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Message ID: 15510     Entry time: Sat Aug 8 07:36:52 2020
 Author: Sanika Khadkikar Type: Configuration Category: Calibration-Repair Subject: BS Seismometer - Multi-channel calibration

Summary :

I have been working on analyzing the seismic data obtained from the 3 seismometers present in the lab. I noticed while looking at the combined time series and the gain plots of the 3 seismometers that there is some error in the calibration of the BS seismometer. The EX and the EY seismometers seem to be well-calibrated as opposed to the BS seismometer.

The calibration factors have been determined to be :

BS-X Channel: $\dpi{150} \small {\color{Blue} 2.030 \pm 0.079 }$

BS-Y Channel: $\dpi{150} \small {\color{Blue} 2.840 \pm 0.177 }$

BS-Z Channel: $\dpi{150} \small {\color{Blue} 1.397 \pm 0.182 }$

Details :

The seismometers each have 3 channels i.e X, Y, and Z for measuring the displacements in all the 3 directions. The X channels of the three seismometers should more or less be coherent in the absence of any seismic excitation with the gain amongst all the similar channels being 1. So is the case with the Y and Z channels. After analyzing multiple datasets, it was observed that the values of all the three channels of the BS seismometer differed very significantly from their corresponding channels in the EX and the EY seismometers and they were not calibrated in the region that they were found to be coherent as well.

Method :

Note: All the frequency domain plots that have been calculated are for a sampling rate of 32 Hz. The plots were found to be extremely coherent in a certain frequency range i.e ~0.1 Hz to 2 Hz so this frequency range is used to understand the relative calibration errors. The spread around the function is because of the error caused by coherence values differing from unity and the averages performed for the Welch function. 9 averages have been performed for the following analysis keeping in mind the needed frequency resolution(~0.01Hz) and the accuracy of the power calculated at every frequency.

1. I first analyzed the regions in which the similar channels were found to be coherent to have a proper gain analysis. The EY seismometer was found to be the most stable one so it has been used as a reference. I saw the coherence between similar channels of the 2 seismometers and the bode plots together. A transfer function estimator was used to analyze the relative calibration in between all 3 pairs of seismometers. In the given frequency range EX and EY have a gain of 1 so their relative calibration is proper. The relative calibration in between the BS and the EY seismometers is not proper as the resultant gain is not 1. The attached plots show the discrepancies clearly :
• BS-X & EY-X Transfer Function : Attachment #1
• BS-Y & EY-Y Transfer Function : Attachment #2

The gain in the given frequency range is ~3. The phase plotting also shows a 180-degree phase as opposed to 0 so a negative sign would also be required in the calibration factor. Thus the calibration factor for the Y channel of the BS seismometer should be around ~3.

• BS-Z & EY-Z Transfer Function : Attachment #3

The mean value of the gain in the given frequency range is the desired calibration factor and the error would be the mean of the error for the gain dataset chosen which is caused due to factors mentioned above.

Note: The standard error envelope plotted in the attached graphs is calculated as follows :

1. Divide the data into n segments according to the resolution wanted for the Welch averaging to be performed later.

2. Calculate PSD for every segment (no averaging).

3. Calculate the standard error for every value in the data segment by looking at distribution formed by the n number values we obtain by taking that respective value from every segment.

Discussions :

The BS seismometer is a different model than the EX and the EY seismometers which might be a major cause as to why we need special calibration for the BS seismometer while EX and EY are fine. The sign flip in the BS-Y seismometer may cause a lot of errors in future data acquisitions. The time series plots in Attachment #4 shows an evident DC offset present in the data. All of the information mentioned above indicates that there is some electrical or mechanical defect present in the seismometer and may require a reset. Kindly let me know if and when the seismometer is reset so that I can calibrate it again.

 Attachment 1: BS_X-EY_X.png  180 kB  Uploaded Thu Aug 13 22:08:12 2020
 Attachment 2: BS_Y-EY_Y.png  185 kB  Uploaded Thu Aug 13 22:08:40 2020
 Attachment 3: BS_Z-EY_Z.png  182 kB  Uploaded Thu Aug 13 22:08:56 2020
 Attachment 4: timeseries.png  246 kB  Uploaded Thu Aug 13 22:09:36 2020
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