Force-balance sensors cannot be tested for instrumental noise with the mass locked. Their self-noise can thus only be observed in the presence of seismic signals and seismic noise. Although these are generally a nuisance in this context, natural seismic signals may also be useful as test signals. Marine microseisms should normally be visible on any sensitive seismograph whose seismometer has a free period of one second or longer; they normally form the strongest continuous signal on a broadband seismograph. However, their amplitude exhibits large seasonal and geographical variations.
For broadband seismographs at quiet sites, the tides of the solid Earth are a reliable and predictable test signal. They have a predominant period of slightly less than 12 hours and an amplitude in the order of 10-6 m/s2. While normally invisible in the raw data, they may be extracted by low-pass filtration with a corner frequency of about 1 mHz. It is helpful for this purpose to have the data available with a sampling rate of 1 per second or less. By comparison with the predicted tides, the gain and the polarity of the seismograph may be checked. A seismic broadband station that records Earth tides is likely to be up to international standards.
For a quantitative determination of the instrumental noise, two instruments must be operated side by side [Holcomb 1989,Holcomb 1990]. One then determines the coherency between the two records and assumes that coherent noise is seismic and incoherent noise is instrumental. This works well if the reference instrument is known to be a good one, but the method is not safe. The two instruments may respond coherently to environmental disturbances caused by barometric pressure, temperature, the supply voltage, magnetic fields, vibrations, or electromagnetic waves. Nonlinear behaviour (intermodulation) may produce coherent but spurious long-period signals. When no good reference instrument is available, the test should be done with two sensors of a different type, hoping that they will not respond in the same way to non-seismic disturbances.
The analysis for coherency is somewhat tricky in detail. When the transfer functions of both instruments are precisely known, it is in fact theoretically possible to measure the seismic signal and the instrumental noise of each instrument separately as a function of frequency. Alternatively, one may assume that the transfer functions are not so well known but the reference instrument is noise-free; in this case the noise of the other instrument and the relative transfer function between the instruments can be determined. As with all statistical methods, long time series are required for reliable results. We offer a computer program UNICROSP for the analysis.