question is dumb, but no one has inquired about the possibility of directly measuring redshift of this event. Therefore, I think this question is somewhat unique. From the comments I gather that LIGO events can never have their redshifts directly measured.
 A: The frequency evolution of the signal can be determined very precisely.  Based on the rate of change of the frequency the 'chirp-mass' is uniquely determined (to some accuracy).  The 'chirp-mass' also determines the intrinsic amplitude of the gravitational wave event.  Comparing the intrinsic amplitude with the observed amplitude then determines the distance (note the 'strain' is inversely proportional to the distance, not the distance squared).
A: DilithiumMatrix has it right. A few more points and a couple references you can read and understand that describes the first black hole merger and some of the key findings. Not that hard, little math, good figures. 
The measurements allows you to determine the chirp mass and the masses of initial black holes, and the final one, to some accuracy. The difference for that so called 091415 event (the date observed) between end and starting masses was 3 solar masses, which therefore is the amount of energy radiated as gravitational waves. From that and the times for the merger (most of the radiation is emitted in the last few orbits and as they merge, and it's been modeled pretty accurately so from the total energy one can estimate the peak power of and actually the amplitude of the waveform emitted) one can get the emitted power over the approximately 1/4 sec that most of it was emitted. From that emitted power, i.e., its inherent luminosity, and comparing it to the detected power, one can get the propagation loss and assuming 1/$R^2$ propagation one gets the distance R. that is the so called luminosity distance, which was 1.3 billion light years. From that one estimates the cosmological redshift, it was about 0.09. 
The first reference is an interesting read, see it at http://www.ligo.org/science/Publication-GW150914/index.php. A good intro. 
Their published professional papers were multiple, but the first one summarized everything important and you can get a sense of the uncertainties (for instance the initial masses were more uncertain, but the mass differences of the final black hole and the initial two is more accurate and is where they got the 3 solar masses approx). It is not a hard read, and also interesting, at 
https://dcc.ligo.org/public/0122/P150914/014/LIGO-P150914_Detection_of_GW150914.pdf
It is interesting to note that the peak power emitted in gravitational radiation, about 3 solar masses in a quarter second or so, was more power than the total instantaneous power emitted from light from all the stars in the observable universe, for that short period of time. 
The LIGO team believes they will get more accurate numbers for the masses, in,causing the initial masses, if they can see more of the whole merger process - they only saw seconds of it. I believe they saw more in the second observation a few months later. 
Another couple interesting points is that they were not able to pin down the exact location where the sources were, they were doing basically time difference of arrival and only had two independent measurements. With more LIGOs around the world they'll locate much better, and they try to compare to optical or other radio or X Ray observations around it, for more astronomical correlations. 
