Barbara Patricelli has studied in more detailed how the frequency noise coupling is modulated, by looking for bilinear coupling using a few dozen other channels, during the time when the frequency noise subtraction was not working well.

Figure 1 shows the most coherent contribution, which are mostly related to the position of PR and the beam pointing into the interferometre. The full list of channels ranked by coherencein each 10mHz frequency bin  is in the attached text file.

Figue 2 the coherence with B1p 56MHz I is more surprising, it could be due to the dark fringe offset itself or to the amplitude of the 56MHz sidebands. Comparing B1p 56MHz I  and B4 112Mhz mag, the coherence and projection is much higher for B1p 56MHz I, so the main driver here is not the change in the 56MHz amplitude but the carrier light itself. This means that the dark fringe offset is fluctuating, and that these fluctuation modulate the frequency noise coupling. The dark fringe offset could fluctuate due to fluctuation in the carrier gain in the PR cavity, or due to alignment fluctuation modulating the matching with the OMC.

In any case, the most coherence in the +/-200mHz range around the 1111Hz laser frequency line is with the ASC_PR_Y_CORR and ASC_PR_X_CORR channels. This would argue that the centering of the PR mirror plays an important role in modulating the frequency noise coupling, and that a better centering of the beam on the PR mirror could make the frequency noise coupling less depend on the PR mirror transversal position control.

Figure 3 shows the region around 1111Hz for h(t), and a fitted projection of LSC_PRCL (out of loop frequency noise signal) and LSC_PRCL*ASC_PR_Y_CORR. LSC_PRCL can explain well the line at 1111Hz itself, and LSC_PRCL*ASC_PR_Y_CORR the wings in +/-1Hz band.

Figure 4 shows an attempt of doing a bilinear noise subtraction in h(t) using LSC_PRCL*ASC_PR_Y_CORR, the code to do that is very crude, but comparing the ASD of h(t) with this additional subtraction with h(t) with the online (linear) noise subtraction, we can find a improvement of ~1% (red line in the figure). So this modulated frequency noise coupling is a good candidate for explaining the 2Mpc sensitivity loss when the linear subtraction is not working well. But the bilinear noise subtraction (at least in this crude implementation) is not able to recover the sensitivity.

/users/mwas/calib/noiseSubtraction_20191113/noiseSubtractionBilinear.m

Figure 5, note that between the bad time (purple) and good time (blue) the fluctuations of ASC_PR_Y_CORR and B1p 56MHz I have reduced only by 20% and only around 300mHz. So the main driver are not the position fluctuations themselves, but something else (maybe some slow trend in global alignment).