Frequency limits for seismometers as determined from signal-to-noise ratios. Part 2. The feedback seismometer
Authors: Rodgers Peter W. 
Published: September 2021

The range of frequencies that a seismometer can record is nominally set by the corner frequencies of its amplitude frequency response. In recording pre-event noise in very quiet seismic sites, the internally generated self-noise of the seismometer can put further limits on the range of frequencies that can be recorded. Some examples of such low seismic noise sites are Lajitas, Texas; Deep Springs, California; and Karkaralinsk, U.S.S.R. In such sites, the seismometer self-noise can be large enough to degrade the signal-to-noise ratio (SNR) of the recorded pre-event data. The widely used low seismic noise model (LNM) (due to Peterson, 1982; Peterson and Hutt, 1982; Peterson and Tilgner, 1985; Peterson and Hutt, 1989) is used as representative of the input ground motion acceleration power density spectrum (pds) at such very low noise sites.

This study determines the range of frequencies for which the SNR of a feedback seismometer exceeds 3 db (a factor of 2 in power and 1.414 in amplitude). Analytic expressions for the SNR are developed for three types of feedback seismometers. These are the displacement feedback, velocity feedback, and coil-to-coil velocity feedback seismometers. It was found that the analytic SNRs of the displacement and velocity feedback seismometers are identical and that the SNRs for the coil-coil feedback seismometer and the electromagnetic seismometer are also the same.

The signal pds using Peterson's LNM as an input is developed for each of the three types of feedback seismometers. Suspension noise is modeled following Aki and Richards (1980). In order to model the electronically caused component of the self-noise, the electronic noise properties of two commonly used operational amplifiers (Precision Monolithics OP-27 and the Burr-Brown OPA2111 FET) are described. Using these, noise models are developed for a synchronous demodulator and a chopper-stabilized amplifier. These noise models are used to numerically compute the SNRs for the two feedback seismometers used as examples, which are the Guralp Systems CMG-3ESP and Sprengnether Instruments SBX-1000 feedback seismometers. For each of the example seismometers, the calculated range of frequencies for which their SNR exceeds 3 db is as follows: the CMG-3ESP, 0.025 to 13.3 Hz; the SBX-1000, 0.098 to 11.3 Hz.

The calculated and measured SNRs for the CMG-3ESP are compared. The calculated upper frequency for a SNR of 3 db was 13.3 Hz compared with 18.4 Hz measured in the noise tests. The calculated lower frequency for a SNR of 3 db was 0.025 Hz, whereas the measured value was 0.047 Hz. The difference is most likely due to the fact the CMG-3ESP is cut off at 0.1 Hz.

Formulas are developed in Appendix A for calculating the SNR and self-noise of identical, colocated seismometers from their recorded outputs. The analytic transfer functions, midband gain, upper and lower corner frequencies, and bandwidths for the three types of feedback seismometers are given in Appendix B for comparison with the frequency limits set by the SNR.