Calibration of the AS-1 Seismometer
(Figure 1.0 Picture of the AS-1 educational seismometer)
This document summarizes a calibration of the AS-1 seismometer. The details of the technique are given in a longer document that is posted on the web site http://quake.eas.gatech.edu/calib/Web version calib chapter.html. If you have any questions, please contact Dr. Leland Timothy Long, School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332-0340.
The response curve Figure 2
Summary of Procedure
The calibration of the AS-1 (Figure 1) proceeded in two independent parts. The first part was the calibration of the mechanical response of AS-1 seismometer, including the sensitivity of the magnet and sensor coil. The second part was the calibration of the digitizing unit. The total response is the combination of the two parts (Figure 2).
The AS-1 seismometer
The AS-1 seismometer shown on the front page is a rotating system. The mass consists of a magnet and other attachments on a beam that is constrained to rotate in the vertical plane about a connecting hinge on a vertical support. The hinge is a knife-edge resting in a groove in the beam. The width of the knife-edge inhibits horizontal movement. The mass is supported by a spring with a relatively low spring constant. The design is much like that of the gravity meter, except that the spring is not zero length. A zero length spring would have allowed a longer natural resonance period. The free period is 1.3 seconds for the instrument tested. The free period was measured by removing the damping oil and timing the duration one oscillation. The duration of 10 oscillations was actually used to obtain a better average estimate for one cycle.
The damping is achieved by an oil bath. For this calibration two-cycle engine oil was used. The water shown in the figure on the cover was not used because the damping was insufficient. The system with the oil gave a response that is very close to critical.
The moment of inertia was computed because the AS-1 is a rotating system. This was accomplished by taking the instrument apart and measuring the weight and dimensions of each element. Then the moment of inertia was computed from the approximate shape of each element and its position relative to the axis of rotation. The moment of inertia was 443300 grams cm2. The total mass was 465.3 grams. The equivalent length for a mass on a beam system was 30.86 cm.
We use a test weight of 0.456 g, placed at a distance of 28.8 cm. The center of mass is at 28.8 cm and we marked this position on the beam with a thin white strip of tape.. The test weight corrected to distance equivalent to the center of mass at 30.86 cm is then 0.0425 g.
Figure 3. Sensing coil of the AS-1 showing calibration coil wire attachment.
In order to create a calibration coil, a number of loops of fine wire were wound around the sensing coil (Figure 3). A digital ammeter was used to measure the current in the calibration coil and held in place with tape. The current was put into the calibration coil using a relay circuit that can be driven by the computer through the parallel port. When the relay is closed, a current is put through the coil, when the relay is open no current goes through the calibration coil.
The Cheap Seis AD unit was used to record the signal from the seismometer. The Cheap Seis AD is a 16 bit analog to digital converter that is flat from DC up to a folding frequency of 10 Hz. The weight lift was performed and the height of the calibration pulse observed and measured. A height of 0.0011 mVolts was obtained for a test weight of 0.04241 grams (corrected for distance from the axis). Similarly, the height of the calibration pulse from the calibration coil was measured. For a current of 96.5 mAmp, the height of the calibration pulse was 0.009 mVolts. The motor constant for the calibration coil is 13217 mAmp/m/ss.
The Cheap Seis AD unit includes an option to generate a timed calibration pulse and record the response to a separate file. The calibration can then be computed as a function of frequency using Fourier transforms. Using the motor constant and calibration current, the frequency response for the AS-1 is given in Figure 4.
Figure 4. Frequency response of AS-1. The high-frequency response is at 21 dB, or 11 Volts/m/s.
The frequency response is typical for a 1.0 Hz velocity transducer that has damping slightly less than critical. The sensitivity falls off at 12 dB per octave below 1.0 Hz. The noise is dominant above 2.0 Hz. However, more high frequencies in the calibration signal would have increased the signal to levels above this noise. The 11 Volts/m/s is lower than the response of commercial 1.0 Hz geophones by about a factor of 10. The high-frequency response is 11 V/m/s and the peak response is 13.5 V/m/s at 1.0 Hz.
The AS-1 Digitizing Unit
The AS-1 digitizing unit was calibrated for frequency response separate from the AS-1 seismometer. A frequency generator was used to generate a signal with a known frequency and amplitude. The signal level was attenuated using a voltage divider to provide an appropriate level for input into the digitizing unit. The response was measured from the screen plot of the signal. The digitizing rate was unknown, perhaps 6 samples per second. The response measurements were limited to frequencies lower than 1.0 Hz, corresponding to those reliably represented by the approximate 6 samples per second digitizing rate.
There was a noticeable non-linearity associated with frequencies below 0.03 (30 seconds period). The response anomaly is caused by the use of polarized components in circuits with both positive and negative voltages. However, these calibration measurements for the AS-1 seismometer suggest that, the AS-1 does not respond to ground motions at periods much greater than 20 seconds.
The response of the digitizing unit is given if Figure 5. Figure 5 also shows the AS-1 instrument response and the combined amplitude response of the total system. The phase response has not been measured. The phase response could be measured for the seismometer, but additional software would have to be developed to find the phase response for the digitizing unit.
Figure 5. Response of the AS-1 and digitizing unit.
The AS-1 digitizing unit has a peak response near 0.08 Hz.(12 seconds). The low frequency response falls off at a rate of 6 dB per octave below 12 seconds. Above 12 seconds the fall off is 12 dB per octave. Close to 1.0 second and above, the response appears to fall off faster, probably because of the existence of anti-aliasing filters. The net effect of the high-frequency attenuation of the amplifier is to cancel out the low-frequency attenuation of the AS-1 seismometer response. This yields a seismometer with a total response that peaks about 0.4 Hz (2.5 second period).
A comparison with the Guralp PEPPV in Figure 6 shows that the PEPPV has a wider response range and a much flatter response in areas of interest, 20 seconds to 1.0 Hz.
Figure 6. Comparison of Guralp PEPPV and AS-1 seismometer response curves.
The AS-1 is a 1.3 second period velocity transducer with a response of 11 Volts/m/s, about 10% that of a conventional 1.0 second period geophone. The digitizing unit applies heavy filtering to lower the peak response to a 3-second period system that will record data in the range of 20 to 0.5 seconds period. The gain varies over this range by over a factor of 10. The instrument calibrated for this report has a free period of 1.3 seconds, and a total response that suggests critical damping.
Applying Calibration to Other AS-1 instruments.
Individual AS-1 systems may be calibrated relative to this system by a fairly simple weight lift procedure. For this test a weight of .0.0114 grams was made out of a 0.5 by 3 cm strip of paper with an average weight of 0.00761 grams /cm2. This was placed on the arm as shown in figure 7. A non-magnetic wire was used to gently lift the weight, and place it back on the mass. Only the weight lifts were measured, ignoring the weight drops. Figure 8 shows the responses we observed. The average height is1025 units, which we measured on the screen by adjusting the zero balance pot and reading the values. The values could also be read by triggering the calibration signal and viewing the trace. The uncertainty in this measure is about 75 digital units, which is caused primarily by the variations in the background noise.
Figure 7. Picture of 0.0114 gram weight placed on center of mass.
If the peak displacement is the same, and the free period and damping are the same, then the displacement response of figure 2 can be used directly.
If the peak displacement for 0.0114 grams is different then the calibration curve should be adjusted to a new peak response by using the equation:
New Peak Response = (Your Displacement in digitizing units)*0.097
If you use a different weight in the weight lift, the relation is
New Peak Response = 0.0011* (Your Displacement)/(Your weight (grams))
This correction should compensate variations in motor constant and other uncertainties related to using electronic components with 10% accuracy. The largest source of error here is measuring the height of the pulse in the presence of background noise.
Figure 8. Sequence of 4 calibration pulses as observed on the monitor.
Correcting for possible differences in response spectra.
A complete evaluation of the calibrations should consider all the elements contributing to the calibration. These effects are lumped into the weight lift signal, directly in terms of its amplitude and indirectly in terms of changed in shape. There are two factors that can measurably affect the shape of the response function. To evaluate these, we simulated the mechanical and electrical response of the seismometer and amplifiers for the digitizer. Using the theoretical response, we varied (a) the free period and (b) the damping of the seismometer.
Figure 9. Effect of changes in free period on velocity response.
a) Figure 9 shows the effect of free period on the velocity response. Below the natural period of 1.3 seconds, the response is changed in proportion to the square of the instrument's free period. Measurement of the free period is described above.
Corrected Response = (free period)*(free period)*0.6*(plotted response)
This works for either displacement or velocity response.
Figure 10. Effect of changes in natural period on the velocity response.
b)Figure 10 shows the effect of damping on the response curve. In general, the use of any heavy oil will give a damping that is near critical, a value of 0.75 to 1.0 in figure 10. Corrections for less damped systems will probably not be necessary unless a fluid less viscous than a heavy oil is used, such as water. In this case it is suggested that the damping fluid should be changed to heavier oil. The effect of damping is confined largely to the response near 1.0 Hz, the range of measurement for body wave magnitudes. This would cause a maximum uncertainty in magnitude of 0.1 units, small compared to natural variations in magnitude measurements. When calibrating the peak amplitude of the response curve above, variations in damping close to critical are largely factored into the amplitude calibration. Complete correction for variations in damping would require calibration as a function of frequency of the total system. Unfortunately, the anti-aliasing filters, which are undefined, start to interact with the response above 1.0 Hz and the effect of these on the apparent damping response is more difficult to determine.