PSN-L Email List Message

Subject: Re: nature of the mesoscopic nonlinearity
From: ChrisAtUpw@.......
Date: Sun, 10 Feb 2008 23:45:35 EST


In a message dated 11/02/2008, Brett3mr@............. writes:

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.  
Hi Brett,
 
    You have to make a spring arrangement such that it  exactly balances the 
mass, but has a very slow rate of change of force with  position, a few % at 
most. Hence the somewhat exotic spring arrangements used in  seismometers.

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.
    Hooke's Law is only an approximation. You get a  time dependant component 
and creep. The creep is noisy and also time dependant.  The changes tend to 
be steps in the characteristic and these decrease with time  after the load is 
applied. New steps may be excited by quakes. The step changes  can give 
problems with velocity feedback circuits - they tend to generate  spikes.

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.   
All common / practical spring materials are like  this. You have the 
electronic noise, the thermal noise of the sensor itself, the  hysteretic noise and 
the background seismic noise.

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)
    Yes you can. You can either re-zero mechanically  with a small motor to 
keep the system in range or use an integrated signal as  force feedback. If you 
integrate the output to say 500 seconds for a 50 second  period instrument, 
you can keep the mean position centred without significantly  effecting the 50 
second response. This will take out most drifts. With  a velocity output, the 
very long period signals are small.

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."


See Wielandt's references on psn for  feedback seismometer design. 
Seismometers are usually designed to give a  velocity law output directly using quite 
complicated feedback loops - this is  'traditional'. High sensitivity 
seismometers usually have periods between 60 and  120 seconds and this covers most 
surface wave periods of maybe 15 to 40 seconds.  A few types go to 360 seconds. To 
cover all the Earth Eigenmodes, you have to go  to about 2,000 seconds. 
 
    Regards,
 
    Chris Chapman



   





In a message dated 11/02/2008, Brett3mr@............. writes:
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>Randall=20 and Chris,

Sorry to be slow in responding to your messages, but you= and=20 Chris have given me much to think about and it's going to take a few days=20= more=20 of thinking to digest it all.

One open issue that I would like to g= et=20 pinned down is getting a rough idea of how large these effects are relativ= e to=20 the overall spring forces.  I think that Chris had implied that they=20 could be of the same order of magnitude, which I am finding very hard to=20 visualize. 
Hi Brett,
 
    You have to make a spring arrangement such that= it=20 exactly balances the mass, but has a very slow rate of change of force with=20 position, a few % at most. Hence the somewhat exotic spring arrangements use= d in=20 seismometers.
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>Also in=20 his message today I think he was implying that the spring can undergo step= like=20 changes
which contain high frequency components.  If too large, t= hey=20 could be deadly--see centering discussion below.  In particular I am=20 mainly interested in the effects which will occur with the spring under=20 constant tension--not moving significantly.
    Hooke's Law is only an approximation. You get a= =20 time dependant component and creep. The creep is noisy and also time dependa= nt.=20 The changes tend to be steps in the characteristic and these decrease with t= ime=20 after the load is applied. New steps may be excited by quakes. The step chan= ges=20 can give problems with velocity feedback circuits - they tend to generate=20 spikes.
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>I find=20 that I need to try to separate the fundamental spring-noise issues which w= ill=20 always be present from ones that can be addressed by manufacturing and des= ign=20 techniques such as limiting spring stress, ageing, heat cycling, material=20 choice, etc.  For example, I'd heard stories of leaf-spring designs t= hat=20 popped and crackled when they were first assembled and which then, over ti= me,=20 would quiet down to an acceptable noise level.  However a noise proce= ss=20 that is fundamental and always present would be of greater concern. =20
    All common / practical spring materials are lik= e=20 this. You have the electronic noise, the thermal noise of the sensor itself,= the=20 hysteretic noise and the background seismic noise.
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>As an=20 engineer, creep itself does not concern me, so long as it is acceptably sl= ow=20 and not too noisy.  Being able to quantify what one might expect to s= ee=20 would be helpful in trying to design
something.

New subject: Bo= th=20 you and Chris had previously written of the idea of using feedback to help= =20 maintain instrument centering.  I came up with the following, which i= f=20 correct has some interesting implications.

"The goal of maintaining= =20 centering by the use of feedback can be restated as the goal of using feed= back=20 to make the instrument insensitive to the unwanted 'noise' forces which wo= uld=20 tend to push it off center.

When trying to do this, however, a prob= lem=20 unfortunately arises of the 'no free lunch' class, which in fact has nothi= ng=20 directly to do with feedback. The (vertical) instrument simply can't=20 distinguish where an input force is coming from.  Is it from the spri= ng=20 getting weaker as the temperature rises, from buoyancy-force changes with=20= the=20 barometer, from spring creep or is it the acceleration-related force from=20= the=20 very low frequency geological signal you wanted to observe?  To the=20 extent that you succeed in reducing the instrument's sensitivity to the=20 'noise' forces you also reduce its sensitivity to the signal force. =20= This=20 can be restated as the well accepted generalization:  'feedback does=20= not=20 affect the signal to noise ratio'. (assuming, of course, that the added=20 feedback components are noise free)
    Yes you can. You can either re-zero mechanicall= y=20 with a small motor to keep the system in range or use an integrated signal a= s=20 force feedback. If you integrate the output to say 500 seconds for a 50 seco= nd=20 period instrument, you can keep the mean position centred without significan= tly=20 effecting the 50 second response. This will take out most drifts.=20= With=20 a velocity output, the very long period signals are small.
<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>I am=20 confident that is the reason why commercial instruments aren't designed to= =20 have large responses to acceleration / force down to very low=20 frequencies.  Instead they are designed to establish a compromise bet= ween=20 letting through sufficiently low-frequency seismic signals to be useful, w= hile=20 at the same time resisting the much larger, though more slowly changing,=20 instrument 'noise' forces.  That may also explain why so much effort=20= has=20 to go into reducing the noise generators at their source, by using exotic=20 alloys in leaf spring suspensions, maintaining constant
(usually low)=20 ambient pressure, and attempting to maintain the temperature as constant a= s=20 possible, etc."
    See Wielandt's references on psn for=20 feedback seismometer design. Seismometers are usually designed to give=20= a=20 velocity law output directly using quite complicated feedback loops - this i= s=20 'traditional'. High sensitivity seismometers usually have periods between 60= and=20 120 seconds and this covers most surface wave periods of maybe 15 to 40 seco= nds.=20 A few types go to 360 seconds. To cover all the Earth Eigenmodes, you have t= o go=20 to about 2,000 seconds. 
 
    Regards,
 
    Chris Chapman

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