Measuring seismometer nonlinearity on a shake table

Wielandt, E, Zumberge M.  2013.  Measuring seismometer nonlinearity on a shake table. Bulletin of the Seismological Society of America. 103:2247-2256.

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We have measured the nonlinear distortion in six broadband seismometers on the vertical shake table at the Institute of Geophysics and Planetary Physics La Jolla: a vertical STS1, three STS2s, a CMG-3T, and a Trillium 240. In each case, low-frequency intermodulation of a two-tone signal was observed for six frequency pairs near 0.25, 0.5, 1, 2, 4, and 8 Hz at a beat frequency of 0.02 Hz. The peak velocity amplitude was 6: 3 mm/s, which is about half of the operating range of an STS2 or CMG-3T. We found similar distortion levels in all seismometers: The average over all distortion ratios is -96 dB +/- 7 dB (standard deviation) in terms of equivalent ground acceleration, with a tendency to higher distortion at higher frequencies. When the same signals are expressed as electric output voltages or equivalent ground velocities, ratios are much higher and increase rapidly with frequency: around -65 dB at 1 Hz and around -40 dB at 8 Hz. The distortion of seismic signals cannot be predicted from the distortion of electrical signals fed into the calibration coil, and the electrical distortion is about 30 dB lower in one of the STS2s. Low-frequency distortion of the table motion has a level of -140 dB at 1 Hz in terms of acceleration, which is far below that of all seismometers. This number does not indicate a super-linear table motion but results from expressing the distortion present in the table displacement at -72 dB as a ratio of accelerations. What may seem to be a trivial conversion has a very practical implication: The linearity of seismometers can be tested on moderately performing shake tables.