In the context of the F0 LVDT correction using the seismometer on the ground, entries 23508, 23528 and 23529 report the calculated noise of the corrected LVDT under different microseismic conditions. The question we still need to answer is, how to experimentally confirm these theoretical calculations. Here, a way to do it, is described.

In order to measure the corrected LVDT noise, from the corrected LVDT readout, we need to remove the displacement of the keystone quantified with respect to an inertial reference frame. We usually use the term GEO to refer to this quantity, although we don't have a geophone for F0.  The usage of this term comes from the IP, where we also use the sensor correction technique. Following entry 22998,

GEO = a × SEIS + LVDT,

where a is the inter-calibration factor, and SEIS and LVDT are the seismometer and uncorrected LVDT readouts. We can write this expression as,

GEO = [ 1 + LVDT / (a × SEIS) ] × a × SEIS,

where the ratio LVDT / (a × SEIS) is a transfer function we have measured before in the context of the inter-calibration factor calculation (see entries 23093 and 23124). Then, the noise N of the corrected LVDT can be written as,

N = LVDTc - GEO = LVDTc - [ 1 + LVDT / (a × SEIS) ] × a × SEIS,

where LVDTc is the corrected LVDT readout.

The noise N could be measured with a simple modification of the real-time model and medm screen. In a filter bank, we can write the mathematical model of the expression  [ 1 + LVDT / (a × SEIS) ] , then multiply it by the seismometer output a × SEIS, and finally subtract it from the corrected LVDT readout LVDTc.