PSN-L Email List Message

Subject: Re: Article on gravimeters
From: ChrisAtUpw@.......
Date: Mon, 8 May 2000 21:40:48 EDT

In a message dated 08/05/00 05:39:38 GMT Daylight Time, hernlund@....... 

> > > What sort of accelerometers were used?

> > I suspect these were very special accelerometers.  They had to be 
> > sensitive enough to measure the difference in
> > g over a distance of one meter.
>  I suspect some high tech piezo-electrics would do the trick.  That
>  would be the reason for rotating too I think.  Recently some newer 
> interesting materials have been developed.....

    I have been looking at piezo-electrics for seismograph applications. One 
limiting factor seems to be the large changes in properties / drift with 
temperature. (The 50 nF types do, however, ease the input impedance / cutoff 
frequency problems considerably and 0.1 Hz is quite easily achieved. >3 V 
output per g also helps a lot.) Remembering the problems with spring 
materials in seismographs and that the accelerometers will be rotating quite 
fast, the 'obvious' solution of a mass + spring + LVDT + damping doesn't seem 
very hopeful, either. Maybe quartz could provide the stability? What is the 
best linearity / stability / sensitivity / lowest noise that can be obtained? 
Do any sensors directly give a frequency or frequency modulated output?
>  The rotation sticks the gravimeters outward and keeps some pressure on 
> at all times I think.  

    OK, let's consider a disk of 1 m diameter rotating in the vertical plane. 
To keep the pressure in the same direction and avoid any 'passing through 
zero' effects, we need a rotation of > 42 RPM. The 1 & 3g level is ~ 60 RPM, 
so we probably operate in between.

>  Because a piezo-electric transducer responds directly to
>  changes in stress the rotation would produce an easy to study signal under
>  ordinary circumstances.  These transducers would not hold their charge for
>  long, however, and the rotation would allow you to take the most useful
>  information from them because it will always be changing.  You could
>  calibrate the loss of charge and everything else if you could find a good
>  absolute gravity station with a vertical gradient measurement.  You can
>  totally predict the signal coming from them using simple mathematics.  

    Only if the response, amplifiers etc. are absolutely linear, otherwise 
you will see 'errors'. You are subtracting large voltages and looking for 
very small remainders. This is not neccessarily disastrous, but will make the 
detection of small signals more difficult. Charge leakage should not be a 
problem, since you are only looking for changes in potential. I don't know 
how you cope with bumps in the road. I suspect that a very good 'soft' 
vehicle suspension system would be needed. When you set down you coffee mug 
on the table, it gets a shock of 10 to 100g. You need to design out that 
problem as far as possible! By rotating the disks, only the changes in signal 
levels need to be considered and the signals from a series of rotations can 
be averaged.
>  Because the data can be averaged over quite a few spins, the noise 
>  could be done easily.  

    I'm not so sure of 'easily'? You have to get the signal in the first 
place and we are talking about ppm 'g' level changes. It's OK in the 
horizontal plane, but in the vertical plane you are seeing signals changing 
from 0 to 2 g minimum. To reduce noise by x2, you need four samples. To 
reduce it by x4, you need sixteen samples.... It depends on how long you can 
wait to get your answer. If the signal is buried in noise and for this 
application we can reasonably assume that the best possible sensitivity is 
required, phased 'Boxcar' detectors might be a better option. They are very 
good at digging signals out of noise. Chopping up a very low level signal and 
feeding it into a computer can result in a 'garbage in / garbage out' 

> The FFTs of both signals could be deconvoluted for the
>  expected zero gradient response and then combined together.  The left over
>  portion (residual) of the signal could be used to get the gradient after 
>  correlated deviations are removed (like from a bump in the road). The phase
>  shift info would give you the direction of the gradient in the plane of the
>  circle and the amplitude would give you the magnitude of the gradient.  
>  would be quite a lot of fun to use!  I think you could increase the 
> confidence
>  in the readings by modulating the frequency of rotation of the disk (i.e.
>  speeding it up and slowing it down) because this would create another 
>  of the response that can easily be used to back out the gravity gradient.

    Holding the rotation speed constant to ppm levels sounds hard enough. 
Changing it in a known way with a known phase sounds like a problem which I 
would wish to avoid.
>  > >     How were the signals and power transferred to the disks?
>  > >     How were the disks driven? Were air bearings used?
>  > >     Was there any automatic gravity alignment system? Naval gyro 
> > >      compasses and aircraft artificial horizons have them built in.
>  > I do not remember or was not told.
>  Ahhhh, those are the real secrets for sure!  It would be great to have
>  magnetic bearings or something like that.  Driving the thing would be tough
>  because you would want to reduce the noise.  Maybe some kind of nice 
> electric motor with its own special bearings could be used.

    Aren't magnetic bearings essentially low load devices? We are talking 
about 1 metre discs with electronics on board, which need to be rigid and 
have an appreciable moment of inertia..... you can't make one weighing just a 
few ounces. You would not need high pressures for air bearings at these 
speeds / loads. They tend to be 'cleaner' than fluid bearings. It might just 
be worth trying out precision ball bearings. Thinking laterally, the record 
industry used two successful drive designs for vinyl disk record players. One 
was a flat rubber belt pulley drive system, but this could give problems with 
slippage, phase and accurate rotor speeds. The other was a direct drive 
stepper motor - which doesn't require separate bearings and whose speed can 
be crystal controlled. These also operate in the required speed range..... 
round about 45 RPM. The rotation sensing would probably be optical. 

> > Honestly, I had trouble believing the thing worked. The physical 
> > principle is simple but how they got the system to work I do not know. 
> > I am sure they did a lot of post collection processing.

> > They claimed that they could drive the thing at 30 miles an hour and get
> > good data.

    Your roads must be a lot better than ours...!
>  That must have something to do with the speed of revolution and the number 
>  of averages needed to back out a gradient at the right resolution from the
>  surface.

    This is why I think that they can't have digitised the raw data and then 
processed it. It must be quite a complex analogue process. Even 16 bit 
resolution is a long way from 1 ppm. Balancing up signals to ppm accuracy is 
not a trivial task.

>  Instruments in orbit may be good for
>  taking gravity data over large regions, but will not be sensitive to stuff
>  close to the subsurface, which is usually what people are interested in.  A
>  good topography data set in the near future will allow for wonderful "
> terrain corrections" used for gravity interpretation.  More powerful 
> are also going to make instruments like this one more practical, because 
> we might be able to make a low tech type and just have to average it over a
> longer  time to get the needed data.  The large amounts of data could then
> be deconvolved.

    Adding a powerful computer won't do much for a poor S/N ratio. There is 
only so much 'information' in the system - and so much noise. If you want 
better data, you have to either improve the S/N ratio or wait for it. 

    Thanks for the analysis of the two accelerometer signals - a VERY useful 


    Chris Chapman

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Larry Cochrane <cochrane@..............>