Randall and Chris,

Sorry to be slow in responding to your messages, but you and Chris have 
given me much to think about and it's going to take a few days more of 
thinking to digest it all.

One open issue that I would like to get pinned down is getting a rough idea 
of how large these effects are relative to the overall spring forces.  I 
think that Chris had implied that they could be of the same order of 
magnitude, which I am finding very hard to visualize.  Also in his message 
today I think he was implying that the spring can undergo steplike changes 
which contain high frequency components.  If too large, they could be 
deadly--see centering discussion below.  In particular I am mainly 
interested in the effects which will occur with the spring under constant 
tension--not moving significantly.

I find that I need to try to separate the fundamental spring-noise issues 
which will always be present from ones that can be addressed by 
manufacturing and design techniques such as limiting spring stress, ageing, 
heat cycling, material choice, etc.  For example, I'd heard stories of 
leaf-spring designs that popped and crackled when they were first assembled 
and which then, over time, would quiet down to an acceptable noise 
level.  However a noise process that is fundamental and always present 
would be of greater concern.  As an engineer, creep itself does not concern 
me, so long as it is acceptably slow and not too noisy.  Being able to 
quantify what one might expect to see would be helpful in trying to design 
something.

New subject: Both you and Chris had previously written of the idea of using 
feedback to help maintain instrument centering.  I came up with the 
following, which if correct has some interesting implications.

"The goal of maintaining centering by the use of feedback can be restated 
as the goal of using feedback to make the instrument insensitive to the 
unwanted 'noise' forces which would tend to push it off center.

When trying to do this, however, a problem unfortunately arises of the 'no 
free lunch' class, which in fact has nothing directly to do with feedback. 
The (vertical) instrument simply can't distinguish where an input force is 
coming from.  Is it from the spring getting weaker as the temperature 
rises, from buoyancy-force changes with the barometer, from spring creep or 
is it the acceleration-related force from the very low frequency geological 
signal you wanted to observe?  To the extent that you succeed in reducing 
the instrument's sensitivity to the 'noise' forces you also reduce its 
sensitivity to the signal force.  This can be restated as the well accepted 
generalization:  'feedback does not affect the signal to noise ratio'. 
(assuming, of course, that the added feedback components are noise free)

However there is one hope.  If you can assign F as a frequency below which 
you will not be looking for signals, you can say that anything changing at 
rates significantly below F, is noise.  This in turn allows you to roll off 
the instrument sensitivity to forces having frequencies below F and to some 
extent favor signal over more slowly-varying noise.

I am confident that is the reason why commercial instruments aren't 
designed to have large responses to acceleration/force down to very low 
frequencies.  Instead they are designed to establish a compromise between 
letting through sufficiently low-frequency seismic signals to be useful, 
while at the same time resisting the much larger, though more slowly 
changing, instrument 'noise' forces.  That may also explain why so much 
effort has to go into reducing the noise generators at their source, by 
using exotic alloys in leaf spring suspensions, maintaining constant 
(usually low) ambient pressure, and attempting to maintain the temperature 
as constant as possible, etc."

Brett

At 09:14 AM 2/10/2008 -0500, you wrote:
>Brett,
>     I've been able now to give enough thought to your comments about 
> "potholes" to
>provide the following response.
>Chris 'hit the nail on the head' with his statement "... to cope with 
>discrete steps in
>the zero level".  In other words, if the term is at all appropriate, it is 
>not your
>'average' pothole as found in northern climate highways where temperatures 
>are at times
>routinely below freezing.  The 'potholes of seismic type' are 'diffusive' 
>in terms of
>both temperature and stress.
>     There is a paper of mine at http://arxiv.org/html/physics/0307016
>titled "Harmonic oscillator potential to describe internal 
>dissipation".  As discussed
>there, the potential function is not fixed.  As the seismometer mass moves 
>back and
>forth,

Actually in a force-balance instrument the mass does very little moving, 
which should be an advantage.  You are trading physical movement of the 
spring-mass for electrical 'movement' in the feedback elements.

>the equilibrium position, to which it would go if motion were suppressed, 
>shifts
>back and forth.  This is the basis for hysteresis--reason the term 
>'hysteretic damping'
>is appropriate.
>     The problem with this hysteresis is that the mesoanelastic steps 
> associated with it
>are not themselves fixed.

Can the amplitude distribution of these steps be predicted?

>My study of creep mentioned earlier is proof positive of that
>fact.  What happens is the strain energy that accumulates at 
>polycrystalline grain
>boundaries causes a rearrangement of the atoms (redistribution of the 
>defect structures)
>when various thresholds are exceeded.  Such is the nature of 
>work-hardening.  In primary
>creep (exponential variation), the material is trying to arrest the 
>changes brought about
>by the external forcing.  'Success' in so doing results in a conversion to 
>secondary
>(linear variation) creep.  If the temperature were zero--end of 
>story.  But temperature
>serves to undo the hardening and so a 'balance' results between hardening 
>and softening.
>If the stress levels become large enough, the defect structural 
>reorganizations become
>much bigger, resulting in cracks and eventual fatigue failure.  Truly, 
>what I'm
>discussing is one of the most important and yet still mysterious of scientific
>phenomena.  Its complexity has so far prohibited  understanding of the 
>processes from
>first principles.



>      Randall


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