# 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 |

Chapter | 7 |

Pages | 221 - 252 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem

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.

### Background

*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).

### Solution

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.

Geophone | Amplifier filter | |||||
---|---|---|---|---|---|---|

(Hz) | (dB) | 10–70 (dB) | alias (dB) | Sum (dB) | ||

4 | 0.4 | 0.17 | –15 | –33 | 0 | –48 |

6 | 0.6 | 0.35 | –9 | –19 | 0 | –28 |

8 | 0.8 | 0.55 | –5 | –11 | 0 | –16 |

10 | 1.0 | 0.70 | –3 | –6 | 0 | –9 |

15 | 1.5 | 0.90 | –1 | –2 | 0 | –3 |

20 | 2.0 | 0.98 | 0 | 0 | 0 | 0 |

40 | 4.0 | 1.00 | 0 | 0 | 0 | 0 |

60 | 6.0 | 1.00 | 0 | –4 | –1 | –5 |

80 | 8.0 | 1.00 | 0 | –8 | –8 | –16 |

100 | 10.0 | 1.00 | 0 | –14 | –30 | –44 |

## Continue reading

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Streamer feathering due to cross-currents | Filter effects on waveshape |

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Characteristics of seismic events | Reflection field methods |

## Also in this chapter

- Radiolocation errors because of velocity variations
- Effect of station angle on location errors
- Transit satellite navigation
- Effective penetration of profiler sources
- Directivity of linear sources
- Sosie method
- Energy from an air-gun array
- Dominant frequencies of marine sources
- Effect of coil inductance on geophone equation
- Streamer feathering due to cross-currents
- Filtering effect of geophones and amplifiers
- Filter effects on waveshape
- Effect of filtering on event picking
- Binary numbers