In the context of the intercalibration between the ground seismometer and the F0 LVDTs, a calculation suggests that the effect of missing data from the displacement transfer function, can be compensated using the force transfer function.
As reported in klog 23095, the lack of a complete set of data does not allow us to calculate the intercalibration factor between the ground seismometer and the F0 LVDT in SR2. A complete set of data includes data points of the three peaks expected in the transfer function, whereas in the SR2 measurement, only one peak stands out from the LVDT noise level. A workaround, proposed by Ushiba-san, is to compensate the missing information using the force transfer function, of which we always have reliable measurements.
I tested this idea using SR3 because we already have a complete set of data (klog 23093), and we can compare the results given by the two approaches.
The procedure I followed is this:
- I fitted a mathematical model to the force transfer function measurement T (Figs. 1 and 2).
- The function T was normalized, and the amplitude a was written as a separate parameter: T → a × T.
- Per klog 22998, I constructed the mathematical model a × ( T - 1 ).
- Then, using a as a free parameter, I fitted the model to the measured displacement transfer function, that goes from the seismometer on the ground to the F0 LVDT (see klog 23093).
Fig. 3 shows the measured data points, the fitted model previously shown in klog 23093, and the fitted model constructed with the force TF data. The values of the intercalibration factor calculated using both methods are:
- With a model with all its parameters free (klog 23093): a = 1.0838.
- With the model given by the force TF: a = 1.0789.
Despite I used only one free parameter for the latter, above 80 mHz the coincidence in the amplitude is very good, and the difference between the two values of the parameter a is only 0.4%!
This suggests that it is possible to compensate the missing data in the displacement TF, with information from the force TF.
