Current high resolution data aquisition systems are designed to match as much as possible with the bandwidth (e.g. 360 s - 10 Hz) and dynamic range (up to 160 dB) of todays broadband and very broadband seismic sensors. These digitizers are based on delta-sigma modulators, which have the property to decrease the quantization error at lower frequencies at the price of increased quantization error at higher frequencies. By using a high initial sample rate (order of tens of kHz) the quantization noise will decrease significantly in the frequency range of interest (e.g. below 100 Hz). The dynamic range of these type of digitizers, often expressed by a single number representing the ratio between the largest and smallest signal that can be recorded, may range up to about 145 dB. However, this single number representation does not reflect the true dynamic range as function of frequency. First, the dynamic range depends on the sampling rate, and second, the the self-noise of the digitizer will increase at lower frequencies like in any other active electronic component (the so-called 1/f noise). It is important to have this kind of information available as the choice for a particular type of sensor or digitizer is often driven by constraints on the frequency band and the amplitude range of interest. So this information may be used as selection criterion for sensors and/or digitizers. But also for the interpretation of data it is required to have knowledge of the dynamic behavior of the system. For example, the presenc of 1/f noise may bias the data analysis at lower frequencies and the resolution of the digitizer at a particular frequency determines the minimum amplitude that can be resolved properly at that frequency.

In the conventional approach to measure instrumental noise (self noise) of linear systems, two systems are feed by a common coherent input signal. Two seismometers, for example, are placed together at the same pier so it can be assumed that they record the same ground motion. The mathematical solution of this technique to extract the noise is very simple, but it requires accurate knowledge of the transfer functions of the systems. Small errors in the two linear systems will cause relatively large errors in the estimated noise levels.

A new approach is developed by R. Sleeman, A. van Wettum and J. Trampert (2005, accepted by BSSA) in which 3 linear systems are used. The mathematical description of a 3-channel system shows that analysis of the output recordings can resolve: (1) the noise spectrum for each channel, and (2) the ratio of transfer functions between the channels. The technique does not use the transfer functions, and is therefore independent of the accuracy of the transfer functions, which is a potential source of error in the 2-channel method. As a consequence the 3-channel method also reveals under which conditions the interpretation of data may be biased by the recording system. Figures 1 and 2 show examples of the measured noise spectra of a 3-channel Q4120 digitizer and the relative gains between each pair of digitizer.

Publications

• Three-channel correlation analysis: a new technique to measure instrumental noise of digitizers and seismic sensors.
  R. Sleeman, A. van Wettum and J. Trampert, accepted by Bull. Seis. Soc. Am., 2005.

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