Chris,

At 02:17 PM 2/13/2008 -0500, you wrote:

>>Numerical integration looks interesting.  What I think I need to make it
>>work is a D/A with something like 24-bit resolution and correspondingly low
>>noise.  Haven't looked too hard, and haven't found any.
>
>        There are some about.

Any suggestions as to what manufacturers to check?

>>My understanding was that the 360 second low-end response of the STS-1 was
>>about as good as you can get, while still maintaining instrument noise
>>below earth noise, and it required using every possible scheme to reduce
>>and slow internal noise sources.
>
>        The STS-2 goes to this. Particular versions of the STS-1 would go 
> out to 1,000 seconds. It is a very hard way to get this performance!

Given the fundamental noise issues in any vertical, I think it's the only way.

>>That also raises the interesting question, whether some of that 'low earth
>>noise' isn't exactly what you are looking to measure.
>
>        There is a lot of earth noise down to the Eigenmodes, which are 
> interesting in themselves. Transient signals occur which look very like 
> quake precursors.

Those transients worry me just a little.

>> >     If we consider a pendulum sensor system, the response is proportional
>> > to the square of the period. If you take a 2 second pendulum and reduce
>> > the restoring force to give a 20 second system, should you get 100x the
>> > response for signals already in the passband?
>>
>>Not sure how you are proposing to reduce the restoring force.  If you are
>>suggesting feedback, it actually doesn't act in that way.
>
>    Positive feedback does and it will reduce the period.

Sounds like an oscillator to me.

>        It effectively
>>applies a very large velocity-damping force on the pendulum in a very 
>>linear manner.  The result is that the low frequency corner is lower and
>>the high frequency corner is higher than the original single peak at 2
>>seconds.  In a sense the system is still acting as a 2 second pendulum but
>>one which is extremely overdamped. see 'FISS'
>>
>> >      Why should a synthesised feedback response to obtain a longer period
>> > result in a much smaller response to the ground motion?
>>
>>The simple answer: Because (negative) feedback always acts to lower the
>>instrument sensitivity to position, velocity and acceleration, (excepting
>>in a few pathological cases).  A complete answer involves actually doing
>>the computations for a particular case and examining the results such as is
>>done in 'FISS'.
>>
>> >      You seem to consider that requiring an increased position
>> > sensitivity is an advantage.
>
>        You are using a position sensor, which will have a measurement 
> range and a  noise level which limits what you can sense. I am enquiring 
> what resolution you can get. The practical limit is likely to be set 
> above this by thermal varriations.

Using the same C/D device, a little better than the SDC, maybe 5-10x the 
displacement sensitivity depending on the plate size, so   5-10x S/N.  I 
have been scratching my head as to how to characterize C/D quantization 
noise relative to feedback.  I'm sure as you apply feedback, reducing the 
sensitivity, the displacement corresponding to one C/D step also reduces, 
so S/N from that source shouldn't get worse.  I need to think about this more.

My approach to the thermal problem is to try to keep the thermal changes 
small and very slow, below the low-end response of the system.  But that 
implies that the system *has* a low end limit, i.e. that its force-response 
will be low near zero frequency.

>> >     If you use a DC path from your position sensor through a long period
>> > integrator to the feedback transducer, you can in theory remove ~all
>> > position drifts.
>>
>>Yes, but when you call it a long-period integrator you imply that there is
>>no DC path. .
>
>        No. They can go down to DC. Randal uses one on his Sprengnether. 
> See my reference. You have a large resistance onto the negative input of 
> a FET opamp and a capacitor (+ resistor?) in the feedback loop.

You are sooooo right.  I went back and looked at my proposed circuit, which 
is similar to what Randall was using, and found that, indeed, with a 
particular capacitor I'd tested it should integrate down to something below 
a microHertz.

>> >      A capacitative position sensor system can have a very high
>> > linearity. What other system nonlinearities were you considering that
>> > could be relevant?
>>
>>Primarily the position sensor system.  That would include, of course,  the
>>C/D converter as well as the capacitor.  When you say very high linearity
>>are you implying 1%, 0.1%, 0.01%....?  Have any measurements been made?
>
>
>     My guesstimate would be in the 0.1% region, probably better. It will 
> depend mostly on the precision of the physical sensor construction. The 
> linearity over a small range will be extreme.

OK, sometime I'll play around with numbers in that range and see what happens.

>      My
>>concern is that even with fairly small nonlinearity, large amplitude,
>>higher frequency signals can mix to generate small low-frequency difference
>>signals which could possibly confound measurements attempted down at very
>>low frequencies.  Only with specific linearity figures could one rule
>>in/out that effect by calculating its magnitude.  Also the spring in a
>>vertical, or pendulum geometry might possibly add nonlinearity.
>
>
>        I would not expect even moderate quakes to generate serious non 
> linearity. You are more likely to run out of detector range. The angles 
> are less than 2 degrees.

Yes, you don't usually notice a vertical pendulum swinging very far in 
response to distant quakes, do you.

Regards,
Brett


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