PSN-L Email List Message

Subject: Pendulum Q
From: Roger Sparks rsparks@..........
Date: Sun, 21 Jan 2007 12:14:28 -0800

Good Morning All,

Of course removing the damper will improve the sensitivity of a 
seismometer.   Yes, it takes power to move a pendulum from the rest 
position, and earthquakes provide that power.  Once moving, the pendulum 
is considered to have stored energy in the form of velocity (which is 
measured in relation to stationary surroundings).

A pendulum will continue to receive energy from ongoing waves as time 
passes, and the pendulum (if friction free and undamped) will integrate 
the positive and negative motions into an instantaneous velocity.   The 
instantaneous velocity would be the sum of all the impulses over the 
time period since the instrument was constructed (a very long time).   
This is only true for an ideal pendulum.

An ideal pendulum can be digitally approximated easily from a damped 
pendulum.   This is done by summing all the readings from the moment of 
first "switch on".   This is not too practical.

More practical,  we can recognize that even an undamped pendulum will 
have friction from hinges, air and sensor interactions.   It will have a 
decay curve as the energy from an initial impulse is lost to friction.   
The pendulum will also have a natural frequency which is constant for 
any dimensionally stable system.  Both the decay curve and pendulum 
frequency can be modeled in software.  Once modeled, the effect of each 
discrete impulse can be subtracted from (or added to) the pendulum's 
ongoing output signals.   Assuming we are using velocity detector, the 
subtracted result would be instantaneous acceleration, the added result 
would be the displacement. 

To use this method, the pendulum's period and Q would be critical 
measurements.   Any difference between the model and actual instrument 
response would result in a digitally introduced error.   In practice, 
the errors should be small over the time periods of interest.

Larry has made available in Winquake a feature called "Integration".  
The help file has the following for this function:

*/"Integrate Data Alt+I/*

Used to integrate the data set. Integration converts acceleration to 
velocity and velocity to displacement."

This brings up a very important point--what is the pendulum sensor 
reading?   Is it acceleration, velocity, or displacement?

I need help here.   I think we could make an acceleration detector with 
a strain gage, which changed resistance under strain.   Magnetic sensors 
are all velocity detectors because they move through a changing magnetic 
field.   A capacitive detector is a displacement detector because the 
output signal is the result of relative positions.  

Back to Larry's integration feature.   He seems to have anticipated at 
least part of this discussion by providing the integration feature.   By 
integrating the signal over what ever time period desired, we accurately 
model the output of an undamped pendulum.   The only difference is that 
about 1/2 the power of the earthquake signal is lost in the damping 
system of the damped pendulum.  This reduces the signal to noise ratio, 
but only the noise from seismometer and electronics, not noise from the 
actual seismic signal.

It is interesting to notice that the process of display can change the 
character of the signal.   For example, a displacement display would 
represent the relative position on a chart.   The larger the difference 
in position, the larger the display difference.   But the sensor must 
have had an acceleration and velocity as it moved, so the display is 
actually an integrated sum of the acceleration and velocity 
components.   The only thing that has really changed from velocity or 
acceleration detection is that the phase of the displayed result has 
changed in time.  If  acceleration or velocity is measured, we can 
predict where we are going.   If displacement is measured, we know where 
we are at the instant of measurement.




Public Seismic Network Mailing List (PSN-L)

[ Top ] [ Back ] [ Home Page ]