On Sun, 7 May 2000, Tom Schmitt wrote:
> > >  and had three disks that rotated at a fairly low rpm, a few Hz at most.
> > >  The disks were less than a meter in diameter.
> > >  The disks had two accelerometers on them.  The acceleration as a
> > >  function of position of the two accelerometers was recorded and some
> sort
> > >  of auto-correlation or FFT was done to get the direction and magnitude
> of
> > >  the gradient.
> >     Did the disks all rotate at the same speed? Were they all the same
> > diameter?  Were they orientated at right angles to each other? Were they
> all
> > mounted on the same frame?
> 
> The all rotated at the same speed.  Each disk had two accelerometers 180
> degrees apart.   At any time the acceleration
> on them was
> 
>                         (1) an omega sqaured r term radially out ward.
> 
>                         (2) the component of gravity resolved to the
> orientation of the line the two
>                              accelerometers were on.
> 
>                         (3) any acceleration due to bumps in the road.
> 
> The two accelerometrs per disk were necessary to compensate for any bumps.
> The difference between
> the readings of the two accelerometers gave the gradient of gravity in the
> direction the disk was pointing at
> that time.  A bump would cause the same acceleration at both accelerometers
> and thus would cancel out
> when the gradient was measured.
> 
> The axeses of rotation were 90 degrees to one another.
> 
> They were all mounted to a very stiff platform.
> What sort of accelerometers were used?
> 
> That is the trick I am sure.  Though the briefing was not classified they
> did not show us the parts manual!
> I suspect these were very special accelerometers.  They had to be sensistive
> 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 that might be ideal for something like this.  
One is a lead niobate, which is a super dielectric and has an incredible
piezoelectric potential.  When the crystals are oriented correctly dielectric
constants in the tens of thousands have been recorded.  This certainly has an
application in recording instrument technology.  I don't think it is in wide
spread use industrially, but we have been studying it at ASU.  It will
beat barium titanate as the super dielectric for sure, which might be what
was available for these gravimeters. It would be fun to try and put one of
these things together.

The rotation sticks the gravimeters outward and keeps some pressure on them at
all times I think.  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.  

Because the data can be averaged over quite a few spins, the noise reduction
could be done easily.  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 the
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.  This
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 aspect
of the response that can easily be used to back out the gravity gradient.

> >     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.

> >     I am trying to understand the principles / practical limitiations of a
> > system which can detect the tiny changes in force that need to be measured
> > against the noise background of even a large ship. Doing it in the
> horizontal
> > plane sounds difficult enough. Doing it in the vertical plane would seem
> to
> > be much more difficult. Doing it while the system is in motion sounds very
> > dificult.

Yes, the horizontal gradient sounds far easier to me!  Another thing that
would be a pain in the but is the levelling, but the instruments might be able
to use their own gyroscopic response to figure out this too.  But this begins
to look like an awful lot of computing and deconvolution to get the desired
data.  Maybe one could simply use the horizontal gradient in some cases.  You
could find a lot of interesting features in the subsurface just from this
alone.  I would love to try this some day, if I find the time.

> 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.

Tens of millions of dollars in research money doesn't hurt either.

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

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.
 
> About that time there was at least one sattelite launched at low altitude
> that had very good elevation measurements.  I suspect that that technology
> replaced the land based measurements.  However, my satelite geodesy is real
> rusty ( never was much good ) and that stuff was not discussed. 

It depends on what you want to look at.  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 computers 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.
After some time, we will have access to libraries of seismic and gravity data
taken over the entire surface of the Earth, but probably long after we are all
dead.

John Hernlund
E-mail: hernlund@.......
WWW: http://www.public.asu.edu/~hernlund/

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