On Mon, 8 May 2000, Charles R. Patton wrote:
> Good work, John.

Thanks, just a half hour out of my day.  I'll post the whole derivation som=
e
day soon when I can recall what "time" means.  The point of my analysis was=
 to
get only at the gradient, not the absolute field.  The absolute field is no=
ise
for gradient determination.  I think the idea though is that the gradient i=
s
far more useful in "resolving" sub-surface structures.  I am still skeptica=
l
about the claim that these out perform seismic reflection techniques in ter=
ms
of time and quality though.  Who knows, maybe they are right.  I can think =
of
a million academic applications for this thing once it reaches the relative=
ly
poor and destitute realm of science (as compared to defense and oil of
course).

> Someone mentioned bumps cancel out.  Not so.  The bump looks just like
> acceleration and acceleration is indistinguishable from gravity.  The
> difference is only in the frequency range, gravity is DC, while the bump
> is transitory so can be integrated out with a sufficiently time.

The noise and main component of the field only cancel in the summed signals
from the two devices.  But this requires a rigid frame and two acceleromete=
rs
acting at very precisely the same response and output sensitivity; a great
mechanical feat in its own right.  I think you could deal with a little bit=
 of
play in the mathematical analysis, but it would be nice to build something
that works right in the first place.  A very small error in the two radii o=
f
the accelerometers would be devastating for these measurements, so some kin=
d
of control would be needed on this parameter as the instrument deforms over
time.

> A corollary of this is that the bearing defects =96 imperfections in the
> balls and races =96 show up as a frequency spectrum in the accelerometers
> also and would have to be removed in the same way, by integration.

Or addition of the signals...  A spectral analysis of each would provide mo=
re
information about the absolute field, but the summed signals would be neede=
d
for the gradients.
=20
> John comments about lead niobate, and barium titanate strike to the
> heart of the matter.  Piezo accelerometers do not have DC response but
> are stable and require high input impedance amplifiers to achieve low
> frequencies.  I touched on this subject in a note to PSN 8/17/97:

This is great info.  I figured somebody else around here would know more ab=
out
the actual instrumentation than I do.  Another problem with lead niobate an=
d
other "perovskite structure" piezo-electrics is that they are "ferri-electr=
ic"
meaning that they act like iron in a magnetic field, only this is applied t=
o
an electric field.  This will give them a definite phase shift in their
response which is also a problem to be worked out mathematically.

> * Re: Piezo accelerometers for seismic work.  Highly unlikely.  I have
> used extensively piezo-ceramic  accelerometers of approximately the size
> in the web site (http://www.oceana.inter.net) illustration (cantilever
> beam types in SMT 1206 like packages from TDK, Murata, and others.)
> All of these have sensitivities of around 1 to 2 mV /g.  They have
> typical capacities of around 200 pF.  So in order to bias the front end
> preamp you have to parallel them with resistors of 10 M or more.  This
> then sets the low frequency rolloff, i.e.:
>     f =3D 1 / (2PiRC) =3D 1/(6.28*200e-12*1e7)=3D79.6 Hz
> So you have an extremely high cutoff problem first of all. Couple that
> with the fact you've got the 10 M resistor generating a noise voltage of
> approximately 300+ nV, you are left with a minimum sensitivity of only
>     g*300nV/1mV=3D300 ug at 80Hz and falling from there.
> If you want to fight the problem of the resistor versus cutoff frequency
> the noise will only go up.  So you're kind of in a catch 22.  I don't
> anticipate that this is a good approach.
>=20
> So higher capacity can lead to lower frequency response.  Today, SMT
> (surface mounting) capacitors (caps) use multi-layer technology to
> achieve high capacitance values.  This technique is just now moving into
> the piezo accelerometers mentioned above.  The caps and accelerometers
> use identical materials with the main differences being in the
> construction to utilize a =93proof mass=94 to put stress into the ceramic
> during acceleration and the =93poling=94 of the ceramic.  Poling requires
> taking the ceramic to its Curie point, applying a high voltage to its
> electrodes, then cooling the part off while the voltage is applied.  One
> variations of the proof mass and higher strain (as it is the strain
> which generates voltage) is the cantilever mentioned above.  One other
> point needs making.  The ceramic materials have high piezoelectric
> coefficients, but also have temperature and mechanical instability
> problems in high resolution applications which is why the expensive
> (repeatable, calibrated) applications use quartz accelerometers.  But
> those accelerometers are relatively low capacity and output.  A proof
> mass on a diaphragm to form a variable capacitance is a possibility and
> would have DC response, but since the given was spinning disks, one has
> to assume this avenue did not have the performance required, so AC
> accelerometers were being used.
>=20
> For those of an experimental bent.  Take an SMT cap, 0.01 to 0.1 uF and
> mount it on a PCB.  Ground one end and feed the other end through a 1
> Mohm resistor from 5 to 10 VDC or so.  This biasing supplies substitutes
> in some measure for the poling.   Monitor the junction with an
> oscilloscope.  Tap or bend the PCB and you should observe 10=92s of mV on
> the scope.  Practical hints on the cap selection:  the higher the
> capacity, the smaller the package, and the lower the voltage is
> generally better.  This is because this will tend to lead to caps with
> the high K dielectrics, which are the more sensitive in this mode.  Plug
> the numbers here into the formula above and you=92ll find that low
> frequency response becomes much easier to achieve with these high
> capacities.  Engineering folklore tells of unaware engineers who chased
> microphonic boards for many hours due to this phenomenon.
>=20
> Anyway, back to the spinning disk gravimeter.  Piezo accelerometers are
> stable and will still have repeatable output for delta G=92s in the midst
> of the constant G=92s even in the several hundred range such as the
> centripetal acceleration you could generate on a spinning disk.  You
> could use magnetic accelerometers, which after all, is what the
> geophones are.  But again, the standard magnetic units also don=92t have
> DC response.  So the use of the spinning disk to convert the DC gradient
> to AC is an excellent way around the DC problems.  Additionally it
> provides two other benefits:  by going to AC it helps move the amplifier
> away from the 1/F noise problem and it makes possible sensing the
> absolute value of the G field.
>=20
> A thought experiment: In the following I=92ll use Ge for earth
> acceleration and Ga for centripetal acceleration.  With a reasonably low
> rotation rate that yields a 1 G centripetal acceleration in the
> accelerometers set the disk vertical so the accelerometer will be
> subjected to a cycle of Ga (0) ,  Ga minus- Ge (90),  Ga (180),  Ga plus
> Ge (270) in a sine wave fashion.  If we subtract the 0 and 180 degree
> values from the 90 and 270 degree positions we are left with a sine wave
> representative of  2 times the Ge value.  The maximum phase position is
> the angle of the Ge component.  The Ga value is an absolute calibration
> because we can measure rotation rate and positions to PPM levels.  The
> bearings are probably air spindles, in order to get below the 10 u in
> runout, which would show up as equivalent accelerations (G
> variations.)   It would be an interesting gadget.

Indeed!

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

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