PSN-L Email List Message

Subject: Simple pendulum response
From: Larry Cochrane lcochrane@..............
Date: Wed, 06 Dec 2006 01:50:18 -0800

Hi Everyone,

Dr. Randall Peters asked me to forward the following message to the list.

Larry Cochrane
Redwood City, PSN

I've been following with interest the discussions concerning instrument 
characteristics.  Now that my schedule is easing somewhat, I felt that I should get 
involved.  Should it happen that any of you respond to these comments and don't hear 
back from me for a while, it's because I will be away for about a week to the Amer. 
Geophys. Union Fall Conference in San Francisco (starting 11 Dec.). There I will give 
a 15 minute oral presentation titled "State of the art Digital Seismograph" .  The 
abstract is posted at

The instrument which will be described (and also demonstrated at one of the booths) 
uses a "simple" compound pendulum with a natural frequency of 0.92 Hz.  It employs my 
fully differential capacitive detector as a displacement sensor (array form), with 
electronics based in Analog Devices' new award winning capacitance to digital 
converter integrated circuit (AD7745).  Kudo's to our own Larry Cochrane as the 
brains behind all of (i) the electronics hardware necessary to do the I2C logic 
operations required of the chip, and (ii) the software operating system in the form 
of WinSDR and WinQuake.

     For those of you who have been monitoring Larry’s instruments at
  you may have noticed two real-time helicord records generated by the 
single-pendulum instrument (N-S orientation) that he placed online.  The 
raw-data-train is lctst.gif, which has been high-pass filtered (corner frequency of 
10 mHz) before display.  The unfiltered waveform is available via download upon 
request from Larry.  This lctst is best suited to the real-time display of 
earthquakes local to the Redwood City, CA site.

      For registering teleseismic earthquakes real-time, Larry has also provided 
lctst1.gif, which is the numerical integration of lctst after first doing a high-pass 
filter.  This operation on the VolksMeter’s output provides a display similar to what 
is provided by ‘bandwidth extension’ using electronic means in other instruments such 
as geophones.

       I was pleased to see John Lahr provide links on his webpage describing (i) 
transfer function differences between velocity and position sensing, and (ii) 
discussion of the zero-length spring that was invented by physicist Lucien LaCoste in 
the early part of last century.

      There are some things that need seriously to be clarified concerning theory of 
seismometers, since there is so much confusion; not only among amateur seismologists, 
but also even many professional geoscientists.  Ultimately, the ONLY source of 
seismograph excitation (no matter the instrument design) is ENERGY.  Additionally, 
the ONLY thing that delivers energy to the seismometer is Earth’s ACCELERATION at the 
site of the instrument.  This is true not only for the instrument’s response to 
earthquake waves whose periods are shorter than about 300 s, but also for earth ‘hum’ 
in which the instrument responds mainly to tilt, when the periods are greater than 
about 300 to 1000 s.

Keep in mind that it is very difficult to see a 300 to 1000 s periodic signal with a 
velocity sensor.  It is equivalent to trying to look at a very low frequency signal 
with an oscilloscope using a.c. coupling.  Only d.c. coupling (position sensing) is 
appropriate in this case.

        There is a dramatic difference between the forcing functions of tilt as 
contrasted with horizontal ground acceleration. The tilt response is independent of 
frequency, whereas the response to earthquakes (horizontal acceleration devoid of 
significant eigenmode oscillatory components) is the classic response given by John 
Lahr at the following website:

    If you look at John’s six transfer function plots provided at
it is the right-most pair (response to acceleration) that ‘summarize the physics’ of 
how a seismometer operates.  Yes, one can configure an instrument to plot data 
according to any one of the six possibilities John has indicated, but the response to 
acceleration is what ‘tells the story’ of performance.  For frequencies above the 
natural frequency of the pendulum, a velocity sensor will always outperform a 
velocity sensor.  On the other hand, for frequencies below the natural frequency, a 
position sensor will always outperform a velocity sensor (all things otherwise 

      I don’t know about you, but I’m not particularly interested in frequencies 
above 1 Hz.  Our Volksmeter easily picks up dynamite blasts and other local 
disturbances that are nearly always manmade.  Because the earth is so large, motions 
it exhibits in response to dynamic changes (earthquakes, tidal forces, ….) are at low 
frequencies (not high).

       At low frequencies where everybody seems increasingly interested in going 
(reason for bandwidth extension) there is no question of the superiority of position 
sensing over velocity sensing.  Why this obvious fact is so muddled in the minds of 
so many is a great mystery to me.  Maybe it’s because even classical physics is 
difficult for most everybody to understand.

      I have placed a paper on my webpage which speaks to this matter, titled 
‘Seismometer design based on a simple theory of instrument-generated noise equivalent 

       For those of you who want to ‘escape the rut’ of velocity detection that has 
held folks captive for way too long—Larry and my other business partner, Les LaZar 
are positioned to provide you with reasonably-priced essential components to build 
your own version of the VolksMeter.  Probably most of you will prefer to do this 
rather than pay the present $1000 ‘turnkey’ price for our single-pendulum instrument.

     I want to point out something that is the result of recently discovered 
physics—why small-mass instruments don’t perform well.  Although conventional wisdom 
says that it’s because of Brownian motion (larger for smaller masses), this is not 
really the culprit.  The performance limitation is really the result of internal 
friction problems that science is only beginning to understand.  The smaller the 
seismic mass, the smaller the spring that supports it.  The smaller the spring, the 
more significant is the internal friction associated with the ‘snap, crackle, pop’ of 
defect structural changes in the spring (processes that operate at the mesoscale). 
For decades we’ve recognized the all-important properties of defects in 
semiconductors (basis for p and n material of which devices are made), but until 
recently very little was understood concerning the importance of defects to internal 
friction that regulates the low-frequency performance of seismometers.

      The influence of defects is worse in instruments with springs than in those 
that use a pendulum, which is more inherently stable.  Until better electronics came 
along, we were stuck with trying to improve low-frequency performance by going to 
lower natural frequencies of the mechanical oscillator.  That is no longer the only 
viable solution.  Although the pendulum lost favor years ago, it is making a 
comeback.  The success of the Shackleford-Gunderson approach should have been a cue 
to many that the pendulum needed to be revisited.  With the digital electronics of 
the AD7745 there are some advantages that did not exist when the S-G instrument was 
developed around its analog circuitry.  For example, the noise of the Volksmeter 
electronics does not increase as rapidly with frequency-decrease as is true of analog 
circuitry (commercial standard in seismometry being synchronous detection).

Dr. Randall Peters


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