KAGRA Logbook

The inter-calibration of geophones and LVDTs (longitudinal, transverse, yaw basis) was done by comparing the transfer functions read from geophones and LVDTs, i.e. (ratio between geophone readout and LVDT readout of a transfer function measurement).
For ideal inter-calibration, the ratio should read a straight flat line at exactly 1.
To inter-calibrate, I simply minimize the cost function

$J(a) = \frac{1}{N}\sum_{n=1}^{N}\left| \log(a\frac{\mathrm{TF}_{\mathrm{geo}}(f_n)}{\mathrm{TF}_\mathrm{LVDT}(f_n)})\right|$

where a is the multiplicative inter-calibration factor that needs to be applied on the geophone readout.
The data is masked such that the frequency of interest is 0.1 to 1 Hz, and coherence between geophone and LVDT is greater than 0.95.
These calibration factors are stored in the ACCBLEND filters (I don't know where to put them).
Also see figure 1-3 for the calibration factors. All scripts can be found in /kagra/Dropbox/Subsystems/VIS/vis_commissioning/srm/notebook/inter_calibration/.

The inter-calibration between LVDT and seismometer is rather involved but conceptually easy.
At free swing, the LVDT readout reads both seismic noise and the motion of the IP. Therefore, it cannot be compared with the seismometers directly to get the inter-calibration factors.
A workaround is to subtract the LVDT readout by the geophone readout (which we have calibrated) so the contribution from the IP motion is removed.
Another approach would be to use the IP transfer function to simulate the IP motion in time-series and subtract it from the LVDT readout.
Both methods work fine in practice but I used the first one to avoid error accumulated from inaccurate models.
However, it's not a straightforward thing to do, we first need to extract the time-series from diaggui, and then recombine them, taking into account the overlapping.
Then we subtract the LVDT signal by the geophone signal, and then re-calculate (welch or otherwise) the subtracted signals' PSDs and CSDs to obtain a ratio between the LVDT and the seismometer in frequency space.
From here we can simply use the geophone-LVDT inter-calibration method to obtain the inter-calibration between seismometers and LVDT.
It's also important that this can only be done when the microseism is high, so both LVDTs and seismometers get a strong coherent signal.
Results can be seen in fig 4.
The inter-calibration factors are stored in SEISINF filter. Do note that LVDT longitudinal is coupled with negative y-arm direction, while transverse is coupled with positive x-arm direction.