MC_F low frequency noise might be due to local damping electronics. I did not measure OSEM noise, but even without it electronics (AA -> ICS 110 -> ADC) provide sufficient amount of noise.
These 2 image show electronics noise and coherence between OSEM signal / seismic
From these 2 plots we might think that SNR > 10 and coherence OSEM / GUR is high at the frequency range 0.1 - 10 Hz and this is not a big problem.
However, at low frequencies the length of seismic waves becomes large enough and relative oscillations of MC2 and MC13 decrease.
For 1 wave ( u(MC2) - u(MC1) ) / u(MC2) = sin(2 * pi * L * f / c), L - distance between MC1 and MC2 where 2 seismometers are located. So MC123 move according to seismic motion and electronics noise is not seen unless we look at MC Length. Here this noise is seen, because mirrors move in a synchronistic manner.
To check this I measured seismic noise with 2 guralps at distance 12 meters - at MC1 and MC2. Then I've computed the difference between these signals. And indeed at low frequencies, relative motion is much less.
Green, blue - GUR1,2_X
Red - differential motion GUR1_X - GUR2_X
The following plot illustrates how electronics noise effects MC_F. Green is the signal to coils. Red - electronics noise. Blue, black, cyan - simulated contribution to MC_F for different seismic waves speed. Most probably seismic waves have waves in the range 50 - 800 m/s, others are deep. The plot shows that electronics noise is big enough to disturb coherence between MC_F and seismic noise.
Here is a rough calculation of the seismic waves speed. The following plot shows the ratio of psd of differential MC2-MC1 motion to MC2 motion.
If seismometers would be very far, ratio would be 1 if we neglect the difference in transfer function SEISMOMETER -> ADC for each channel. The drift of the ratio from 1 to 1.3 demonstrates this effect. Ratio starts to decrease at 15 Hz according to sin (2*pi*L*f/c) ~ 2*pi*L/c * f. So 2*pi*L/c * f_0 = pi/2 => c = 4 * L * f = 600 m / sec.