This entry reports the results of the recalibration of the geophones.

Recalibration was necessary because a bump appeared in the transfer functions around 1 Hz. See the original report in klog 20534.

It's better to describe what I did in a document and upload it to JGWDoc, for this klog entry I just give a cursory description:

1. I measured the TFs from yaw actuation to two different sets of outputs:
   • Set 1: raw output of the individual geophones, in units of cnt/cnt.
   • Set 2: displacement output of the individual geophones, using their calibration transfer functions that produce the bumps, in units of um/cnt.
2. I fitted each of these TFs in Set 2 with a mathematical model that does not allow the bump to appear, and fits well the resonance frequency and DC amplitude. For the fit, the values were weighed with a factor 1/f in order to favor lower frequencies where the resonance is.
3. Then I defined a function containing the geophone parameters to determine (Ge , f0 and eta):  integrator(s) * m2um * ( 1 / H_geo ) * hp(s) * ( 1 / preamp ) * cnt2V * tf_raw
   • Integrator: conversion from velocity to displacement,
   • m2um: conversion from metres to micrometres.
   • H_geo( Ge, f0 , eta ) = Ge * s**2 / (omega0**2 + 2 * omega0 * eta * s + s**2 )
   • s = 1j *2 * pi * f
   • omega0 = 2 * pi * f0
   • hp: high-pass filter with four poles located at 3 mHz.
   • preamp = 940, this factor compensates the preamplifier gain.
   • cnt2V = 2 * 20 / 2**16, ADC conversion factor in units of V/cnt.
   • tf_raw: raw transfer function from Set 1.
4. Then I fitted the function defined in step 3 to data generated with the function calculated in step 2.
5. With Foton, I put all these filters in the filter banks and measured again TFs.

In the table, the original values measured by Fujii-kun (entry 7059) and the new ones are shown.

265.114

1.079

0.2990

260.6117

1.125

0.2881

248.8686

1.204

0.2386

The observations are:

• All the resonance frequencies f0 decreased, namely, by 15, 68 and 197 mHz for H1, H2 and H3 respectively.
• The damping factors Eta decreased by factors of 0.49, 0.51, 0.54 for H1, H2 and H3 respectively.

The plots show the following quantities:

• With new filters: TF measured with corrected geophone parameters (step 5 above).
• Aimed with measured velocity: TF calculated with the measured raw TF (Set 1 in step 1) and the geophone calibration function with new parameters.
• Theoretical aim: Transfer function calculated in step 2.
• Original with bump: the name is explanatory.

From the plots, it's clear that the results are alright and, therefore, I'll continue with the following step, which is inter-calibration between geophones and LVDTs. However, it seems the results could still be improved.