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’.
=