The operating range of force-balance seismometers

The electric operating range of a well-designed seismometer is, at least in its passband, limited by clipping at the output, at a signal level slightly below the internal supply voltage. The seismic operating range is the electric range divided by the amplitude response, and thus in general frequency-dependent. Clipped waveforms can normally be recognized when the signal has been recorded with adequate bandwidth. However, when clipping occurs in earlier stages of the circuit or in the feedback loop, or when the signal is low-pass filtered in the recorder, clipping may go unnoticed and the record may look quite normal even if it is severely distorted; an example is presented by Wielandt [Wielandt 1983].

The operating range at very low frequencies requires a separate consideration. Due to the presence of an integrator in the feedback loop, the condition that clipping should occur only at the output cannot be maintained at very low frequencies. The operating range is then limited by saturation of the integrator. Since the integrator also generates noise, it determines the dynamic range of the whole system at long periods. This has direct consequences for the ranges of drift and tilt in which force-balance seismometers can be operated. We give an order-of-magnitude estimate: the integrator may have a noise level of $0.1 \mu V$ rms (in an appropriate bandwidth) and a saturation level of $\pm10 V$; the sensor may have been designed to resolve 10^-12 g rms. Then the integrator will be saturated by static accelerations of $\pm10^{-4} g$. A vertical sensor whose suspension has a temperature coefficient of 10^-5 per Kelvin could be operated with this feedback system in a temperature range of $\pm10$ Kelvin; a horizontal sensor would have to be levelled to within 0.1 mm per meter.

The designer of a force-balance seismometer has a considerable freedom in the choice of the responsivity and thus of the seismic operating range. The dynamic range of sensors and recorders is however limited, so a decision must be made whether the operating range or the self-noise of a system should be specified in the first place. Recording systems for strong motion usually have a certain level of ground acceleration specified as the operating range. General-purpose seismographs are normally designed to resolve ground noise; their operating range is then made as large, and their gain as small, as this requirement permits.