Seismic Filter Considerations

Whenever the output of a given seismometer is subject to noise, i.e., signals that represent anything other than the true motion of the earth, some form of filtering of the output signal is needed to eliminate that noise. There are two major forms of electrical noise that seem to present the most trouble to amateur seismic recording systems: 60-Hz powerline noise with it's harmonics, and the very low-frequency noise caused by the characteristics of the preamplifier used to amplify the faint signal from the pickup coil. Treating the former is easy. Treating the latter is a bit more difficult. The remaining form of noise is not electrical in nature, but rather is a true earth-motion. It is caused by local, manmade disturbances such as building vibrations resulting from nearby traffic or machinery. This form of noise however, has a periodicity sufficiently different from those of the earthquake waveforms we are interested in, and can thus be filtered without causing too severe a degradation to the waveforms of interest. The preamplifier, as shown, incorporates a simple, 1st-order filter in the feedback loop, consisting of the 0.01 µFd capacitor and the 10-Megohm resistor. The cutoff, or "turnover" frequency of this network is 1/(2*pi*R*C), or 1.6 Hz. This is the frequency where the output response of the filter is 1/2 the power of the unfiltered signal (also referred to as the -3 dB point). A 1st-order lowpass filter has a 6-dB per octave falloff response beyond this half-power point. Thus, any 60-Hz powerline "noise" will be reduced in amplitude by a factor greater than 1000, (31-dB to be exact). Because we are interested in seismic signals that have a period greater than 1-second, such a filter has no adverse effect on the quality of our recorded waveforms. Very low frequency noise, typical of op-amps such as the 741 or even the so-called "low-noise" bi-FET op-amps like the NE5532, can cause erratic baseline shifts in recorded waveforms, with periodicities ranging from 1-second to several hours. This type of noise is inherent in most typical op-amps. You can check any existing system for this type of noise by simply recording the signal while the seismometer's pendulum is blocked. Any variance at all from a straight-line (zero-signal) trace is indicative of this type of noise. A quick and easy cure is to use a commutating-auto-zero op-amp that virtually eliminates this type of noise by periodically sampling it's own offset drift and automatically correcting for it. As mentioned in the referring page, they can be a bit "pricey," but their use is well-worth the added cost. Filtering out the signals resulting from nearby ground-motion disturbances, without degrading the waveforms resulting from earthquakes, requires a more elaborate approach. Because the amplitude of the disturbances is of similar magnitude to those of the earthquakes, we need a filter that has a much sharper "turnover" curve -- i.e., one that drastically reduces signals above about 1-Hz in frequency, without attenuating those signals of longer period. Creating a sharper cutoff curve is accomplished by increasing the filter order. A 2nd-order filter attenuates frequencies at a rate of 12- dB per octave. Each order of increase adds an additional 6-dB per octave attenuation for those frequencies above the design cutoff frequency. The preamplifier/filter as described, utilizes a 2nd-order filter tuned to a cutoff frequency of 0.31-Hz, corresponding to a 3.2-second period. Examination of the response characteristics for this filter shows that signals with a period of 4-seconds or longer are unattenuated. Signals with a period of 3.2-seconds are attenuated by 3-dB, while those with a period of 1/2-second are attenuated by 31-dB. Thus, localized, short-period disturbances are effectively eliminated from the seismic waveform. Incidentally, the 2nd order filter completely removes any residual 60-Hz electrical noise that may remain in the output of the preamplifier stage.