[Mirko, Den]

We still think about the coherence between seismic noise and mode cleaner length. We beleive that

1. Below ~0.1 Hz tilt affects on the seismometers as was simulated http://nodus.ligo.caltech.edu:8080/40m/5777

2. From 0.1 to 1 Hz is an interesting region. We try to figure out why we do not see any coherence here. Tilt does not seem to dominate.

At 1 Hz coherence might be lost because of the sharp resonance. For example, if the mirror is suspended to the platform by wires with f = 1 Hz and Q = 1000, then the coherence between platform motion and mirror motion will be lost as shown on the figure below.

For this reason we tried to "help" to the adaptive filter to guess transfer function between the ground motion and mirror motion by multiplying seimometer signal by the platform -> mirror transfer function. As we do not know exactly eigen frequency and Q of the wires, we did a parametric simulation as shown on the figure below

The maximum coherence that we could achieve with treak was 0.074 compared to 0.056 without. This was achieved at f=1.0011 Hz but with surprisingly high Q = 330. And though this did not help, we should keep in mind the tecnique of "helping" the adaptive filter to guess the transfer function if we partly know it.

Another unexpected thing is that we see come coherence between gur1_x and mode cleaner WFS pitch signal at frequencies 0.1 - 1 Hz

 From this we can suggest that either mode MC_F channel does not completely reflect the mc length at low frequencies or WFS2 shows weard signal.