For broadband seismic recording with high sensitivity, an output signal
proportional to ground acceleration is unfavourable. At high
frequencies, sensitive accelerometers are easily saturated by traffic
noise or impulsive disturbances. At low frequencies, a system with a
response flat to acceleration generates a permanent voltage at the
output when the suspension is not completely balanced. The system would
soon be saturated by the offset voltage resulting from thermal drift or
tilt. What we need is a band-pass response in terms of acceleration, or
equivalently a high-pass response in terms of ground velocity, like
that of a normal electromagnetic seismometer (Fig. 6)
but with a lower corner frequency. The desired velocity broadband (VBB)
response is obtained from the FBA circuit by adding paths for
differential feedback and integral feedback (Fig. 17). The capacitor C
is chosen so large that the differential feedback dominates throughout
the desired passband. While the feedback current is still proportional
to ground acceleration as before, the voltage across the capacitor C
is a time integral of the current, and thus proportional to ground
velocity. This voltage serves as the output signal. The output voltage
per ground velocity - the apparent generator constant Eapp of the feedback seismometer - is
The output signal of the second integrator in Fig. 17 is normally accessible at the ``mass position'' output. It does not indicate the actual position of the mass but indicates where the mass would go if the feedback were switched off. ``Centering'' the mass of a feedback seismometer has the effect of discharging the integrator so that its full operating range is available for the seismic signal. The mass-position output is not normally used for seismic recording but is useful as a state-of-health diagnostic, and is used in some calibration procedures.
The relative strength of the integral feedback increases at lower frequencies while that of the differential feedback decreases. These two components of the feedback force are of opposite phase ( and relative to the output signal, respectively). At some low frequency, the two contributions are of equal strength and cancel each other. This is the lower corner frequency of the closed-loop system. Since the closed-loop reponse is inverse to that of the feedback path, one would expect to see a resonance in the closed-loop response at this frequency. However, the proportional feedback remains and damps the resonance; the resistor R acts as a damping resistor. At lower frequencies, the integral feedback dominates over the differential feedback, and the closed-loop gain decreases with the square of the frequency. As a result, the feedback system behaves like a conventional electromagnetic seismometer and can be described by the usual three parameters: free period, damping, and generator constant. In fact electronic broadband seismometers, even if their actual electronic circuit is more complicated than presented here, follow the simple theoretical response of electromagnetic seismometers more closely than these ever did.
As far as the response is concerned, a force-balance circuit as described here may be seen as a means to convert a moderately stable short- to medium-period suspension into a stable electronic long-period or very-long-period seismometer. The corner period may be increased by a large factor, for example 24-fold (from 5 to 120 sec) in the Streckeisen STS2 seismometer or even 200-fold (from 0.6 to 120 sec) in a version of the Guralp CMG3. But this factor is not necessarily a figure of merit. Feedback does not reduce the instrumental noise; according to section 3.2, short-period suspensions must be combined with extremely sensitive transducers for a satisfactory sensitivity at long periods.
At some high frequency, the loop gain falls below unity. This is the upper corner frequency of the feedback system which marks the transition between a response flat to velocity and one flat to displacement. A well-defined and nearly ideal behaviour of the seismometer like at the lower corner frequency should not be expected there, both because the feedback becomes uneffective and because most suspensions have parasitic resonances slightly above the electrical corner frequency (otherwise they could have been designed for a higher corner). The detailed response at the high-frequency corner does however rarely matter since the upper corner frequency is usually outside the passband of the recorder. Its effect on the transfer function can in most cases be modelled as a small, constant delay (a few milliseconds) over the whole VBB passband.