# Difference between revisions of "Diffraction traveltime curves"

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which is a straight line with slope <math>+1/V</math> for <math>x>0</math>,<math>-1/V</math> for <math>x<0</math>. The traveltime approaches these asymptotes as <math>x\to \pm \infty .</math> | which is a straight line with slope <math>+1/V</math> for <math>x>0</math>,<math>-1/V</math> for <math>x<0</math>. The traveltime approaches these asymptotes as <math>x\to \pm \infty .</math> | ||

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+ | [[file:Ch06_fig6-5a.png|thumb|center|{{figure number|6.5a.}} Diffraction traveltime curves.]] | ||

=== Alternative solution === | === Alternative solution === |

## Latest revision as of 16:16, 8 November 2019

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 |

## Contents

## Problem 6.5a

Show that the slope of the diffraction curve with source in Figure 6.5a(i) approaches for large .

### Solution

The diffraction path is in Figure 6.5a(i), so the traveltime curve is

For , the equation of the curve becomes

which is a straight line with slope for , for . The traveltime approaches these asymptotes as

### Alternative solution

The slope of the traveltime curve is

For , the slope is as before.

## Problem 6.5b

What is the asymptote slope for a coincident source-receiver?

### Solution

The traveltime curve for Figure 6.5a(ii) is given by

As increases, . The asymptote has the equation , which is a straight line with slope

## Continue reading

Previous section | Next section |
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Effect of reflector curvature on a plane wave | Amplitude variation with offset for seafloor multiples |

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