Fantastic information!=C2=A0greatly appreciated! Thank you=C2=A0Dr=C2=A0Pet=
ers!=0A=0A=0A=0A=0A________________________________=0AFrom: Randall Peters =
=0ATo: "psnlist@.............." =0ASent: Thu, April 14, 2011 8:36:02 AM=0ASubject: modulated seismic sig=
nals=0A=0A=0AGeoff,=0A=C2=A0=C2=A0=C2=A0=C2=A0 I=E2=80=99m glad to see inte=
rest in this matter, since there is at least one place =0Awhere modulation =
of seismic signals occurs; i.e., eigenmodes (usually called =0Afree-oscilla=
tions by seismologists) in records containing earthquakes.=C2=A0 Since an =
=0Aearthquake is a =E2=80=98sharp=E2=80=99 disturbance containing very broa=
d spectral content, it =0Aought to instantaneously drive many modes of our =
planet, including eigenmodes at =0Anearly all frequencies.=C2=A0 An FFT of =
a 24 hour record with the earthquake at its =0Acenter usually does not show=
 these low frequency components.=C2=A0 They are =0Aconventionally studied a=
fter the high frequency =E2=80=98stuff=E2=80=99 dies away; like a bell =0At=
hat has been hit with a hammer, leaving the =E2=80=98pure=E2=80=99 tones af=
ter the =E2=80=98harsh=E2=80=99 =0Astuff decays.=C2=A0 The reason the eigen=
modes are not immediately visible =C2=A0is that =0Athey modulate higher fre=
quency components and thus would be present only as sums =0Aand differences=
 that cannot be readily =E2=80=98extracted=E2=80=99 from the many other =0A=
vibrations.=C2=A0 If one demodulates the record before doing the FFT, they =
become =0Avisible.=C2=A0 The easiest way to perform the demodulation is to =
simply =E2=80=98chop off=E2=80=99 =0A(half-wave rectify) the signal before =
doing the FFT.=C2=A0 Not every spectral line =0Athat then becomes visible i=
n the frequency range from 0.3 mHz to 10 mHz is =0Aactually an eigenmode, b=
ecause noises can masquerade as such.=C2=A0 But there is a =0Away to discri=
minate between eigenmodes and noise.=C2=A0 A totally different =0Ademodulat=
ion scheme is one that is based on the Teager Kaiser Energy operator=C2=A0 =
=0A(TKE).=C2=A0 As used conventionally by folks in the life sciences, this =
TKE operator =0Ais not suited to the methodology; however, I modified it to=
 produce what I call =0Athe =E2=80=9Cpeak tracker=E2=80=9D.=C2=A0 This was =
a natural modification for me to do because the =0ATKE is based in the =E2=
=80=98holy grail=E2=80=99 of physics called the =E2=80=98simple harmonic =
=0Aoscillator=E2=80=99=C2=A0 (SHO).=C2=A0 Thus when you look at two demodul=
ated record spectra=E2=80=94(i) =0Aone from rectification (either half-wave=
 or full wave by taking the absolute =0Avalue), and (ii) the other from usi=
ng the peak tracker before doing the FFT=E2=80=94if =0Athey show identical =
spectral lines, you can be confident that what is being =0Adisplayed is not=
 noise, but rather a true motion of the Earth.=C2=A0 Of course, to =0Asee t=
hese very low frequency motions, you must use a seismograph that is capable=
 =0Aof measuring them; i.e., one having a low enough frequency cutoff.=C2=
=A0 The =0AVolksMeter is ideally suited to such studies, because it respond=
s to tilt all =0Athe way down to d.c.=C2=A0 When the Earth oscillates in an=
 eigenmode, the direction =0Aof the earth=E2=80=99s field changes by about =
a nanoradian, meaning it can be seen by an =0Ainstrument sensitive to tilt =
whose frequency response allows seeing it.=C2=A0 The =0Amagnitude of g =3D =
9.8 m/s^2 does not change enough to be seen with anything but =0Athe most s=
ensitive instruments, such as a superconducting gravimeter operating =0Aon =
the Meissner effect.=C2=A0=C2=A0 For those interested in knowing more about=
 my work in =0Athis area, I=E2=80=99ve written some relevant papers that ar=
e available online; i.e.,=0A=E2=80=9CSignal Peak tracker based on the Teage=
r Kaiser Energy Operator=E2=80=9D,=0Ahttp://arxiv.org/abs/1010.5166=0A=E2=
=80=9CFree-oscillations coincident with earthquakes=E2=80=9D,=0A=C2=A0http:=
//arxiv.org/ftp/arxiv/papers/1010/1010.5690.pdf=0A=E2=80=9CAmplitude modula=
tion effects in seismic signals=E2=80=9D=0Ahttp://physics.mercer.edu/hpage/=
modulation/modulation.html=0AInterestingly, the Earth at one megameter scal=
e is similar to the human body at =0Aone meter scale, since seismocardiogra=
phy studies show a similar phenomenon.=C2=A0 =0AEven though one might expec=
t the 1 Hz signal of the heart beat to be the =0Adominant spectral line in =
a record of SCG type, it usually is not readily =0Avisible because of ampli=
tude modulation effects.=C2=A0 The same is true even of the =0AECG.=C2=A0 I=
t was my discovery of =E2=80=9CAmplitude modulation effects in cardiac sign=
als=E2=80=9D, =0Aonline at=0Ahttp://arxiv.org/abs/1011.1880=0Athat prompted=
 me to start looking at earthquake records in the way that I =0Amention abo=
ve.=C2=A0 I would be delighted to see some of you amateur seismologists =0A=
start looking at spectral records in this manner.=C2=A0 Have hoped that the=
 =0Aprofessionals would take interest and do the same, but I haven=E2=80=99=
t seen them doing =0Aso yet.=C2=A0 Maybe you folks can =E2=80=98lead the ch=
Fantastic information! greatly appreciated! Thank you =
;Dr Peters!
=0A

=0A
=0A
=0AFrom: R=
andall Peters <PETERS_RD@..........>
To: "psnlist@.............." <psnlist@..............&=
gt;
Sent: Thu, April 14,=
 2011 8:36:02 AM
Subject: modulated seismic signals

=0A=
=0A=0A
=0A
Geoff,
=0A
     I=E2=80=99m glad to see interest in=
 this matter, since there is at least one place where modulation of seismic=
 signals occurs; i.e., eigenmodes (usually called free-oscillations by seis=
mologists) in records containing earthquakes.  Since an earthquake is =
a =E2=80=98sharp=E2=80=99 disturbance containing very broad spectral conten=
t, it ought to instantaneously drive many modes of our planet, including ei=
genmodes at nearly all frequencies.  An FFT of a 24 hour record with t=
he earthquake at its center usually does not show these low frequency compo=
nents.  They are conventionally studied after the high frequency =E2=
=80=98stuff=E2=80=99 dies away; like a bell that has been hit with a hammer=
, leaving the =E2=80=98pure=E2=80=99 tones after the =E2=80=98harsh=E2=80=
=99 stuff decays.  The reason the eigenmodes are not immediately visib=
le  is that they modulate higher frequency components and thus would b=
e present only as sums and differences that
 cannot be readily =E2=80=98extracted=E2=80=99 from the many other vibratio=
ns.  If one demodulates the record before doing the FFT, they become v=
isible.  The easiest way to perform the demodulation is to simply =E2=
=80=98chop off=E2=80=99 (half-wave rectify) the signal before doing the FFT=
..  Not every spectral line that then becomes visible in the frequency =
range from 0.3 mHz to 10 mHz is actually an eigenmode, because noises can m=
asquerade as such.  But there is a way to discriminate between eigenmo=
des and noise.  A totally different demodulation scheme is one that is=
 based on the Teager Kaiser Energy operator  (TKE).  As used conv=
entionally by folks in the life sciences, this TKE operator is not suited t=
o the methodology; however, I modified it to produce what I call the =E2=80=
=9Cpeak tracker=E2=80=9D.  This was a natural modification for me to d=
o because the TKE is based in the =E2=80=98holy grail=E2=80=99 of physics c=
alled the =E2=80=98simple harmonic
 oscillator=E2=80=99  (SHO).  Thus when you look at two demodulat=
ed record spectra=E2=80=94(i) one from rectification (either half-wave or f=
ull wave by taking the absolute value), and (ii) the other from using the p=
eak tracker before doing the FFT=E2=80=94if they show identical spectral li=
nes, you can be confident that what is being displayed is not noise, but ra=
ther a true motion of the Earth.  Of course, to see these very low fre=
quency motions, you must use a seismograph that is capable of measuring the=
m; i.e., one having a low enough frequency cutoff.  The VolksMeter is =
ideally suited to such studies, because it responds to tilt all the way dow=
n to d.c.  When the Earth oscillates in an eigenmode, the direction of=
 the earth=E2=80=99s field changes by about a nanoradian, meaning it can be=
 seen by an instrument sensitive to tilt whose frequency response allows se=
eing it.  The magnitude of g =3D 9.8 m/s^2 does not change enough to b=
e seen with
 anything but the most sensitive instruments, such as a superconducting gra=
vimeter operating on the Meissner effect.   For those interested =
in knowing more about my work in this area, I=E2=80=99ve written some relev=
ant papers that are available online; i.e.,
=0A
=E2=
=80=9CSignal Peak tracker based on the Teager Kaiser Energy Operator=E2=80=
=9D,
=0A
http://arxiv.org/abs/1010.5166
=0A
=E2=80=9CFree-oscillations coincident with earthquakes=E2=
=80=9D,
=0A
 http://arxiv.=
org/ftp/arxiv/papers/1010/1010.5690.pdf
=0A
=E2=
=80=9CAmplitude modulation effects in seismic signals=E2=80=9D
=0A
http://physics.mercer.edu/hpage/m=
odulation/modulation.html
=0A
Interestingly, the=
 Earth at one megameter scale is similar to the human body at one meter sca=
le, since seismocardiography studies show a similar phenomenon.  Even =
though one might expect the 1 Hz signal of the heart beat to be the dominan=
t spectral line in a record of SCG type, it usually is not readily visible =
because of amplitude modulation effects.  The same is true even of the=
 ECG.  It was my discovery of =E2=80=9CAmplitude modulation effects in=
 cardiac signals=E2=80=9D, online at
=0A
http://arxiv=
..org/abs/1011.1880
=0A
that prompted me to start=
 looking at earthquake records in the way that I mention above.  I wou=
ld be delighted to see some of you amateur seismologists start looking at s=
pectral records in this manner.  Have hoped that the professionals wou=
ld take interest and do the same, but I haven=E2=80=99t seen them doing so =
yet.  Maybe you folks can =E2=80=98lead the charge=E2=80=99. 
=0A 
=0A
 
=0A
 
=0A
 
=