K. Venkateswara, J. Kissel

I'm starting to look at how ground rotation affects the ISI stages and what improvements could be achieved with rotation sensor. I considered the data taken on Aug 21, 2014 night. I took three 10k second sets starting from GPS time: 1092707816. Initially I took the following channels:
H1_ISI-GND_STS_ETMX_X_DQ
H1_ISI-GND_BRS_ETMX_RY_OUT_DQ
H1_ISI-ETMX_ST1_BLND_X_T240_CUR_IN1_DQ

I then made ASD and coherence plots as shown in the attached file for each of the three sets. The seismometer velocity data has been multiplied with (2*pi*f)/g to convert to units of radian. Stage 1 had the "TBetter" isolation filters (see alog 11400). HPI was in the 'floating' state.

In the first data set, the ground rotation was quite small and BRS/GND_STS are very quiet in the 10-100 mHz range. Stage 1 however has very large motion in this range. There is no coherence between Stage 1 and BRS/GND_STS up to ~0.2 Hz, after which it shows strong coherence with the GND_STS.
In the second and the third data set, ground rotations were larger as seen in the BRS/GND_STS channels, but Stage 1 performance and the coherence looks identical to the first. It is clear that in this state, Stage 1 noise (in the 10-100 mHz band) is not due to ground rotation.

The final plot shows the coherence between Stage 1_T240_X and Stage1_T240_RY, HPI_IPS_X and HPI_IPS_RY showing very good coherence below 0.2 Hz.

After discussing further with Jeff, and reading P1200040-v40 (by F. Matichard et al, very useful document!), it seems that the above result is expected when the HEPI is in a floating/open loop state. Please look at pages 28-30 which states that HEPI tilt-horizontal coupling corner frequency is ~0.2 Hz when it is in an open loop state.

Here's my rough interpretation of what is happening: Stage 0 and subsequent stages can be thought of as a boat floating on pool of water (or hockey puck on an air-bearing table). If you stand inside the boat and move a table on the boat, the entire boat will move w.r.t. the walls of the pool, from momentum conservation. In addition there is known tilt-horizontal coupling below 0.2 Hz, so linear motion of the boat produces rotation below 0.2 Hz. As the TBetter isolation loop is trying to isolate down to 50 mHz (and amplifying motion in the 10-100 mHz band), the net result is large rotations of Stage 1, which have nothing to do with ground rotation. 

Where is this excess noise coming from? I'm not sure, but there are a number of candidates: it could be displacement sensor noise of Stage 0/1, actuator/force noise of HEPI, thermal gradients across HEPI springs and so on. Regardless of the noise source, I feel that HEPI floating (with fc~0.2 Hz for rotation) and TBetter filter (isolating to 50 mHz) is probably not the optimum configuration for good low-frequency isolation, given that we may now be measuring ground rotation precisely.

I'm very new to this so I hope others will correct me if I'm mistaken. It would be very useful to try out the HEPI closed-loop configuration and HEPI locked rigid states with BRS measuring ground rotation to understand this issue more clearly.