Angel,

Regarding your question about adding a displacement detector and 
feedback to a geophone to make a broadband sensor: Back in May I
went into some detail in discussing this, so I have re-compiled the
material and edited it to the point in question.
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I have been experimenting for several years with making almost any 
seismometer into a VBB sensor if the physical parameters are suitable, 
like the coil resistance. THe largest is a WWNSS LP (15 second T0 and
11 kg mass) vertical that I am running at 600 seconds.

I have been experimenting for about two years with making the 4.5 hz HS-1
(by Geospace, but similar to the GSC-11d and the Mark Products L-15B)
into a broadband instrument. I use the VRDT displacement sensor mounted 
externally above the case, with the sensing vane attached to the upper 
mass ring.  With VBB parameters set for 20 seconds and the proper coil 
resistance, the VBB output is 750 volts/meter/second and the calibrations 
fit the transfer functions. 

But the data is to noisy for a sensitive broadband sensor, and I am usually 
barely able to see an elevated 6-second microseism background of 1 to 2 
microns/second. Of course these were very clear (~10x) when hurricane 
Bonnie passed last August. I also made a nice record  (from St. Louis)
of the Ohio quake in September, with peak velocities of Lg of about 10 
microns/second at about 8 seconds.

The trouble with the 4.5hz phone is that the mass is only 23 grams, and
the intrinsic damping of 0.28 means that the Q is not very high. 
From the Riedesel paper this would be expected to have a Brownian noise 
power spectral density (PSD) level of about -165db (figure 12). (For 
reference, the USGS low noise model has the 6-second microseism peak 
at about -140db, the 12-second peak at -160db, and the quiet earth minimum 
between 40 and 200 seconds is about -185 db.) But the Brownian noise 
is only one of many noise sources; the circular suspension leaf springs 
and the fine-wire signal output leads are significant contributors.
The Reidesel paper finds that when using the velocity signal coil and
a properly selected amplifier, the noise level is -130db at 1 hz, and
the 6-second microseisms cannot be seen. We could do much better with 
a VBB fedback configuration.

Initial tests with a fedback geophone were encouraging in this direction.
The PSD of several noise samples was about -145db at 6 seconds, but 
levels off at about -155db at 10 seconds. It has trouble recording
teleseisms compared with a larger VBB seis, like a Mb5.O west of Mexico 
or a 6.2 in China, where the 20-second surface waves were only about
2X the noise. It did make a reasonable record of a Ms 6.0 in the Queen
Charlotte Islands (51N,130W).

Other problems are with the thermal sensitivity of the mass position and
suspension resonances within the high-frequency portion of the VBB
passband. THe manufacturers are mum on these; the most notorious are
the resonances of the 1-hz L4-C at 16 and 22 hz. The mass position change
with temperature is a "don't care" for a velocity sensor, but it causes 
problems with a displacement output of 250 millivolts/micron, even with
reasonable VBB loop gains.

The Brownian noise is only one of many noise sources; the circular 
suspension leaf springs and the fine-wire signal output leads are 
significant contributors that can raise the noise level by as much as
100 to 1000 times the theoretical calculation of the Brownian noise.

We have to properly understand the value that is obtained (in both
Riedesel and Melton: references below for the curious reader) for 
the PSD (Power Spectral Density) of the Brownian noise. The equation 
simply describes the ideal thermal noise imparted to an isolated mass 
levitated in a standard atmosphere by a suspension that controls the 
period and where motion is limited by a dissipative damping system. 

Note that it says nothing about the noise caused by the physical
components of the geophone. The mass of a seismometer is always in
motion, even under the quietest conditions. This causes the suspension
members to flex, and when non-linearities of the suspension forces are 
of the order of the forces of earth accelerations applied to the mass, 
noise results. For example, if the microseism background causes an 
acceleration of one nano-g (10^-9), which is applied to a mass of 0.023kg, 
(in the 4.5 hz geophone), F=M*A, and a force of 2.3 x 10^-11 Newtons is 
applied to the suspension. This is very small compared with the force
supporting the mass (F=0.023kg*g= 0.225N), but the suspension still 
has to flex in a linear fashion to produce an undistorted velocity 
output. But simple suspensions, such as the etched leaf springs of a 
geophone, are never intended to be linear at these force levels, so 
micro-bending and warping, along with hysteresis and edge contact effects, 
result in fairly broadband noise.  Obvously, a larger mass will overcome
these effects proportionately.

This is why very compact but very high quality flexures are used for
low noise sensors. A straight flat flexure clearly  has a simple and
well defined bending pattern compared to the etched spiral leaf spring
of a geophone. Its support or contact points are very well constrained,
compared to the circularly clamping rings of a geophone. A linear hinge
results in linear mass motion, compared to the small rotation caused
by the circular leaf spring. THe epitome of compact self-contained
rotational flexures are the pricy "Bendix" devices.

The other noise source is the fine wire leads for the signal, calibration,
and displacement data. In a common geophone, these are fine coils or
"pig-tails" run from the moving coil to terminals on the case. In some
geophones, the mass, which is usually a brass ring that the coils are
wound on, is split by an epoxy ring, and the leaf-spring suspensions at 
each end carry the signal to insulated shims that anchor the case ends
of the springs. I have found that if the coils are long enough so that
they touch themselves, the broadband noise is over 20x of when the coils
are stretched so that even successive loops don't touch. And having a
calibration coil doubles the number of "pig-tails" making noise, but I
need one to verify the response, which I have done with the 4.5hz-VBB.

My latest efforts to try to try to reduce the mechanical self noise 
were only marginally successful . In the data from the Mw 7.1 Monday 
May 10 in New Britain, P.N.G., the 4-second p-wave was about 4x the noise 
level at about 20 microns/second, but the 20-second surface waves were less 
than 2x the noise. A plot of the the PSD of the noise of the sensor shows a 
relatively flat level of about -130db to -140db from 3 to about 20 seconds
where the flat response rolls off; I don't have any higher frequency data. 
Of course, this is all the mid-day noise of the sensor in the basement 
10m from the street, including thermal and barometric noise. 

Other problems remain: the thermal sensitivity of the mass position (about
4 microns/degree C, dropping with increasing temperature). The mass position 
change with temperature is a "don't care" for a velocity sensor, but it 
causes problems with a displacement output of 250 millivolts/micron, even 
with reasonable VBB loop gains. I use a precision potentiometer to re-balance 
the sensing bridge over a range of 30 microns (about 600 microns with the
feedback on), but this pot adds noise.

____________________________________________________________

A digression for those unfamiliar with the expression:

Brownian noise: 	PSD = (8*pi*k*T)/(M*P*Q)

	where T is the temperature in Kelvins, M is the mass in kg, P is
	the period in seconds, and Q is the inverse of the damping (lambda)

For example, for the L-4C, M = 1 kg, P = 1 second, and Q is set to 1 ,;
T = 300 (room temperature) and k = 1.38*10^-23.
Cranking out the numbers gives a PSD for the L4-C of 10^-19.
If we substitute the values for the 4.5hz phone, M = 0.023 and 
P = 0.222, the ratio is 198, so the noise is about 2*10*-17


Some assorted references regarding seismometers and noise:

"Limits of Sensitivity of Inertial Seismometers with
Velocity Transducers and Electronic Amplifiers";
by Mark A Riedesel, R.D.Moore, and J.A.Orcutt; Bulletin of
the Seismological Society of America, Vol. 80, No. 6, December 1990.

"The Sensitivity and Dynamic Range of Inertial Seismographs";
by Ben S. Melton; Reviews of Geophysics and Space Physics, 
Vol 14, No. 1; February 1976; C. American Geophysical Union.

"The Design of Miniature Wideband Seismometers" by M.J.Usher,
C. Guralp, and R.F. Bursch; Geophysical Journal of the Royal
Astronomical Society, vol 55; 1978.

"Observations and Modeling of Seismic Background Noise", by
Jon Peterson; USGS open file report 93-322, Albuquerque, NM, 1993.

A Direct Method for Calculating Instrument Noise Levels in 
Side-by-Side Seismometer Evaluations", by L. Gary Holcomb,
USGS open-file report 89-214, Albuquerque, NM, 1989

A Numerical Study of Some Potential Sources of Error in
Side-by-Side Seismometer Evaluations, by L. Gary Holcomb,
USGS open-file report #90-preprint, Albuquerque, NM, 1990.
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The 6.0 and aftershocks in the CA/NV border region on May 20 gave everyone
some nice data. THe S-TM here, recording on the drum, shows a very nicely
dispersed surface wave with periods starting at about 40 seconds. THe 
later 7.0 at P.N.G. showed several hours of surface waves. The experimental 
VBB geophone showed the 20-second surface waves, but only at about 4x the 
noise of 3,5 microns/second. The concurrent pre-event microseisms from
the 90-second S-TM were running about 0.24 microns/second, showing clean 
sine waves with the noise below the least count of my digitizer of 0.1 
millivolt, which at 4200 V/m/sec, is about 24 nanometers/second. I do not
think that a VBB instrument is worth considering unless it clearly shows
the 6-second microseism background.

Regarding the mechanical self noise question of the small geophone. As 
I mentioned, this is the essentially broadband noise, of interest here 
in the range from 100 seconds to 100 hz, that is caused by the earths' 
background noise, mostly the 6-second microseisms, (but also from random
motion caused by the Brownian thermal noise), moving the suspension 
and wiring components of the seismometer and causing non-linear motion of
the mechanical suspensions. If we dunked the seis in liquid helium to
kill the thermal noise, or evacuated it, and/or made a quartz fiber
suspension so the Q would be 1000 (damping = zilch), this noise would still
be present. The great art of sensor design has focussed on how to allow
the mass to move within the frame without the springs, hinges, and wires
producing nonlinear forces that are position dependent. Successful designs
are very simple, with minimal surface contacts, relatively small hinges
or flexures, etc, all of which make them quite fragile. A geophone, however,
is mostly the opposite, with the design focussed on robustness and high
intrinsic damping (of .3 to .6) that limits the mass excursions in handling.

So thermal noise and mechanical noise are not the same, and while a
theoretical number can be placed on the Brownian thermal noise, only
experimentation can characterize the mechanical noise caused by 
micropositioning of the moving elements of a seismometer. And the data
so far indicate that  a geophone is not a promising candidate for a
sensitive broadband sensor. Feedback can be used to broaden the response,
but it will be sensitive only to larger local and teleseismic events.

Regards,
Sean-THomas

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