The response curve
This document summarizes a calibration of the AS-1 seismometer performed by L.T.Long. The details of the technique are given in a longer document at http://quake.eas.gatech.edu. 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.
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 and the velocity response of the sensor coil. The second part was the calibration of the digitizing unit. The total particle velocity response is the combination of the two components (Figure 2). Multiply this curve by angular frequency to obtain the displacement curve.
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 pivots vertically about a connecting hinge on a vertical support. The hinge is a knife-edge on the beam in a flat groove that 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. Hence, the long period is not optimized and the free period is about 1.0 seconds.
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 was still slightly under damped. Heavier oil or more area on the damping mechanism could push the damping closer to the more desirable 0.7 critical damping.
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 0.0456 g, placed at a distance of 28.8 cm. The test weight corrected to the equivalent length is then 0.0425 g.
Figure 3. Sensing coil of the AS-1 with the calibration coil wire attachment.
For the 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. 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 slightly under damped 1.0 Hz velocity transducer. 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 eliminated this noise. The 11 Volts/m/x 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, but the high-frequency response was limited to 1.0 Hz.
There was a noticeable non-linearity associated with frequencies below 0.03 (30 seconds period). The response anomaly is most likely caused by 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 these low frequencies.
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 computed. The phase response can be obtained easily 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 at 0.1 Hz (10 seconds). The low frequency response falls off at a rate of 6 dB per octave below 10 seconds. Above 10 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 is to compensate for the low-frequency attenuation of the AS-1 seismometer response. This yields a seismometer with a total response that peaks at 0.4 Hz (2.5 seconds period). The measured response agrees to within the tolerance of the electronic components with the expected response for the amplifier circuits used in the digitizer. The amplifier consists of a low-cut filter of 6dB per octave at 0.12 Hz and two high-cut filters at 6dB per octave at 0.12 Hz. Two additional high-cut filters are used for anti aliasing for frequencies above 1.0 Hz.
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 1.0 Hz velocity transducer with a response of 11 Volts/m/s, about 10% that of a conventional 1.0 Hz geophone. The digitizing unit applies high gain and heavy high-cut 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.