Seismometer Frequency Response

Algorithms were developed to determine the free period ($T_{s}$) and fraction of critical damping ($h_{s}$) and to determine the high-frequency corner ($f_{g}$) and fraction of critical damping ($h_{g}$) parameters by measuring the frequency response of the seismometer to known stimuli. The free period ($T_{s}$) and fraction of critical damping ($h_{s}$), which describe the low-frequency response, were determined via a grid search for the maximum variance reduction between the observed response and the theoretical time series response to a 40-1100 second period swept sine wave. The high-frequency corner ($f_{g}$) and fraction of critical damping ($h_{g}$), which describe the high-frequency response, were determined via a grid search for the maximum variance reduction between the observed response and the theoretical phase response to a 0.5-40 Hz stepped sine wave. Both of these stimuli are generated by the Metrozet E300 electronics as well as output to the STS-1 calibration coils, and they can be remotely invoked. Figure 3.29 shows an example of the observed and theoretical time series response to the swept sine wave stimulus, and Figure 3.30 shows an example of the observed and theoretical phase response to the stepped sine wave stimulus.

Figure 3.29: Plot of the HOPS STS-1 vertical seismometer observed time series response (solid line) and the corresponding theoretical time series response (dashed line). The best fitting theoretical response was determined via an adaptive migrating grid search to find the $T_{s}$ and $h_{s}$ which maximizes the variance reduction. The best fit was obtained for $T_{s}$ = 360.08 seconds and $h_{s}$ = 0.6768 critical.
\begin{figure}\begin{center}
\epsfig{file=uhr, bb=92 104 540 700, clip=, width=9cm}\end{center}\end{figure}

Figure 3.30: Plot of the HOPS STS-1 vertical seismometer observed phase response (solid line) and the corresponding theoretical phase response (dashed line). The best fitting theoretical response was determined via an adaptive migrating grid search to find the $f_{g}$ and $h_{g}$ which maximizes the variance reduction. The best fit was obtained for $f_{g}$ = 14.998 Hz and $h_{g}$ = 0.371 critical.
\begin{figure}\begin{center}
\epsfig{file=uhr2, bb=92 104 540 700, clip=, width=9cm}\end{center}\end{figure}


Table 3.17: Comparison of the sensitivities of the HOPS STS-1's with Streckeisen and with Metrozet electronics. The Streckeisen sensitivities were obtained from the factory calibration sheets supplied with each seismometer. The Metrozet sensitivities were calculated using the STS-1 Calibration Software Applet supplied by Metrozet.
Comp S/N Streckeisen BRB Streckeisen LP Metrozet BRB Metrozet LP Percent
    V/(m/s) V/(m/$s^{2}$) V/(m/s) V/(m/$s^{2}$) Change
Z 109114 2452 83.4 2386 80.5 -2.7
N 29219 2284 77.4 1984 66.9 -13.1
E 29215 2304 78.0 1993 67.0 -13.5



Table 3.18: HOPS STS-1 calibration results.
Comp $T_{s}$ $h_{s}$ $f_{g}$ $h_{g}$ C
Z 360.08 0.6768 15.00 0.371 0.00939
N 362.93 0.6889 16.28 0.328 0.00909
E 388.37 0.9920 16.29 0.343 0.00844


Berkeley Seismological Laboratory
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