Calibration of Seismometers Using Ground Noise

We have developed and tested a new technique for calibration of seismometers using continuous recordings of ground noise. The method is founded on analytic techniques recently developed for estimation of transfer functions in magnetotellurics. We find that the technique can produce precise, absolute calibration measurements on sensors that do not have calibration coils. The data used are obtained by placing two sets of sensors close enough together that we can assume they record the same ground motion. It is further assumed that one of the sensors has a known, absolute calibration. One then records ground noise of sufficiently high amplitude to guarantee that one is recording above the amplifier noise floor across the entire frequency band of interest. Data are recorded for a time period that depends upon the lowest frequency that is to be resolved. The data is then divided into a series of N partially overlapping time windows, transfer-function estimates are calculated from each of these N time windows, and finally a robust mean estimation procedure is used to produce transfer-function estimates at a set of discrete frequencies. We applied this technique to produce calibration estimates for four different types of sensors (GS-13, triaxial 4.5-Hz L-28, STS-2, and triaxial L4) in various recording arrangements. We found that the technique worked extremely well in every case at frequencies above the point where the sensor output dropped into the instrument noise floor. Problems were consistently encountered above some high-frequency limit that depended upon the site and sensor being tested, and, as a result, we conclude that obtaining reliable results at higher frequencies requires more care in the experimental procedure. We show results from 4.5and 1-Hz passive sensors plastered onto the same pier, which show nearly perfect coherence out to 100 Hz, and excellent agreement with theoretical predictions between 0.03 and 20 Hz. However, above 20 Hz, a systematic phase error plagues our results. Other cases were comparable when care was taken in the experimental procedure, but differed in detail. We argue that there are fundamental problems recording ground noise at these higher frequencies as a result of the following three experimental problems that can be difficult to control: (1) coupling of sensors to a common, stable platform, (2) contamination by acoustic and pier resonances in typical recording vaults, and (3) resonances of the sensor-pier-ground system.