Frequency limits for seismometers as determined from signal-to-noise ratios. Part 1. The electromagnetic seismometer

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 an electromagnetic seismometer exceeds 3 db (a factor of 2 in power and 1.414 in amplitude). In order to do this, an analytic expression is developed for the SNR of a generalized electromagnetic seismometer. The signal pds using Peterson's LNM as an input is developed for an electromagnetic seismometer. Suspension noise is modeled following Usher (1973). In order to determine the electronically caused component of the self-noise, noise properties are compared among three commonly used amplifiers. The advantages and disadvantages of the inverting and noninverting configurations in terms of their SNR are discussed. In most cases, the noninverting configuration is to be preferred as it avoids the use of the large gain setting resistances required in the inverting configuration to avoid loading the seismometer output. A noise model is developed for a typical low noise operational amplifier (Precision Monolithics OP-27). This noise model is used to numerically compute the SNRs for the three electromagnetic seismometers used as examples. The degradation in SNR caused by large gain setting resistances is shown. Numerical examples are given using the Mark Products L-4C and L-22D and the Teledyne Geotech GS-13 electromagnetic seismometers. For each of the example seismometers, the calculated range of frequencies for which their SNR exceeds 3 db is as follows: the GS-13, 0.078 to 56.1 Hz; the L-4C, 0.113 to 7.2 Hz; and the L-22D, 0.175 to 0.6 Hz. For the GS-13, the calculated lower and upper frequencies at which the SNR is 3 db are 0.078 and 56.1 Hz. This compares with the values 0.073 and 59 Hz measured in the noise tests on the vertical GS-13. Expressions for the total noise voltage referred to the input of an operational amplifier are developed in Appendix A. It is shown that in the inverting configuration, although no noise current flows in the input resistor, the noise current appears in the expression for the total noise voltage as if it did. In Appendix B, it is shown that any noise current flowing through an electromagnetic seismometer having a generator greater than several hundred V/m/sec generates a back emf that adds significantly to the noise of the system. This implies that system noise tests that substitute a resistor at the noninverting input of the preamplifier or clamp the seismometer mass will tend to underestimate the system noise.