AS1 Calibration

I've run into an interesting problem with my lift-test calibration of the AS1 system.  I followed Larry Braile's instructions for a "relative" calibration.  

The first task was to make a small test mass.  I cut a piece of cardboard, like that attached to the back of a pack of lined paper, 6 mm by 12 mm.  This was folded to form a tent shape (like an "A" without the cross bar). I attached a very fine thread with tape to the top center of the "tent" so that it would land upright when lowered onto the boom.  Another piece of tape was attached to the other end of the thread so that I could find it.

The weight of this "test mass" is 0.0374 grams.  Here's one way to make a test mass.

Next I marked a place on the AS1's horizontal boom 10 cm from the hinge.  I first made a rather broad line perpendicular to the boom with white correction fluid and then, when dry drew a thin line at exactly 10 cm.  I then drilled a hole in the Plexiglas cover right over this mark. The hole was just large enough to allow the test mass to pass through.  The hole is located 14.5 cm from the end and 7.7 cm from the edge of the Plexiglas cover.

I lowered the test mass onto the boom and waited for the signal to die down.  Then I quickly raised the test mass to see the response of the AS1 system to a step in acceleration.  The upper portion of Figure 1 shows the result of this lift test.  Note the ringing superimposed on the low frequency pulse.  The ringing has a period of about 1.6 seconds, which is the period of the sensor.

Figure 1. 3 3/8" diameter container with two different grades of oil.

I decided that the damping must be too low.

I then carried my AS1 instrument into the USGS to do a side-by-side comparison with the instrument located at the USGS. The only component that I left behind  was the container of damping oil.  Both instruments worked well and the amplitude of any ringing was greatly reduced.

I then returned home, switched to back to my damping cup and oil and the ringing was back again (Figure 2, lower).

Since the original Plexiglas container had leaked, I was using a cut-off lower 3 inches of a water bottle with an inside diameter of 3 3/8 inches.  I thought that perhaps the plastic was too flexible, so I tried a 3-inch inside diameter coffee cup.  This didn't help.  I then changed to a 2 5/8 inside diameter aluminum cup, made by cutting off the lower 3 inches of a soft drink container.  This worked much better (Figure 2, upper).  This is similar to the container used at the USGS.

 

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Figure 2. Upper: Oil in Smaller Container with 2 5/8" diameter. (SAC file)
Lower: 3 3/8" diameter container with the same oil.

As an additional test of damping, I attached the system with the aluminum oil cup to an amplifier with high input impedance, and then to a DATAQ AD.   This amplifier did not produce the very low frequency pulse seen above, but the 1.6 second sensor signal was clearly highly under damped.  With a very small resistor across the coil, the latter system was over damped.

In conclusion, I now believe that the size and possibly the shape of the damping-oil container has a big effect on the damping of the AS1 system.   The depth of the washer below the surface of the oil is probably important as well.  I think that the input impedance of the AS1 "black box" amplifier must be low enough to further dampen the motion of the boom.

I don't have the container that is supplied with the AS1 or one of the Plexiglas containers that IRIS provided, but it would be interesting to compare the damping with these.

October 18, 2004, Update

I recently returned from visits to 6 schools that are running AS1 systems. (See http://jclahr.com/science/earth_science/iris_sept_2004/)  As suggested by Chris Chapman, it isn't the depth of the washer within the oil container, but rather the distance of the washer from the bottom of the container that is important for proper damping.  For the lift test below I've now switched to one of the square dishes provided with the AS1.

Figure 3.  Oil in square dish. (SAC file)

To eliminate the ringing apparent in Figure 3, I've raised the square oil dish by the thickness of two CD's.

Figure 4. Oil in square dish resting on 2 CD's (SAC file)

October 25, 2004

 
Using the new version of AmaSeis, this is the instrument response of WGCO, based on a 30-s lift-test calibration record of October 18.  2 CD's.

October 26.

The damping was not as great today, so I added a third CD.  Upper: 2 CD's. Note that damping is now less than on October 18 (SAC file).  Lower: 3 CD's. (SAC file),

 

3CD Instrument Response.

October 31, 2004.  More work on damping.

I tried just running the AS1 directly into a Dataq DI154 AD and looking at the lift test.  The gain was so low, that to get any signal I had to use a much larger mass located at the end of the boom.

The .sac calibration file I got (with 5w30 oil, square dish on 3 CD's) is here:
DI154cal.sac  and it indicates that the system is under damped (at least with these high amplitudes).  This record was made with a sample rate of 6 Hz.

November 1

Yesterday I ran a lift calibration of the AS1 system directly into a DATAQ DI154 AD unit.  The output indicated that the system was a bit under damped, but I was concerned because I had to use quite a large weight to get enough motion to register on the AD.  Even then the maximum amplitude was only a few counts.

Tonight I set up an amplifier so that I could look at a lift test calibration with smaller amplitude.  The circuit is here:  amp1000a.jpg  This amplifier has a gain of 1000 and a Low-Pass Filter corner at 4.8 Hz.

The .sac calibration file from today, with 120 Hz sample rate and using the amplifier is here:  DI154g1000.sac .

Both calibrations are quite similar with respect to the implied damping and both indicate that the system is under damped.  It's at least good to see that the oil damping is quite similar over this large range in amplitudes.

The lift test with my standard weight and and the AS1 black box, is here:
wgco_sq3cda.sac

November 2

I took a look at the peaks of the lift test I did yesterday ( DI154g1000.sac ) to see what the ratio of actual damping to critical damping would turn out to be.
Peak    Amplitude
A1      -1359
A2      669
A3      -330
A4      163

I computed the ratio of actual damping to critical damping from a measurement of the height of adjacent peaks, using the calculator on this page:
http://jclahr.com/science/psn/damping/
 

Peaks        Damping Ratio
                Actual/Critical Damping
A1 / A2     .22
A2 / A3     .22
A3 / A4     .22

Since we're shooting for a ratio of .7 to .8, this system clearly has a ways to go.

November 3

Today I tried a number of different oils to see which would give sufficient damping.  I'm using the small square dish and I've removed all of the CD's from under the dish.  Here are the results:

Oil Sac File  Damping Ratio Amp. of 1st Peak (counts)
5W30 5w30cal.sac 0.22 1307
20W50 20w50cal.sac 0.41 1036
1/2 STP and 1/2 10W40   Over damped  
1/3 STP and 2/3 10W40 thirdstp_10w40.sac 0.65 679

The graph above shows the lift test for 1/3 STP and 2/3 10W40 oil.  This is only slightly less damped (0.65) than the target range of 0.7 to 0.8.  This is a "thin spring" system.

November 8

At the GSA meeting in Denver I set up the "thin spring" AS1 instrument and used this opportunity to check its damping.  I used the small, square oil container with a combination of 10w40 oil and STP Oil Treatment and the same weight (0.0374g) as for my tests at home.

Lift response with 10w40 oil.  SAC file.

This is the same lift test but the AS1 "black box" has been replaced with a simple 1000x amplifier that has a single high cut corner at 4.8 Hz feeding a DATAQ DI-154RS AD.  Also, a larger mass has been used for this test. The system is clearly quite under damped with just 10w40 oil.  SAC file.

This is a repeat of the last lift test using 1/3 STP and 2/3 10w40 oil.  The damping is much better, as the ratio of the peaks above implies that the ratio of the actual damping to the critical damping is 0.6.  SAC file.

Switching back to the AS1 "black box" amplifier and the smaller weight, the lift test no longer shows the inflection point on the first up swing or the extra ripples that are characteristic of an under damped system.  SAC file.

 

As an alternative to lifting a weight from the boom, this calibration was done by placing a large metal washer just outside of the Plexiglas cover, weighting for the boom to adjust to a lower position due to attraction between the magnet and the washer, and then pulling the washer away quickly using an attached thread.  I used a hefty washer with outside diameter of 1 1/4 inches.  Although the amplitude of the pulse can not be accurately set with this calibration technique, one can check the shape of the pulse to determine if the system is under damped, as well as verify that the polarity is correct.  SAC file.

References

Calibration pulses from a number of schools are also posted here.

Larry Braile's Calibration Page: http://www.eas.purdue.edu/~braile/edumod/as1mag/as1mag1.htm

Tim Long's Calibration Page: http://quake.eas.gatech.edu/MagWeb/CalReptAS-1.htm

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