Bulletin of the Seismological Society of America
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Bulletin of the Seismological Society of America; February 2006; v. 96; no. 1; p. 258-271; DOI: 10.1785/0120050032
© 2006 Seismological Society of America
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Three-Channel Correlation Analysis: A New Technique to Measure Instrumental Noise of Digitizers and Seismic Sensors

Reinoud Sleeman1, Arie van Wettum2 and Jeannot Trampert2

1 Royal Netherlands Meteorological Institute (KNMI)
Seismology Division
Wilhelminalaan 10
3732 GK, De Bilt, Netherlands
sleeman{at}knmi.nl
 (R.S.)

2 University of Utrecht
Faculty of Geosciences
Budapestlaan 4
3584 CD, Utrecht, Netherlands
wettum{at}geo.uu.nl
jeannot{at}geo.uu.nl
 (A.V.W., J.T.)


Figure 001
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  		Figure 1. One-sided power spectral density (PSD) levels (P1 and P2) for an ideal quantization process using two different sampling rates with corresponding Nyquist frequencies F1 and F2. The area of the rectangle bounded by frequency F1 and PSD level P1 equals the area bounded by F2 and P2. Both areas are equal to the quantization noise power in equation (2).

 

Figure 002
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  		Figure 2. Noise floors (PSDs) for three digitizers in the Q4120 datalogger, using short-circuited (50-ohm) input recordings sampled with 100 samples/sec (top) and 20 samples/sec (bottom). The left axes represent the resolution (smallest input voltage that can be resolved) of the digitizer in decibels (relative to 1 V2/Hz), the right axes show the corresponding dynamic range of the system, which has a full-scale (peak to peak) input of 40 V. The horizontal, dashed lines show the resolution of the digitizer in bits, which follows from equation (7). Notice the effect of the FIR filters beyond 80% of the Nyquist frequency.

 

Figure 003
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  		Figure 3. Self-noise floor (measured with common, vertical STS-2 signal, in black) for one digitizer in the Q4120 datalogger compared with the shorted-input self-noise (taken from Fig. 2, in gray), for 100 samples/sec (top) and 20 samples/sec (bottom).

 

Figure 004
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  		Figure 4. Measured gain ratios in the Q4120 datalogger using the 20 samples/sec recordings (common input), using equation (12). The ratios are smoothed over a tenth of a decade and compared with the ratios derived from the calibration sheet (black, horizontal lines).

 

Figure 005
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  		Figure 5. Observed digitizer noise in a NARS datalogger at 20 samples/sec. The light-gray noise level is observed using terminated inputs, the dark-gray noise level is observed while recording a broadband signal. The additional self-noise decreases the dynamic range by a few decibels.

 

Figure 006
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  		Figure 6. A behavioristic model of the digitizer noise in the Q4120 datalogger, based on the observed total noise floor in Figure 3 at a sampling rate of 20 samples/sec.

 

Figure 007
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  		Figure 7. Observed and modeled digitizer noise in the NARS datalogger. The light- and dark-gray levels are taken from Figure 5. The behavioristic model is based on the observed self-noise level (dark-gray level) at a sampling rate of 20 samples/sec.

 

Figure 008
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  		Figure 8. Digitizer models for the Q4120 and NARS dataloggers (at 20 samples/ sec), compared with the NLNM convolved with a noise-free sensor with a flat velocity response and a gain of 1500 V/m/sec (NL0), a noise-free STS-1 sensor (NL1), and a noise-free STS-2 sensor (NL2). The PSDs are relative to 1 V2/Hz. The figure visualizes for which frequencies the digitizer can be used without precaution.

 

Figure 009
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  		Figure 9. Seismic background noise recorded at station HGN by the STS-2 + Q4120 datalogger (gray) and the STS-1 + gain range datalogger (black). From top to bottom are shown the north-south (N), east- west (E), and vertical (Z) components. Each line represents an estimate of the background noise averaged over one day in 2002. All estimates are corrected for the instrument response.

 

Figure 010
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  		Figure 10. STS-2 noise (Wielandt and Widmer-Schnidrig, 2002) compared with the Q4120 noise and NL0 (see Fig. 8), by showing the corresponding PSDs relative to 1 V2/Hz. For this purpose the STS-2 model is multiplied by 1500.

 

Figure 011
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  		Figure 11. PSDs of seismic background noise levels at station HGN in 2002 observed by the vertical component of the STS-1 and a STS-2 sensor, compared with the STS-2 noise model from Wielandt and Widmer-Schnidrig (2002).

 




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