## PSN-L Email List Message

Subject: RE: Integrating in WinQuake
From: Randall Peters PETERS_RD@..........
Date: Mon, 7 Dec 2009 09:43:23 -0500

```It is high time that everybody in the amateur seismology community (as well=
as the professional one) understand something 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 law=
s as treated in elementary textbooks, but also Einstein's principle of rela=
tivity. The direct response to acceleration that I'm talking about is the m=
otion of the instrument's main mass (called inertial) relative to the case =
of the instrument. The only thing that can cause relative motion between th=
ese 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) ea=
rth 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 n=
ot only by this relative motion of these two mechanical components but also=
by the nature of the electronics that monitors the motion. With a coil/mag=
net (Faraday law) detector of classical type, the output voltage is proport=
ional to the time rate of change (derivative) of the relative motion of mas=
s and case. (assuming `flat electronics' for the amplifier circuits.) It is=
a velocity sensor only in terms of what it is measuring; i.e., the relativ=
e velocity of mass and case. This IS NOT, however, necessarily a measure 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 frequency of the =
harmonic acceleration that causes an output. There are two parts to this ma=
tter, both the frequency respnse of the mass/case and also the frequency re=
sponse of the detector. The easiest mechanical type to understand is a simp=
le pendulum. If the frequency of the earth's acceleration is lower than the=
natural frequency of the pendulum, then the angular displacement of the pe=
ndulum is proportional to the acceleration. For this frequency regime, the =
coil/magnet output is therefore proportional to the derivative of local-ear=
th acceleration. In engineering terminology, this is called a `jerk' detect=
or.  On the other hand, for local-earth acceleration frequencies higher tha=
n the natural frequency of the pendulum, the output is indeed proportional =
to the local-earth velocity. This is because the pendulum response to accel=
eration 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 Wielandt has agreed with =
me on this matter; i.e., the coil/magnet detector is a measure of local-ear=
th velocity for harmonic motions having a frequency higher than the natural=
frequency of the pendulum. Conversely, for frequencies lower than the natu=
ral frequency, the detector is a jerk detector; i.e., it measures the time =
derivative of the acceleration of the earth. Now concerning a capacitive de=
tector, it is important that one understands the architecture with which it=
is employed. With the VolksMeter, the most important to me (non-integrated=
) output is one in which the symmetric-differential-capacitive (SDC) detect=
or measures the angular displacement of the pendulum. For earth's harmonic =
accelerations that are at a frequency lower than the natural frequency of t=
he VM (0.92 Hz), the pendulum response (and thus the SDC output) are propor=
tionall to the earth's acceleration. One obtains then the earth's velocity =
(for frequency less than 0.92 Hz) by integrating this SDC output. In the ca=
se of a force-feedback instrument like those of STS type (influenced by the=
expertise of Erhard Wielandt, built by Gunar Streckeisen), the output is g=
overned by the poles/zeroes of the electronics designed to behave like a lo=
ng-period-equivalent pendulum. The total system (`pendulum plus all of the =
electronics) mimics that of a classical coil/magnet system monitoring a pen=
dulum whose period is about 30 s. In other words, for earth accelerations i=
n which the frequency is higher than the lower corner frequency of the STS =
(approximately 0.03 Hz), the output is proportional to earth velocity. For =
the spectral region of interest to many of us (teleseismic observations), o=
ne thus sees that the integrated output of the VM can be compared directly =
and meaningfully with the helicord display of conventional force balance se=
nsors whose pendulum-equivalent natural frequency is no greater than about =
0.03 Hz. The same can be said of the garden-gate instruments that many of y=
ou use, IF your period has been adjusted to be at least as great as 20 s. S=
o can one talk about earth displacement or earth velocity or earth accelera=
tion on the basis of what one's instrument is measuring? The answer is obvi=
ously a qualified yes, but it is imperative that the transfer properties of=
both the mechanical part (such as a pendulum) and also that of the electro=
nics be properly factored into what is concluded. In summary, different sys=
tems give different results concerning what is direct output, as opposed to=
indirect, depending on the detector type. A capacitive sensor as used in t=
he VM measures earth-acceleration directly for frequencies lower than 0.92 =
Hz. STS instruments, though they use a capacitive sensor, but with sophisti=
cated electronics involving an actuator, measure earth-velocity directly fo=
r frequencies higher than about 0.03 Hz. Consequently, the integrated outpu=
t from the VM can be compared directly with the output from an STS. Keep in=
mind that integrating a second time may or may not yield earth displacemen=
t, depending on the natural frequency of the instrument. One must `back out=
' the system response (total system transfer function) if the result is to =
have any meaning. For those of you using geophones, where the natural frequ=
ency is higher than 1 Hz; your output is proportional to the derivative of =
earth acceleration.  Relative to earth motion (not the geophone mass) your =
detector is for frequencies of interest to most of us (not the local-enviro=
nment high frequency parts) -- a jerk detector and not a velocity detector,=
even though it uses a Farady law detector.

Randall Peters

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MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px
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-->

It is high time that everybody in the amateur seismology community (as w=
ell as the professional one) understand something that is FUNDAMENTAL PHYSI=
CS.. 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 tex=
tbooks, but also Einstein's principle of relativity. 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 moti=
on between these two components of the instrument is acceleration of the ca=
se. The case acceleration is the same as the acceleration of that part of t=
he (local) earth on which the instrument
sits (at rest relative to this piece of earth). The nature of the trace th=
at is output from the instrument is determined not only by this relative mo=
tion of these two mechanical components but also by the nature of the elect=
ronics that monitors the motion.
With a coil/magnet (Faraday law) detector of classical type, the output vo=
ltage is proportional to the time rate of change (derivative) of the relati=
ve motion of mass and case. (assuming `flat electronics' for the amplifier =
circuits.) It is a velocity sensor
only in terms of what it is measuring; i.e., the relative velocity of mass=
and case. This IS NOT, however, necessarily a measure of the velocity of t=
he local-earth itself. The earth velocity is the integral of the accelerati=
on of the earth. The nature of the
instrument's response to the earth's quintessential acceleration depends o=
n the frequency of the harmonic acceleration that causes an output. There a=
re two parts to this matter, both the frequency respnse of the mass/case an=
d also the frequency response of
the detector. The easiest mechanical type to understand is a simple pendul=
um. 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 proportiona=
l to the derivative of local-earth acceleration. In engineering terminology=
, this is called a `jerk' detector.  On the other hand, for local-eart=
h acceleration frequencies higher than
the natural frequency of the pendulum, the output is indeed proportional t=
o the local-earth velocity. This is because the pendulum response to accele=
ration for frequency higher than its natural frequency is proportional to r=
eciprocal frequency squared. Since
Chris 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/m=
agnet detector is a measure of local-earth velocity for harmonic motions ha=
ving 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 t=
he time derivative of the acceleration of the earth. Now concerning a capac=
itive detector, it is important
that one understands the architecture with which it is employed. With the =
VolksMeter, the most important to me (non-integrated) output is one in whic=
h the symmetric-differential-capacitive (SDC) detector measures the angular=
displacement of the pendulum. For
earth's harmonic accelerations that are at a frequency lower than the natu=
ral frequency of the VM (0.92 Hz), the pendulum response (and thus the SDC =
output) are proportionall to the earth's acceleration. 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 instrument like those of STS type (influenced by the expertise of =
Erhard Wielandt, built by Gunar Streckeisen), the output is governed b=
y the poles/zeroes of the electronics
designed to behave like a long-period-equivalent pendulum. The total syste=
m (`pendulum plus all of the electronics) mimics that of a classical coil/m=
agnet system monitoring a pendulum whose period is about 30 s. In othe=
r words, for earth accelerations in which
the frequency is higher than the lower corner frequency of the STS (a=
pproximately 0.03 Hz), the output is proportional to earth velocity. For th=
e spectral region of interest to many of us (teleseismic observations), one=
thus sees that the integrated output
of the VM can be compared directly and meaningfully with the helicord disp=
lay of conventional force balance sensors whose pendulum-equivalent natural=
frequency is no greater than about 0.03 Hz. The same can be said of t=
he garden-gate instruments that many
of you use, IF your period has been adjusted to be at least as g=
reat 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 imperative that the transfer properties of both the mechanical part =
(such as a pendulum) and also that of the electronics be properly factored =
into what is concluded. In summary, different systems give different result=
s concerning what is direct output,
as opposed to indirect, depending on the detector type. A capacitive senso=
r as used in the VM measures earth-acceleration directly for frequencies lo=
wer than 0.92 Hz. STS instruments, though they use a capacitive sensor, but=
with sophisticated electronics
involving an actuator, measure earth-velocity directly for frequencies&nbs=
p;higher than about 0.03 Hz. Consequently, the integrated output from the V=
M can be compared directly with the output from an STS. Keep in mind that i=
ntegrating a second time may or may not
yield earth displacement, depending on the natural frequency of the instru=
ment. One must `back out' the system response (total system transfer functi=
on) if the result is to have any meaning. For those of you using geophones,=
where the natural frequency is
higher than 1 Hz; your output is proportional to the derivative of earth a=
cceleration.  Relative to earth motion (not the geophone mass) your de=
tector is for frequencies of interest to most of us (not the local-environm=
ent high frequency parts) -- a jerk detector and
not a velocity detector, even though it uses a Farady law detector.
Randall Peters

```