Barry,

The combination of a VBB instrument and a 24-bit digitizer is
designed to get an on-scale record of a maximum likely magnitude
near-field quake, like a 7.0 at 1000km distance, while still having
good signal-to-noise (SNR) for a minimal quake of interest, like
a 3.0 at 100 km. In his Harvard thesis on the VBB seismograph system
(including the VBB sensor and the digitizer), J.M.Steim demonstrates 
these parameters in considerable detail with nice graphics.
I hope to find time this weekend to make a table of the data to
show what a PSN seis should expect to be able to record.
Like one gets roughly similar amplitudes (within a factor of 10)
for a M6.0 at 3 degrees (330km), a 8.0 at 30deg, and a 3.0 at 10km.

So for a VBB seis, if the digitizer limit level is 20 volts and the 
output 2000 V*sec/m, the clipping level is 10mm/second ground velocity.
The minimal signal is the noise floor of the displacement transducer,
which, with proper amplifiers, could be assumed to be 10 micro-volts
or less, or 5 nanometers/sec. So the digitizer should try to encompass
this range. 

A common 24-bit digitizer has a maximum voltage of 40 volts for
use with VBB seises with 20 volt maximum outputs. 24-bits is
16 777 216 counts, or 419 430 counts/volt. Inverting, this is
2.38 microvolts/count, or about 0.4 times the expected noise floor
of 10 microvolts. Any additional amplifiers will only raise this
noise level, which is why they are low or unity gain.

So with a 16-bit digitizer, we need to have a maximum value of
1 volt or less to avoid the need for additional amplification. 
With 1 volt full scale, the least count is 15.3 microvolts. If
we want to push the noise floor, a 10x line amplifier would be
needed, or, as you suggest, the VBB feedback can be modified for
higher output (but this has its own problems). With a 10x amp,
assuming that it doesn't clip or add considerably more noise,
an output of 20 000 V*sec/m into a 1-volt digitizer will limit at 
50 microns/second. The least count will be 0.76 nanometers/second,
about 1/10th the expected noise floor. But the clipping at 50u/sec
will limit recording of large events. SO, we also need a lower gain.

Since the input to the 10x amplifier is (often) also the 
high pass filter (the high-pass removes the DC thermal noise, etc),
dividing its output by 100 is preferable to using the unfiltered 
output for a low gain channel.  So after a 100:1 divider the low 
gain is 200 V*sec/m, which at a clip level of 1 volt of the 16-bit 
digitizer is 5mm/second, with a least count of 76 nanometers/second.

While the 100:1 is not the difference between 16 and 24 bits (=256:1),
the low gain will still usually record some data, where a 1000:1 
low gain will be a pretty dull channel. And the result will cover
data from 5mm/second to lower than the instrument noise floor.

I think that Larry's digitizer is 10 volts full scale. This would
still work, but with an upper limit of 0.5 millimeters/second and a 
least count value of 7.6 nanometers/second (using the values above).
Then the 100:1 low gain would have a range of 50mm/second to
a least count value of 0.76 microns/second, which would put it
in the range of moderate strong motion recording.

For the experimental STM-8 VBB here at the farm, I am still using
the Radio Shack digital multimeter as a 12-bit digitizer. The maximum
is 200 millivolts, with a minimum of 0.1 millivolt. With a VBB signal
of 5.29mv*second/micron (aka 5293 V*sec/m), the maximum signal is
37.8 microns/second and the minimum is 18.9 nanometers/second. The
6-second microseisms today run about 2 millivolts, or 0.38 microns/sec.
Since 6 seconds is close to 2*pi, so w (omega) ~=1, the displacement
is also about 0.38 microns. With a minimum value of 0.1 millivolt, the
noise threshold (again at 6 seconds) is about 0.02 microns (20 nanometers).
(I need to use another 10x gain to see the sensor self noise.)
So it has good sensitivity to small signals, but does clip on larger
quakes like Izmet, Turkey, and the recent central Mexico event. The
7.0 in S.CA (Hector Mines) clipped for half an hour.

Regards,
Sean-Thomas

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