This is my idea of a calibration plan for my S-G seismometers.  So look
it over and shoot holes in it!!  I am going to use a computer that has
an A/D (12 bit) Board and LABview.  I will plot the output of the S-G
circuitry (high output) and plot voltage vs time.  I can get fairly
accurate readings of voltages and time using the LABView software.  Most
of my calibration plan comes from the "Manual of Seismological
Observatory Practice".  Keep in mind that this is pure theory, I haven't
tried any of these procedures yet!!  I am also going to disassemble my
SGs and weight each pendulum and measrure center-of-gravity using a
knife-edge or string loop.

Measure the natural period:

1.  Connect the S-G output to the data plotting system and install
calibration coil (see my webpage).
2.  Disconnect damping (I have a toggle switch on controller box).
3.  Using leveling screws, adjust the voltage output to as close to 0 as
possible (I have 1/4"-80 leveling screws).  This can be roughed in using
the 'tilt' LED on SG card (which I have moved to outside of box).
4.  Set pendulum into oscillation by discharging a capacitor into
calibration coil.
5.  Record the the oscillations on plotting system.
6.  Measure several periods and average to determine the apparent period
T's.
7.  Measure the amplitude of the waveform from the 0 line to peak and
label each successive crossing of 0 line as a[1],a[2],...a[n].
8.  Calculate the mean value of logarithmic decrement L[r] =
log[(a[r]+a[r=1])/(a[r+1]+a[r+2])] {log base 10}.  I am a little unclear
as to how to calculate the "mean value".  The best I can come up with is
to 'slide a window' three (3) samples wide down through the data and
calculate the L for each 'stop'and then average these values.  I have
looked through my math books and found nothing on logarithmic decrement
(anybody got a reference?).
9.  Calculate the true period Ts = T's/(1+0.53/(L*L))**0.5.

Measure static magnification:

I have three leveling screws (1/4"-80) located in a triangular pattern.
The distance from the back (2) leveling screws and the front (1)
leveling screw is 10.00".  If my trig is right, one turn of leveling
screw is 0.00125 radian of tilt.  I also plan to use a dial indicator to
measure the actual lift of front edge of base and modify my trig
accordingly.

Also, the scheme I am using is described in the Manual of Seismological
Observatory Practice to calibrate the magnification of the tilt of
seismometer and mechanical indicator.  I think it should work to give
the magnification of the seismometer and the voltage output of the S-G
board.  Once I have that, I should be able to convert the voltage levels
into SDR A/D units.  I have a voltage calibrator at work that outputs
voltage to three places to the right of decimal point.  I plan to
generate a series of readings and plot on spreadsheet.

1.  Measure the natural period as above (Ts).
2.  Connect the S-G output to the data plotting system and verify that
damping is off.
3.  Using front leveling screw, adjust the voltage output to as close to
0 as possible.
4.  Apply a know tilt (single turn of leveling screw or via dial
indicator) and record voltage level.
5.  Keep increasing tilt until output (voltage) reaches level that
indicates maximum travel (to be determined--maybe where the linearity
falls apart).  Record each step change in tilt and resoluting voltage
level.  Keep the step changes equal.
6.  Return tilt to 0 volts.
7.  Repeat step #5 with tilt in opposite direction.
8.  Enter the recorded data into spreadsheet and generate calibration
curve.
9.  Calculate the undamped natural frequency Omega = (2*PI)/Ts
10. Solve for the static magnification (l/l')

          (l/l') = a/(tilt*g*Omege*Omega)  a is voltage deflection
                                           g is gravity (9.81m/(s*s))

Now, this is where I am having a problem!  I am now like the dog who
chases cars, what am I going to do if I catch one! :).  I now should
have a binary_count_SDR/radian calibration factor or factors (if
linearity too bad, maybe a piecewise linearization would help), how do I
convert this into parameters that can be used to correlate data between
stations??

Measuring Damping:

1.  Reconnect damping.
2.  Connect the S-G output to the data plotting system.
3.  Install calibration coil.
4.  Apply pulse to calibration coil by discharging a capacitor into it.
5.  Record oscillations on plotting device.
6.  Measure the elapsed (t)time from first peak of oscillation (a[1]) to
the second peak on the other side of 0 line (a[2]).
7.  Calculate normalized time (t')  t' = omega*t
8.  Calculate a[2]/a[1] to determine which curve to use in Fig 4.2.4 in
Manual of Seismological Observatory Practice.  Look up value of damping
(Beta) based on proper curve and t'.

According to Larry's SG Sensor Damping Adjustment instructions, the
damping potentiometer should be set so that the oscillation should die
away in about 1-1/2 cycles.  This adjustment can be accomplished by
using steps 1-5 until the waveform has proper decay and then continue to
convert that setup into a damping factor.

---------

Have mercy!!  I am really a neophyte in the seismometer design area!!


--
Rex Klopfentein, Jr.
rklopfen@.........
http://www.wcnet.org/~rklopfen



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