At low frequency, DARM is coherent with many ASC and LSC channels. However, ASC channels are not uncorrelated to each other, and the same is true for DRMI LSC channels. So if one wants to use coherence to estimate how much of DARM is explanable with coupling from a set of auxliary channels, it is important to avoid over counting due to the cross coheence between the aux signals.

To cope with this, I wrote a multi-channel cohrence code, which takes into account the cohrence between the aux channels and estimates the total contribution of a set of correlated aux channels to a target channel. The attached script multicoherence.m does this in MATLAB.

I computed this multi-channel coherence (and the projection of noise into DARM) for DRMI LSC signals (plot 1) and all ASC signals (plot 2). In each of those plots, the top panel shows the total coherence of DARM with the set of channels being considered. This coherence is defined as (PSD_DARM - PSD_LINEAR_COMBINATION_AUX) / PSD_DARM and so gives an idea of how well the combination of aux channels can explain the noise we see in DARM. In each plot, the bottom panel shows a coherence-baed projection of the aux channels into DARM.

As expected, we see that the low frequency region of DARM (<20 Hz) is dominated by the sum of all ASC noises. Similarly, the LSC noises are not far from the measured sensitivity (as already known, we need a MICH FF retuning).

I attached a brief not describing how the multi-channel coherence is computed. This kind of computation is not new material, it's been around for a long time.