Yesterday, Rana, Jessica and I measured the Transfer function from LSC-YARM-EXC to LSC-YARM-IN1.
The plot below shows the magnitude and the phase of the measured transfer function. It also shows the normalized standard error in the estimated transfer function magnitude; the same quantity can be applied to the phase, only in this case it is interpreted as its standard deviation (not normalized). It is given by
![\frac{[1-\gamma_{xy}^2(f)]^{1/2}}{|\gamma_{xy}(f)|\sqrt{2n_{d}}}](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5B1-%5Cgamma_%7Bxy%7D%5E2%28f%29%5D%5E%7B1/2%7D%7D%7B%7C%5Cgamma_%7Bxy%7D%28f%29%7C%5Csqrt%7B2n_%7Bd%7D%7D%7D)
where  is the ordinary coherence function and  is the number of averages used at each point of the estimate, in the case here we used 9 averages. This quantity is of interest to us in order to understand how the accuracy of transfer function measurement affects the ammount of subtraction that can be achieved online.
Since this transfer function is flat from 1-10 Hz (out of phase by 180 deg), this means that we can apply our IIR wiener filters direclty into YARM without taking into account the TF by prefiltering our witnesses with it. Of course this is not the case if we care about subtractions at frequencies higher than 10 Hz, but since we are dealing with seismic noise this is not a concern.
The coherence for this transfer function measurement is shown below,
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