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.

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.

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	á360.08	á0.6768	á15.00	á0.371	á0.00939
N	á362.93	á0.6889	á16.28	á0.328	á0.00909
E	á388.37	á0.9920	á16.29	á0.343	á0.00844