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Subject: tuned-compound-pendulum teleseismic earthquake detector
From: Randall Peters PETERS_RD@..........
Date: Thu, 27 Mar 2008 12:42:35 -0400

For reason of the recent discussions of a long-period pendulum whose
physical length is short--some may find the following worth considering:

    I am preparing to write a tutorial on pendulums for the Bulletin of
the Seismological Society of America (a BSSA special edition publication
concerned with rotation).  In preparation for that article I have been
simulating compound pendulums and verified a 'hunch' that I have had for
some time.
    If you want a really sensitive teleseismic earthquake detector, then
consider the following design.  The part hanging below the axis can be a
uniform rigid rod of length 50 cm.  Very close to the axis and supported
just above it, you place a compact, nearly-point-mass that is roughly
ten times heavier than the rod.  The friction associated with both the
(i) axis and (ii) material used, responsible for internal friction
damping--needs to be small, so that the quality factor Q is as large as
     A small mass whose position on the rod is adjustable--allows the
instrument's period to be set at 20 s.  For the times 10 ratio
indicated, the center-of-gravity of this upper mass needs to be about
2.4 cm above the axis.
    The sensitivity to ground displacement of this instrument is for
high frequency motions (localized earth noises with periods less than 20
s) only 1% of the displacement sensitivity of a simple pendulum of the
same 20-s period (having a length of 99 m!)  As compared to a near
critically damped simple pendulum (customarily Q = 0.8) having this same
period, the compound instrument that I'm describing would have the same
sensitivity at 20-s as the simple pendulum-- if  Q = 100.  (Only time
will tell if a Q this large is reasonably attainable.)
    The compact tuned instrument would have some properties that are
even better than the 99 m simple pendulum-- because it is much less
responsive to high frequency, localized (man-made) earth noises (such as
the daily trains that disturb our VolksMeter here at Mercer University).

    There are those who will dismiss my idea summarily, because 'it is
well known' that the only useful seismograph is one whose transient
response is eliminated by damping.  This antiquated view is one that
derives from a 'rut of thinking' that is restricted to the time domain.
Even amateurs now routinely generate spectra, since Amaseis and WinQuake
provide that capability.  One can easily correct a spectrum (through
knowledge of the transfer function that accounts for Q), to obtain the
power spectral density (where PSD data is in the frequency domain).  The
otherwise troublesome 'resonance' peak at 20 s disappears by this means,
and information concerning the earthquake is then readily visible.  If
one generates the cumulative spectral power by integrating over the PSD,
then from this CSP, evolutionary features of the earth's motion before,
during and after the earthquake--become readily visible from data that
was generated with a sensitive, bastardized instrument.
      It should be further noted that for periods longer than 20 s,
there is no difference in acceleration sensitivity between the compound
instrument and the simple pendulum 200 times longer.  In other words,
they are equally sensitive when it comes to recording earth hum.  To
observe motions at these very low frequencies, a displacement (rather
than velocity) sensor is necessary.

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