PSN-L Email List Message

Subject: modulated seismic signals
From: Randall Peters PETERS_RD@..........
Date: Thu, 14 Apr 2011 08:36:02 -0400


Geoff,
     I'm glad to see interest in this matter, since there is at least one p=
lace where modulation of seismic signals occurs; i.e., eigenmodes (usually =
called free-oscillations by seismologists) in records containing earthquake=
s.  Since an earthquake is a 'sharp' disturbance containing very broad spec=
tral content, it ought to instantaneously drive many modes of our planet, i=
ncluding eigenmodes at nearly all frequencies.  An FFT of a 24 hour record =
with the earthquake at its center usually does not show these low frequency=
 components.  They are conventionally studied after the high frequency 'stu=
ff' dies away; like a bell that has been hit with a hammer, leaving the 'pu=
re' tones after the 'harsh' stuff decays.  The reason the eigenmodes are no=
t immediately visible  is that they modulate higher frequency components an=
d thus would be present only as sums and differences that cannot be readily=
 'extracted' from the many other vibrations.  If one demodulates the record=
 before doing the FFT, they become visible.  The easiest way to perform the=
 demodulation is to simply 'chop off' (half-wave rectify) the signal before=
 doing the FFT.  Not every spectral line that then becomes visible in the f=
requency range from 0.3 mHz to 10 mHz is actually an eigenmode, because noi=
ses can masquerade as such.  But there is a way to discriminate between eig=
enmodes and noise.  A totally different demodulation scheme is one that is =
based on the Teager Kaiser Energy operator  (TKE).  As used conventionally =
by folks in the life sciences, this TKE operator is not suited to the metho=
dology; however, I modified it to produce what I call the "peak tracker".  =
This was a natural modification for me to do because the TKE is based in th=
e 'holy grail' of physics called the 'simple harmonic oscillator'  (SHO).  =
Thus when you look at two demodulated record spectra-(i) one from rectifica=
tion (either half-wave or full wave by taking the absolute value), and (ii)=
 the other from using the peak tracker before doing the FFT-if they show id=
entical spectral lines, you can be confident that what is being displayed i=
s not noise, but rather a true motion of the Earth.  Of course, to see thes=
e very low frequency motions, you must use a seismograph that is capable of=
 measuring them; i.e., one having a low enough frequency cutoff.  The Volks=
Meter is ideally suited to such studies, because it responds to tilt all th=
e way down to d.c.  When the Earth oscillates in an eigenmode, the directio=
n of the earth's field changes by about a nanoradian, meaning it can be see=
n by an instrument sensitive to tilt whose frequency response allows seeing=
 it.  The magnitude of g =3D 9.8 m/s^2 does not change enough to be seen wi=
th anything but the most sensitive instruments, such as a superconducting g=
ravimeter operating on the Meissner effect.   For those interested in knowi=
ng more about my work in this area, I've written some relevant papers that =
are available online; i.e.,
"Signal Peak tracker based on the Teager Kaiser Energy Operator",
http://arxiv.org/abs/1010.5166
"Free-oscillations coincident with earthquakes",
 http://arxiv.org/ftp/arxiv/papers/1010/1010.5690.pdf
"Amplitude modulation effects in seismic signals"
http://physics.mercer.edu/hpage/modulation/modulation.html
Interestingly, the Earth at one megameter scale is similar to the human bod=
y at one meter scale, since seismocardiography studies show a similar pheno=
menon.  Even though one might expect the 1 Hz signal of the heart beat to b=
e the dominant spectral line in a record of SCG type, it usually is not rea=
dily visible because of amplitude modulation effects.  The same is true eve=
n of the ECG.  It was my discovery of "Amplitude modulation effects in card=
iac signals", online at
http://arxiv.org/abs/1011.1880
that prompted me to start looking at earthquake records in the way that I m=
ention above.  I would be delighted to see some of you amateur seismologist=
s start looking at spectral records in this manner.  Have hoped that the pr=
ofessionals would take interest and do the same, but I haven't seen them do=
ing so yet.  Maybe you folks can 'lead the charge'.




Geoff,

     I’m glad to see in= terest in this matter, since there is at least one place where modulation o= f seismic signals occurs; i.e., eigenmodes (usually called free-oscillation= s by seismologists) in records containing earthquakes.  Since an earth= quake is a ‘sharp’ disturbance containing very broad spectral c= ontent, it ought to instantaneously drive many modes of our planet, includi= ng eigenmodes at nearly all frequencies.  An FFT of a 24 hour record w= ith the earthquake at its center usually does not show these low frequency = components.  They are conventionally studied after the high frequency = ‘stuff’ dies away; like a bell that has been hit with a hammer,= leaving the ‘pure’ tones after the ‘harsh’ stuff d= ecays.  The reason the eigenmodes are not immediately visible  is= that they modulate higher frequency components and thus would be present o= nly as sums and differences that cannot be readily ‘extracted’ = from the many other vibrations.  If one demodulates the record before = doing the FFT, they become visible.  The easiest way to perform the de= modulation is to simply ‘chop off’ (half-wave rectify) the sign= al before doing the FFT.  Not every spectral line that then becomes vi= sible in the frequency range from 0.3 mHz to 10 mHz is actually an eigenmod= e, because noises can masquerade as such.  But there is a way to discr= iminate between eigenmodes and noise.  A totally different demodulatio= n scheme is one that is based on the Teager Kaiser Energy operator  (T= KE).  As used conventionally by folks in the life sciences, this TKE o= perator is not suited to the methodology; however, I modified it to produce= what I call the “peak tracker”.  This was a natural modif= ication for me to do because the TKE is based in the ‘holy grail̵= 7; of physics called the ‘simple harmonic oscillator’  (SH= O).  Thus when you look at two demodulated record spectra—(i) on= e from rectification (either half-wave or full wave by taking the absolute = value), and (ii) the other from using the peak tracker before doing the FFT= —if they show identical spectral lines, you can be confident that wha= t is being displayed is not noise, but rather a true motion of the Earth.&n= bsp; Of course, to see these very low frequency motions, you must use a sei= smograph that is capable of measuring them; i.e., one having a low enough f= requency cutoff.  The VolksMeter is ideally suited to such studies, be= cause it responds to tilt all the way down to d.c.  When the Earth osc= illates in an eigenmode, the direction of the earth’s field changes b= y about a nanoradian, meaning it can be seen by an instrument sensitive to = tilt whose frequency response allows seeing it.  The magnitude of g = =3D 9.8 m/s^2 does not change enough to be seen with anything but the most = sensitive instruments, such as a superconducting gravimeter operating on th= e Meissner effect.   For those interested in knowing more about m= y work in this area, I’ve written some relevant papers that are avail= able online; i.e.,

“Signal Peak tr= acker based on the Teager Kaiser Energy Operator”,

http://arxiv.or= g/abs/1010.5166

“Free-oscillat= ions coincident with earthquakes”,

 ht= tp://arxiv.org/ftp/arxiv/papers/1010/1010.5690.pdf

“Amplitude modulation effects in seismic signals”= ;

http://physics.mercer.edu/hpage/modulation= /modulation.html

Interestingly, the = Earth at one megameter scale is similar to the human body at one meter scal= e, since seismocardiography studies show a similar phenomenon.  Even t= hough one might expect the 1 Hz signal of the heart beat to be the dominant= spectral line in a record of SCG type, it usually is not readily visible b= ecause of amplitude modulation effects.  The same is true even of the = ECG.  It was my discovery of “Amplitude modulation effects in ca= rdiac signals”, online at

http://arxiv.org/abs/1011.1880=

that prompted me to start looking at earthqu= ake records in the way that I mention above.  I would be delighted to = see some of you amateur seismologists start looking at spectral records in = this manner.  Have hoped that the professionals would take interest an= d do the same, but I haven’t seen them doing so yet.  Maybe you = folks can ‘lead the charge’.

 

 

 

 

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