Randall, as a rule I very seldom respond to articles on PSN however, this i=
s a rare exception. Your opinion and thoughts on seismology=A0are right on =
and when you express your opinions one knows you are completely correct . W=
hat a refreshing article. I commend you my friend. John Cole, Pearland,Tx. =
..( amateur seismologist)=A0=0A=0A=0A=0A=0A________________________________=
=0AFrom: Randall Peters =0ATo: "psn-l@.............."=
 =0ASent: Mon, December 7, 2009 8:43:23 AM=0ASubject:=
 RE: Integrating in WinQuake=0A=0A=0AIt is high time that everybody in the =
amateur seismology community (as well as the professional one) understand s=
omething that is FUNDAMENTAL PHYSICS.. The ONLY thing that ANY seismometer'=
s mechanical parts EVER respond to is ACCELERATION. Let the skeptic of this=
 claim go study not just Newton's laws as treated in elementary textbooks, =
but also Einstein's principle of relativity. The direct response to acceler=
ation that I'm talking about is the motion of the instrument's main mass (c=
alled inertial) relative to the case of the instrument. The only thing that=
 can cause relative motion between these two components of the instrument i=
s acceleration of the case. The case acceleration is the same as the accele=
ration of that part of the (local) earth on which the instrument sits (at r=
est relative to this piece of earth). The nature of the trace that is outpu=
t from the instrument is determined not only by this relative motion of the=
se two mechanical components
 but also by the nature of the electronics that monitors the motion. With a=
 coil/magnet (Faraday law) detector of classical type, the output voltage i=
s proportional to the time rate of change (derivative) of the relative moti=
on of mass and case. (assuming `flat electronics' for the amplifier circuit=
s.) It is a velocity sensor only in terms of what it is measuring; i.e., th=
e relative velocity of mass and case. This IS NOT, however, necessarily a m=
easure of the velocity of the local-earth itself. The earth velocity is the=
 integral of the acceleration of the earth. The nature of the instrument's =
response to the earth's quintessential acceleration depends on the frequenc=
y of the harmonic acceleration that causes an output. There are two parts t=
o this matter, both the frequency respnse of the mass/case and also the fre=
quency response of the detector. The easiest mechanical type to understand =
is a simple pendulum. If the frequency of the earth's acceleration
 is lower than the natural frequency of the pendulum, then the angular disp=
lacement of the pendulum is proportional to the acceleration. For this freq=
uency regime, the coil/magnet output is therefore proportional to the deriv=
ative of local-earth acceleration. In engineering terminology, this is call=
ed a `jerk' detector.=A0 On the other hand, for local-earth acceleration fr=
equencies higher than the natural frequency of the pendulum, the output is =
indeed proportional to the local-earth velocity. This is because the pendul=
um response to acceleration for frequency higher than its natural frequency=
 is proportional to reciprocal frequency squared. Since Chris has mentioned=
 the highly-esteemed Erhard Wielandt, let me point out that Professor Wiela=
ndt has agreed with me on this matter; i.e., the coil/magnet detector is a =
measure of local-earth velocity for harmonic motions having a frequency hig=
her than the natural frequency of the pendulum. Conversely, for
 frequencies lower than the natural frequency, the detector is a jerk detec=
tor; i.e., it measures the time derivative of the acceleration of the earth=
.. Now concerning a capacitive detector, it is important that one understand=
s the architecture with which it is employed. With the VolksMeter, the most=
 important to me (non-integrated) output is one in which the symmetric-diff=
erential-capacitive (SDC) detector measures the angular displacement of the=
 pendulum. For earth's harmonic accelerations that are at a frequency lower=
 than the natural frequency of the VM (0.92 Hz), the pendulum response (and=
 thus the SDC output) are proportionall to the earth's acceleration. One ob=
tains then the earth's velocity (for frequency less than 0.92 Hz) by integr=
ating this SDC output. In the case of a force-feedback instrument like thos=
e of STS type (influenced by the expertise of Erhard Wielandt, built by Gun=
ar Streckeisen), the output is=A0governed by=A0the poles/zeroes of the
 electronics designed to behave like a long-period-equivalent pendulum. The=
 total system (`pendulum plus all of the electronics) mimics that of a clas=
sical coil/magnet=A0system monitoring a pendulum whose period is about 30 s=
.. In other words, for earth accelerations in which the frequency is=A0highe=
r than the lower corner frequency of the STS (approximately 0.03 Hz), the o=
utput is proportional to earth velocity. For the spectral region of interes=
t to many of us (teleseismic observations), one thus sees that the integrat=
ed output of the VM can be compared directly and meaningfully with the heli=
cord display of conventional force balance sensors whose pendulum-equivalen=
t natural frequency is no=A0greater than about 0.03 Hz. The same can be sai=
d of the garden-gate instruments that many of you use, IF your period has b=
een adjusted to=A0be at least as=A0great as 20 s. So can one talk about ear=
th displacement or earth velocity or earth acceleration on the basis of
 what one's instrument is measuring? The answer is obviously a qualified ye=
s, but it is imperative that the transfer properties of both the mechanical=
 part (such as a pendulum) and also that of the electronics be properly fac=
tored into what is concluded. In summary, different systems give different =
results concerning what is direct output, as opposed to indirect, depending=
 on the detector type. A capacitive sensor as used in the VM measures earth=
-acceleration directly for frequencies lower than 0.92 Hz. STS instruments,=
 though they use a capacitive sensor, but with sophisticated electronics in=
volving an actuator, measure earth-velocity directly for frequencies=A0high=
er than about 0.03 Hz. Consequently, the integrated output from the VM can =
be compared directly with the output from an STS. Keep in mind that integra=
ting a second time may or may not yield earth displacement, depending on th=
e natural frequency of the instrument. One must `back out' the system
 response (total system transfer function) if the result is to have any mea=
ning. For those of you using geophones, where the natural frequency is high=
er than 1 Hz; your output is proportional to the derivative of earth accele=
ration.=A0 Relative to earth motion (not the geophone mass) your detector i=
s for frequencies of interest to most of us (not the local-environment high=
 frequency parts) -- a jerk detector=A0and not=A0a velocity detector, even =
Randall, as a rule I very seldom respond to articles o=
n PSN however, this is a rare exception. Your opinion and thoughts on seism=
ology are right on and when you express your opinions one knows you ar=
e completely correct . What a refreshing article. I commend you my friend. =
John Cole, Pearland,Tx. .( amateur seismologist) 
=0A
=0A
=0AFrom: Randall Peters <PETERS_RD@=
mercer.edu>
To: "psn-=
l@.............." <psn-l@..............>
Sent: Mon, December 7, 2009 8:43:23 AM
Subject: RE: Integrating in WinQuake<=
BR>
=0A=
=0A=0A=0A
=0AIt is high time that everybody in the amateur seismology community (as wel=
l as the professional one) understand something that is FUNDAMENTAL PHYSICS=
... The ONLY thing that ANY seismometer's mechanical parts EVER respond to i=
s ACCELERATION. Let the skeptic of this claim go study not just Newton's la=
ws as treated in elementary textbooks, but also Einstein's principle of rel=
ativity. The direct response to acceleration that I'm talking about is the =
motion of the instrument's main mass (called inertial) relative to the case=
 of the instrument. The only thing that can cause relative motion between t=
hese two components of the instrument is acceleration of the case. The case=
 acceleration is the same as the acceleration of that part of the (local) e=
arth on which the instrument sits (at rest relative to this piece of earth)=
.. The nature of the trace that is output from the instrument is determined =
not only by this relative motion of these two mechanical
 components but also by the nature of the electronics that monitors the mot=
ion. With a coil/magnet (Faraday law) detector of classical type, the outpu=
t voltage is proportional to the time rate of change (derivative) of the re=
lative motion of mass and case. (assuming `flat electronics' for the amplif=
ier circuits.) It is a velocity sensor only in terms of what it is measurin=
g; i.e., the relative velocity of mass and case. This IS NOT, however, nece=
ssarily a measure of the velocity of the local-earth itself. The earth velo=
city is the integral of the acceleration of the earth. The nature of the in=
strument's response to the earth's quintessential acceleration depends on t=
he frequency of the harmonic acceleration that causes an output. There are =
two parts to this matter, both the frequency respnse of the mass/case and a=
lso the frequency response of the detector. The easiest mechanical type to =
understand is a simple pendulum. If the frequency of the earth's
 acceleration is lower than the natural frequency of the pendulum, then the=
 angular displacement of the pendulum is proportional to the acceleration. =
For this frequency regime, the coil/magnet output is therefore proportional=
 to the derivative of local-earth acceleration. In engineering terminology,=
 this is called a `jerk' detector.  On the other hand, for local-earth=
 acceleration frequencies higher than the natural frequency of the pendulum=
, the output is indeed proportional to the local-earth velocity. This is be=
cause the pendulum response to acceleration for frequency higher than its n=
atural frequency is proportional to reciprocal frequency squared. Since Chr=
is has mentioned the highly-esteemed Erhard Wielandt, let me point out that=
 Professor Wielandt has agreed with me on this matter; i.e., the coil/magne=
t detector is a measure of local-earth velocity for harmonic motions having=
 a frequency higher than the natural frequency of the pendulum.
 Conversely, for frequencies lower than the natural frequency, the detector=
 is a jerk detector; i.e., it measures the time derivative of the accelerat=
ion of the earth. Now concerning a capacitive detector, it is important tha=
t one understands the architecture with which it is employed. With the Volk=
sMeter, the most important to me (non-integrated) output is one in which th=
e symmetric-differential-capacitive (SDC) detector measures the angular dis=
placement of the pendulum. For earth's harmonic accelerations that are at a=
 frequency lower than the natural frequency of the VM (0.92 Hz), the pendul=
um response (and thus the SDC output) are proportionall to the earth's acce=
leration. One obtains then the earth's velocity (for frequency less than 0.=
92 Hz) by integrating this SDC output. In the case of a force-feedback inst=
rument like those of STS type (influenced by the expertise of Erhard Wielan=
dt, built by Gunar Streckeisen), the output is governed
 by the poles/zeroes of the electronics designed to behave like a long=
-period-equivalent pendulum. The total system (`pendulum plus all of the el=
ectronics) mimics that of a classical coil/magnet system monitoring a =
pendulum whose period is about 30 s. In other words, for earth acceleration=
s in which the frequency is higher than the lower corner frequency of =
the STS (approximately 0.03 Hz), the output is proportional to earth veloci=
ty. For the spectral region of interest to many of us (teleseismic observat=
ions), one thus sees that the integrated output of the VM can be compared d=
irectly and meaningfully with the helicord display of conventional force ba=
lance sensors whose pendulum-equivalent natural frequency is no greate=
r than about 0.03 Hz. The same can be said of the garden-gate instruments t=
hat many of you use, IF your period has been adjusted to be at least a=
s great as 20 s. So can one talk about earth displacement or
 earth velocity or earth acceleration on the basis of what one's instrument=
 is measuring? The answer is obviously a qualified yes, but it is imperativ=
e that the transfer properties of both the mechanical part (such as a pendu=
lum) and also that of the electronics be properly factored into what is con=
cluded. In summary, different systems give different results concerning wha=
t is direct output, as opposed to indirect, depending on the detector type.=
 A capacitive sensor as used in the VM measures earth-acceleration directly=
 for frequencies lower than 0.92 Hz. STS instruments, though they use a cap=
acitive sensor, but with sophisticated electronics involving an actuator, m=
easure earth-velocity directly for frequencies higher than about 0.03 =
Hz. Consequently, the integrated output from the VM can be compared directl=
y with the output from an STS. Keep in mind that integrating a second time =
may or may not yield earth displacement, depending on the natural
 frequency of the instrument. One must `back out' the system response (tota=
l system transfer function) if the result is to have any meaning. For those=
 of you using geophones, where the natural frequency is higher than 1 Hz; y=
our output is proportional to the derivative of earth acceleration.  R=
elative to earth motion (not the geophone mass) your detector is for freque=
ncies of interest to most of us (not the local-environment high frequency p=
arts) -- a jerk detector and not a velocity detector, even though=
 it uses a Farady law detector.
=0A
  &n=
bsp; Randall Peters
=0A
=0A

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