Three-channel correlation analysis: A new technique to measure instrumental noise of digitizers and seismic sensors

This article describes a new method to estimate (1) the self-noise as a function of frequency of three-channel, linear systems and (2) the relative transfer functions between the channels, based on correlation analysis of recordings from a common, coherent input signal. We give expressions for a three-channel model in terms of power spectral densities. The method is robust, compared with the conventional two-channel approach, as both the self-noise and the relative transfer functions are extracted from the measurements only and do not require a priori information about the transfer function of each channel. We use this technique to measure and model the self-noise of digitizers and to identify the frequency range in which the digitizer can be used without precaution. As a consequence the method also reveals under which conditions the interpretation of data may be biased by the recording system. We apply the technique to a Quanterra Q4120 datalogger and to a Network of Autonomously Recording Seismographs (NARS) datalogger. At a sampling rate of 20 samples/sec, the noise of the Q4120 digitizer is modeled by superposition of a flat, 23.6-bit spectrum and a 24.7-bit spectrum with 1/f(1.55) noise. For the NARS datalogger the noise level is modeled by superposition of a 20.8-bit flat spectrum and a 23.0-bit spectrum with 1/f(1.0) noise. The measured gain ratios between the digitizers in the Q4120 datalogger, smoothed over a tenth of a decade between 0.01 Hz and 8 Hz for data sampled with 20 samples/sec, are within 1.6% (or 0.14 dB) of the values given by the manufacturer. Finally, we show an example of seismic background noise observations at station HGN as recorded by both an STS-1 and a STS-2 sensor. Between 0.01 and 0.001 Hz the vertical STS-2 noise levels are 10-15 dB above the STS-1 observations. The Quanterra Q4120 digitizer noise model enables us to exclude the contribution of the digitizer noise to be responsible for this difference.