## PSN-L Email List Message

Subject: RE: Integrating in WinQuake
From: RSparks rsparks@..........
Date: Wed, 09 Dec 2009 10:26:55 -0800

```Hello Randall,

Thanks for the informative posting relating sensors for seismometers.

Here is an example that might complement the discussion.

We all seem to agree that a coil/magnet sensor measures velocity and the
displacement sensor measures location, both relative to boom and case.
What I would like to add is that neither measurement completely defines
conditions at the instant of measurement.  The measurement of velocity
ignores location, and measurement of location ignores the component of
velocity.  What we should do is to measure BOTH components (two sensors
on each boom) at the same instant.  Of course this would result in two
data streams which would not be identical.  For any one sine wave,
maximum displacement would be measured when the velocity measurement was
zero,  and maximum velocity at a zero displacement measurement.

If we want to relate the two measurements, we can easily see that the
distance traveled between any two DISPLACEMENT measurements is the
difference between the two measurements.  This difference is also
velocity when considered as distance per sample (which is distance per
unit time).  This can also be considered as the differential of the data.

On the other hand, if we want to convert our  VELOCITY readings to
distance, we would need to find the average velocity between each of two
measured velocities which would be the sum of the two velocities divided
by two, also considered as the integral of the data.  We can not expect
to simply integrate the velocity data and obtain distance because we
would be using the velocities measured at the distance points, not the
average velocity that actually caused the resulting measured  traveled
distance.

Now assume that we want to calculate acceleration from the DISPLACEMENT
DATA.  We would first calculate velocity by taking the difference
between the two readings.  Then we would take the difference between two
of the velocity readings (a second differential of displacement) to find
the velocity change per time per time.  We would need at least three
data points to make this series of calculations.

To find acceleration from the VELOCITY data, we can not simply find the
difference between two velocity readings (which is the velocity change
per time per time (the first differential) ) because we would be using
the velocities measured at distance points.  Instead, we should find the
average velocity between two points and then find the difference between
that average velocity and a previous average velocity to reach an
average acceleration.  Again, three data points would be required.

We should notice that both of these processes to find acceleration are
frequency sensitive and will suppress higher frequency data fluctuation's.

Finally, let us consider the STS device with a degenerative feedback
system installed.  Our two sensors would register nearly zero output
because the feedback system works to minimize both velocity and travel
of the boom.  As a result, energy as found in the kinetic energy of
velocity or energy in a spring is not allowed to be stored.  The reduced
storage energy can be expected to minimize the carry-over of energy from
one data sample to another, thus reducing  distortion of the true wave
form of the seismic disturbance.  When a displacement sensor is used to
generate the feedback signal, the resultant trace should still be a
displacement location.  When a velocity sensor is used to generate the
feedback signal, the resultant trace should still be a velocity trace
but the output should about 1.4 times higher than the externally damped
velocity output  because (nearly) all of the incoming energy is
available to generate a detectable reading (rather than being stored in
the boom as kinetic energy or in the spring as potential energy).

Unfortunately, I do not have an STS device so I can not test this
explanation.  Perhaps you or others can enlighten us about the
correctness or failure of this conjecture.

Food for thought,

Roger

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