From Dr. Randall Peters....

There is this myth that the only way to see teleseismic events is by working with a 
long period instrument in which the characteristics are governed by force feedback. 
  Why the myth has persisted for so long remains a mystery to me, as I now explain.

	The response of a seismometer involves the convolution of two parts: (i) the 
mechanical, and (ii) the electronics.  When electronics wasn’t very good, the obvious 
thing to do was ‘wring every ounce’ of performance out of the mechanical parts.  Now 
that the electronics is much better understood than the mechanical characteristics 
(because of complex internal friction—concerning which I am an internationally 
recognized expert), a paradigm shift is called for.  It’s not an easy shift for 
people who are steeped in the tradition that has ruled now for many decades.

	The LaCoste spring instrument was an example of a major mechanical improvement over 
previous vertical seismometer designs.  Before the use of capacitive sensors, force 
feedback was not employed, since the Faraday law (velocity) detectors that were 
employed, still functioned well over a large mechanical range.  All that changed with 
the introduction of gap-varying capacitive sensors.  Their mechanical range is so 
small that force balance became necessary.

	I see force balance as something of a mix of better electronics, but having 
mechanical properties not much better than the situation before LaCoste’s 
contribution.  Force-balance has been built around fairly-early-generation solid 
state, analog electronics (now more than twenty years old).  The mix has yielded an 
outstanding but complicated (expensive) instrument for earthquake detection.  When it 
comes to frequencies below about 10 mHz, however, I predict that the Volksmeter that 
Larry has online (having a period of about 1 s and no feedback whatsoever) will 
outperform the $50K instruments, when it comes to the matter of studying low 
frequency earth motions.  (In a later note I will explain why the response of 
conventional force-balance instruments below their lower corner frequency is a 
disaster.  It’s tantamount to operating an oscilloscope in the a.c. coupled mode, 
when d.c. coupling is called for.)

	The Volksmeter (VM) doesn’t need feedback  This designer doesn’t even want to ever 
consider feedback!  Yes, feedback would improve the appearance of teleseismic surface 
waves in the VM raw data displayed by the helicord being generated by Larry Cochrane. 
  But it is not necessary.  Once a teleseismic event has been observed above noise in 
the helicord (if not observed, it probably would not have been readily seen even with 
feedback), it is a simple matter with the WinQuake software to ‘present that 
earthquake’ to the world in the form with which the world is accustomed to ‘viewing 
earthquake records’.  All that is necessary, after having downloaded the pertinent 
segment, is to (i) do a high pass filter whose cutoff is just below the lowest 
frequency component of the surface waves, and then (ii) integrate the filtered 
result, using Larry’s “I” button.  What is immediately displayed is a nearly ‘flat to 
velocity’ record, the display choice to which seismology became long ago addicted 
(apparently in large measure because of Faraday law detectors).

	I just heard from Larry today that he is planning to provide a channel in addition 
to lctst, which is the output from our displacement (d.c. position) detector, whose 
attenuation is proportional to frequency squared below about 1 Hz).  This new channel 
will be a filtered/integrated output of the lctst signal; i.e., a ‘velocity’ output. 
  With it, teleseismic events should be more readily observed, whereas the 
still-present ‘mother signal’ lctst will still be available as a superior channel for 
purpose of local, higher frequency events.  Thus we will have something very similar 
to the two channels of lc8 and lc3—output from Larry’s Shackelford-Gunderson (SG) 
seismometer.  Though it was many years ago, the amateur messrs S & G were ‘right on 
target’ with their approach—using an ordinary pendulum with the best electronics 
available to them at the time.

	The reason this simple filter/integrate operation works so surprisingly well (nearly 
as good as force balance at a very, very small fraction of the cost and complexity) 
has to do with the nature of the Volksmeter’s (i) pendulum, and (ii) sensor.  Insofar 
as the viscous damped, driven harmonic oscillator as an approximation to the behavior 
of a seismometer is concerned, the pendulum is the best candidate having some chance 
of being adequately described by it (the model everybody uses, even for the many 
cases where it is inappropriate).

	When the frequency of drive is below the natural frequency of the pendulum (which 
for the VM is eddy-current damped near critical using a rare earth magnet 
sub-assembly), the transfer functions falls off as frequency squared.  (Velocity 
detectors below their lower corner fall off even faster, as frequency cubed, 
expressed relative to displacement).  The quadratic in frequency falloff of the VM in 
this region, means that the signal for teleseismic surface waves corresponds to what 
is called ‘acceleration response’.  Actually, every seismometer responds only to 
acceleration and NOTHING else.  ( I will address this in a later note—even plan to 
write an article titled “Seismometer physics for dummies”.)

	Because the VM sensor output is one of position, the integral of the teleseismic 
filtered signal is a decent approximation to ground velocity.  I have satisfied 
myself concerning this approximation by looking at the Fiji Islands earthquake and 
comparing the integration result against artifacts that were shown by modeling to be 
possible, due to transients.  For those who should employ this ‘trick’, keep in mind 
that the spectral components way below periods of about 15 s (which are present in 
the VM output if not high-pass filtered) can generate huge artifacts.  Also, before 
doing Larry’s FFT, which does not use apodization (such as a Hanning window, for 
which I am glad), a high pass filter is necessary before the spectrum is meaningful.

	I am pleased with what I’ve seen in this method, and to make the earthquake signal 
comply more perfectly with signals generated by the Global Seismographic Network’s 
broadband $50 K instruments -- would require a deconvolution based on the FFT.  I 
doubt that anybody is interested in ‘going there’.

	I need to point out something concerning the ‘drift’, as some might label the 
secular component of the output from the VM.  Yes, this can result largely from 
electronics instability, due to the thermal coefficient of the AD774x .  But don’t be 
too hasty to pigeon-hole everything into that category.  Operated in a reasonably 
isothermal environment, these slowly changing features are the basis for the very 
(earth-related) dynamics for which the VM will shine. For those interested only in 
earthquakes, this secular trend can be easily removed with a simple recursive filter, 
as Larry already does before posting lctst on seismicnet.  In my planned ‘dummies’ 
article I will try to help people understand, on the basis of the simple RC network, 
the infinite impulse response filters (esoteric world of digital signal processing 
(DSP), based on the formidable Z-transform—a discrete form of the Laplace transform, 
with which all electrical engineers are trained; which is more general (but less 
numerically powerful) than the Fourier transform, with which all physicists are 
trained—last one being the basis for the remarkable ‘fast version’ FFT, wonderfully 
embedded within Larry’s Winquake)

	The transfer function of the pendulum has no frequency dependence whatsoever when it 
comes to one of the two forms of acceleration to which it responds—that of tilt. Tilt 
acceleration is nothing other than the component of the earth’s field that is 
perpendicular to the direction in which an object falls.  Einstein’s famous theories 
of relativity say that we cannot (local observation) tell the difference between this 
acceleration and horizontal ground acceleration devoid of tilt.

	For whatever reason, I appear to be the only person to have ever recognized what a 
marvelous opportunity this ‘tilt’ business is for purpose of studying the standing 
wave oscillations (hum) of the earth.  The VM mechanical response is ‘flat to tilt 
displacement’, and global standing waves of the earth cause the direction of ‘little 
g’ to change at nrad levels for many such oscillations (for an instrument positioned 
somewhere along a nodal line).  Thus the VM is the obvious, inexpensive means to 
study something that has mainly eluded the herculean efforts of some scientists who 
have become very much interested in earth hum.

	I was a participant in the IRIS Broadband Workshop concerned with extending the 
low-frequency response of seismic instruments.  I am confident that the VM is an 
instrument that should be of interest to those who organized the conference, yet 
there is reluctance on their part to believe that something so simple (and cheap) as 
the VM could be of any real value to them.   I hope that I can motivate some of you 
in the amateur community to participate with me in such studies.

	I have just become aware of some recent questions about the VM, to which I now respond.

	Seismometers with mechanical amplification are inherently ‘unstable’ and require 
force-balance when operating with gap-varying capacitive sensors.  The biggest 
culprit is the temperature coefficient of the modulus of the spring constant.  This 
is typically much worse than effects dues to the thermal coefficient of expansion 
differences between dissimilar materials.

	When constructed to provide inherent ‘gain’ by period lengthening, mechanical 
oscillators become not only more sensitive to earthquakes—but also more sensitive to 
the myriad problems associated with creep in their structures.  My career has been 
devoted to the study of these problems (friction at the mesoscale) and I will in due 
time discuss some of its features with readers if they are interested.

	 I have worked with many different forms of capacitive detectors.  My PhD research 
used a gap varying transducer (non-differential) to measure harmonic distortion of 30 
MHz longitudinally polarized ultrasonic (acoustic) waves in copper single crystals as 
a function of temperature—distortion due to the interatomic anharmonic (nonlinear) 
potential.  Using a boxcar integrator this sensor could easily measure displacements 
less than 0.1 nm (1 Angstrom for you old-timers).  For some purposes, these 
gap-varying sensors are without equal in terms of sensitivity, particularly if one 
uses cryogenic amplifiers as was done by some Russians in the late 1960’s—to get 
resolutions approaching nuclear dimensions (100,000 times smaller).

	Their biggest problem, when it comes to use in seismometers, is that the gap-varying 
capacitor is very much less versatile than the area-varying type that I have 
patented.  The sensitivity of a single-element of one of my area-varying (first) 
fully-differential capacitive sensors does not compete favorably with the best 
gap-varying types.  But when configured as an array, enormous mechanical dynamic 
range (as compared to the gap-varying units) is still possible without the 
sensitivity being inadequate.  I will in due time also explain this to readers who 
are interested.

	The simple pendulum is without a doubt the most stable of all seismic instruments. 
Historically, it was one of the first seismographs, and it remains the instrument 
against which ‘sophisticated’ seismometers are compared—always, it seems, with an 
accompanying statement that the ordinary pendulum is not good enough for ‘real’ work 
because the period of an ‘acceptably small’ instrument is always too short for 
‘adequate’ sensitivity..  When the pendulum operates with the ‘right’ sensor and 
electronics, none of this conventional rhetoric remains appropriate

	As compared to ‘unstable’ conventional instruments, the VM is exquisitely ‘stable’. 
  I use quotes here because at the nm and smaller level there is no such thing as a 
truly static system.  Indeed stress is always present and there is no level below 
which creep does not occur.   Where we hope to eventually operate seismographs 
reliably, creep is not even ‘smooth’ and its ‘snap, crackle, and pop’ (the Portevin 
LeChatelier effect) are the nemesis of long-period seismometers.  For too many years 
now, in the compromise between deficiencies of (i) electronics and (ii) mechanical 
structures, the emphasis was on trying to improve the mechanical.  It is time to 
return to the simplest mechanical structure (pendulum) and ‘wring from the 
electronics’ (augmented by numerical methods such as Larry is planning) everything 
that the electronics can be (to use an army expression).  To me, the award winning 
AD774x is a brand new, wonderful technology.  I am delighted to have the apparent 
opportunity to work with talented amateur seismologists.  I see us having the 
opportunity to become first in the world to show even the pro’s a thing or two.

	I expect that a collective effort, centered around this new chip, will result in 
discoveries of importance to the world of geoscience.  I want everybody to rest 
assured that I have no intention of trying to ‘hog the glory’ that might result from 
such discovery.  From what I’ve so far seen, I admire greatly the attributes of 
various individuals in this amateur community; and it is my promise to give you 
credit where it is due.  (In the mountain country where I come from, a man is no 
better than his word.  If you find me at anytime deviating from this promise, then 
broadcast the evidence for my transgression to the whole world by means of the 
list-serve.)

Randall Peters PhD


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