Filtering effect of geophones and amplifiers
|Series||Geophysical References Series|
|Title||Problems in Exploration Seismology and their Solutions|
|Author||Lloyd P. Geldart and Robert E. Sheriff|
|Pages||221 - 252|
|Store||SEG Online Store|
Use Figures 7.11a and 7.11b to determine the filter equivalent of a geophone with Hz and , feeding into an amplifier with a 10–70 Hz bandpass filter and a 4-ms alias filter.
A filter, whether analog or digital, is a device that attenuates certain ranges of frequencies present in a signal. A geophone is equivalent to a filter because the response determined by equation (7.9b) is frequency dependent; when the input is harmonic such that the vertical velocity of the geophone is , the solution is [see Sheriff and Geldart, 1995, 220, equation (7.20)]
where the impedance and the phase shift are both functions of , being the natural frequency of the geophone (see problem 7.9) and the frequency of the ground motion.
The geophone sensitivity is a measure of the geophone output for a given ground velocity; it is defined by the relation
Because the numerator is proportional to , is independent of and depends only upon the properties of the geophone and the ratio (see Sheriff and Geldart, 1995, 220, for more details).
Figure 7.11a shows (rationalized) as a function of for various values of the damping factor (see problem 7.9).
Seismic amplifiers include various types of filters. Band-pass filters pass a band of frequencies and discriminate sharply against frequencies outside the band, as shown in Figure 7.11b; the limits of the passband are usually taken as the frequencies at which the attenuation is 3 dB. Alias filters have a very steep high-frequency cutoff and are used to attenuate alias frequencies (see problem 9.4).
In Table 7.11a the column headed gives values of the geophone sensitivity for taken from Figure 7.11a; since the sensitivity is a ratio of amplitudes, we change the values to decibels in the 4th column. We obtain attenuation of the band-pass filter for the normalized frequencies 0.4, 0.6, etc., from Figure 7.11b using the 10-Hz low-cut and 70-Hz high-cut curves. The alias filter for 4-ms sampling rate is used to obtain the 6th column. The sum of the three attenuations is plotted in Figure 7.11c.
|(Hz)||(dB)||10–70 (dB)||alias (dB)||Sum (dB)|
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|Characteristics of seismic events||Reflection field methods|
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