Hi Geoff,

At 10:34 AM 7/11/2012, you wrote:
>On 2012-07-01 12:48, Brett Nordgren wrote:
>>Hello Geoff,
>>
>>Yes, lots of  ETC.  I'll give it try.
>>
>>I guess that anything might be possible, but in general, no.  If you
>>could, its data would not be very useful scientifically.  Ground
>>oscillations have both an amplitude and a 3-d direction (which can vary
>>a lot from minute to minute).  An omni sensor would tell you the
>>amplitude, but nothing about vibration direction, which is frequently
>>not related to wavefront arrival direction.  You would need both
>>vibration amplitude and direction to make most scientifically useful
>>measurements, which you could get only if you had x, y and z recordings.
>
>Isn't First Time of arrival important to tomography ?
>To the average velocity of the various phases ?

Yes, you're quite right.  I may have generalized too much.  For 
measurements where you are only looking for arrival times, it should 
work fine.  I'm not very conversant with tomography, but in the few 
papers I've read, the mathematics generally seem to require all three 
ground motion components.

>>For amateur work, a single vertical will probably give the best results,
>>since background noise in the vertical direction is much lower,
>>especially at amateur sites.  And you really don't miss that much by
>>ignoring the horizontal.  Nearly everything except the LQ phase usually
>>contains at least some vertical motion.  You could simulate an omni
>>instrument by combining x y and z channels from three instruments (hard
>>to do properly with voltage signals, but easy mathematically on their
>>data).  But the additional noise you'd add from the horizontal channels
>>would make it harder to see weak quakes than with the vertical alone.
>>However, I know good verticals aren't that easy to make.
>
>I saw a device at Arizona State University which could measure
>three components of velocity using only two inverted pendulums
>at possibly a 45 degree angle to the vertical pointing N/s and E/w.
>It was all open for everyone to see how it worked. located
>at the physics building.

If you ever find a Web reference for that, I'd be interested.

>Possibly you know who built the device or what
>it real name would be ?

Theoretically it should require three pendulums.  The problem is, I 
think, that although it would detect motion along all three axes, you 
could not separate what you saw on the two channels, unambiguously, 
into N, E, and Z motions.  It's trying to solve for three variables 
when you only have two equations.

You can actually do the algebra, if I understand the setup you were describing:

Assume ground motion components N, E and Z, in the three 
perpendicular directions.
We can observe the motions of two 45 degree inverted pendulums having 
horizontal pivots in the E-W and N-S directions, whose motions we 
will respectively call Pn and Pe.
For simplicity let us define the constant 'Q' as 1/sqrt(2).

 From the geometry  Pe = Q(E-Z)  and Pn = Q(N-Z)

Here we have three independent variables N,E, and Z but just two 
equations.  Knowing only Pe and Pn, there are an infinite number of 
combinations of N, E, and Z which will satisfy them.  That's the basic problem.
See: 
http://en.wikipedia.org/wiki/System_of_linear_equations#Describing_the_solution

If you add a third pendulum you can do the job, with the most common 
approach being the Galperin or symmetrical-triaxial configuration 
that is used in many modern instruments.  Using one, and comparing 
the N and E signals with the Z is how we have been able to observe 
that the horizontal noise is usually ten times (or more) greater than 
the vertical at Dave's site.  It is interesting to note that the 
Metrozet m2166, replacement for the STS-1, uses a vertical instrument 
along with two horizontals, and is not a Galperin.
http://metrozet.com/products_m2166-vbb.html

>I have not seen such a device on the internet
>and am sure other designs exist which are
>not being talked about.

My sense is that if anyone had any major improvement, they would 
definitely be talking about it.

>I should imagine math or special circuits
>are needed to extract the vertical
>from the two sensors.

I'm, afraid it would take Harry Potter to do that.  Only magic could 
work when algebra doesn't.

Regards,
Brett


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