# Directivity of a harmonic source plus ghost

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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 | 6 |

Pages | 181 - 220 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 6.9

Show that equation (6.7c) gives the directivity diagrams shown in Figure 6.9a.

### Solution

The directivity is given by equation (6.7c). We take , and , 0.5, and 1.0 for the three parts of Figure 6.9a. Then equation (6.7c) gives

Substituting the three values of , we have:

The results of the calculations are shown in Tables 6.9a,b.

Ignoring the minus signs (which indicate phase reversals), the curves for and , shown in Figure 6.9b, conform closely to Figure 6.9a. However, we need more points to plot the -curve properly and Table 6.9b shows calculated values for intermediate points. The -curve in Figure 6.9b also conforms closely to Figure 6.9a.

0 | 0.59 | 0.00 | 0.00 |

15 | 0.57 | 0.15 | −0.20 |

30 | 0.52 | 0.44 | −0.74 |

45 | 0.43 | 0.81 | −0.97 |

60 | 0.31 | 1.00 | −0.01 |

75 | 0.16 | 0.72 | 1.00 |

90 | 0.00 | 0.00 | 0.00 |

5 | −0.01 | 50 | −0.79 |

10 | −0.08 | 55 | −0.46 |

20 | −0.35 | 65 | 0.46 |

25 | −0.54 | 70 | 0.83 |

35 | −0.90 | 80 | 0.89 |

40 | −0.99 | 85 | 0.52 |

## Continue reading

Previous section | Next section |
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Directivity of a source plus its ghost | Differential moveout between primary and multiple |

Previous chapter | Next chapter |

Geometry of seismic waves | Characteristics of seismic events |

## Also in this chapter

- Characteristics of different types of events and noise
- Horizontal resolution
- Reflection and refraction laws and Fermat’s principle
- Effect of reflector curvature on a plane wave
- Diffraction traveltime curves
- Amplitude variation with offset for seafloor multiples
- Ghost amplitude and energy
- Directivity of a source plus its ghost
- Directivity of a harmonic source plus ghost
- Differential moveout between primary and multiple
- Suppressing multiples by NMO differences
- Distinguishing horizontal/vertical discontinuities
- Identification of events
- Traveltime curves for various events
- Reflections/diffractions from refractor terminations
- Refractions and refraction multiples
- Destructive and constructive interference for a wedge
- Dependence of resolvable limit on frequency
- Vertical resolution
- Causes of high-frequency losses
- Ricker wavelet relations
- Improvement of signal/noise ratio by stacking