# Directivities of linear arrays and linear sources

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Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 8 |

Pages | 253 - 294 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem

Show that the directivity equations (8.6d) and (7.5d) are consistent.

### Solution

Since equation (8.6d) applies to a discontinuous array of geophones whereas equation (7.5d) applies to a continuous source, we find the limit of equation (8.6d) as the number of geophones becomes infinite. We require that while in such a way that , being the same constant as in problem 7.5, thus keeping the array length equal to the source length. In the limit the numerator of equation (8.6d) becomes . To get the limit of the denominator, we replace the sine by its argument (because ) and get . Substituting these values in equation (8.6d), we obtain

Because the angles and are equivalent, equations (8.6d) and (7.5d) are equivalents.

## Continue reading

Previous section | Next section |
---|---|

Response of a linear array | Tapered arrays |

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Seismic equipment | Data processing |

## Also in this chapter

- Effect of too many groups connected to the cable
- Reflection-point smear for dipping reflectors
- Stacking charts
- Attenuation of air waves
- Maximum array length for given apparent velocity
- Response of a linear array
- Directivities of linear arrays and linear sources
- Tapered arrays
- Directivity of marine arrays
- Response of a triangular array
- Noise tests
- Selecting optimum field methods
- Optimizing field layouts
- Determining vibroseis parameters
- Selecting survey parameters
- Effect of signal/noise ratio on event picking
- Interpreting uphole surveys
- Weathering and elevation (near-surface) corrections
- Determining static corrections from first breaks
- Determining reflector location
- Blondeau weathering corrections