PSN-L Email List Message
Subject: Re: nature of the mesoscopic nonlinearity
From: Brett Nordgren Brett3mr@.............
Date: Sun, 10 Feb 2008 21:37:36 -0500
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
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."
At 09:14 AM 2/10/2008 -0500, you wrote:
> 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
>'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
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,
>back and forth. This is the basis for hysteresis--reason the term
> 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
>boundaries causes a rearrangement of the atoms (redistribution of the
>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
>(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
>If the stress levels become large enough, the defect structural
>much bigger, resulting in cracks and eventual fatigue failure. Truly,
>discussing is one of the most important and yet still mysterious of scientific
>phenomena. Its complexity has so far prohibited understanding of the
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