Abstract

Efficient low-frequency calibration of the entire seismograph system can be accomplished by Fourier analysis of the system response to automatically generated transient test functions applied to the seismometer calibration coil. Typically, such calibrations are restricted to frequencies less than 10 Hz by the ambient ground motion, system noise, and limited dynamic range. To extend the calibration to a broader frequency range, we disconnect the seismometer and take advantage of the fact that the relative amplitude response of the electronic components in most systems can be measured with high accuracy at frequencies from as low as 0.02 Hz to the Nyquist frequency (e.g., 50 Hz) using standard electronics test equipment. The low-frequency amplitude response of the seismometer can then be isolated by dividing the total system response by that obtained for the electronic components. An iterative least-squares procedure is used to estimate the natural frequency and damping coefficient of the seismometer, along with a scaling parameter that specifies the absolute gain of the system. The phase response of the system is calculated directly from the amplitude response using the Hilbert transform. The procedure assumes that the seismometer is an ideal damped harmonic oscillator and that the system as a whole acts as a minimum phase filter. The only instrumental constants that must be known from independent measurement are the seismometer calibration coil force constant and the inertial mass.

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