PSN-L Email List Message
Subject: Simple pendulum response
From: Larry Cochrane lcochrane@..............
Date: Wed, 06 Dec 2006 01:50:18 -0800
Dr. Randall Peters asked me to forward the following message to the list.
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
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
Public Seismic Network Mailing List (PSN-L)
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