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## Latest revision as of 16:28, 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 6.16a

Determine the traveltime curve for the refraction and the refraction multiple in Figure 6.16a.

### Solution

We assume that the velocities are known to three significant figures. Then, using equation (3.1a),

The traveltimes can be obtained either graphically or by calculation. Calculating, we get for the refraction traveltimes

The critical distance (see equation (6.15a) is

The traveltime curve for *SMNTUWPQR* is parallel to that for *SMNPQR* and displaced toward longer time by the amount where

The critical distance for *SMNTUWPQR* is increased to

The traveltime curves are plotted as curves (a) in Figure 6.16b.

## Problem 6.16b

Determine the traveltime curves when both refractor and reflector dip down to the left, the depths shown in Figure 6.16a now being the slant distances from to the interfaces.

### Solution

A combined graphical and calculated solution probably provides the easiest solution although Adachi’s method (see problem 11.5) could be used to give greater precision if the data accuracy warranted. A large-scale graph was used to achieve better accuracy; Figure 6.16c is a reduced-scale replica. The traveltime curves are shown in Figure 6.16b labeled (b).

The critical distance for the refraction is km, and

The -layer outcrops at km,

The headwave has a different slope to the right of . To plot the curve in this zone, we use point at the offset . Then,

and the headwave curve is a straight line joining the traveltimes at the points and .

We have two types of reflected refractions: a typical path for the first type is , the reflection occurring at the shallow dipping interface, The second type, , involves reflection at the surface. The first type exists between and , and the curve is parallel to the head-wave curve to the right of . The second type exists to the right of and the curve is parallel to the other reflected refraction. To plot the reflected-refraction curves, we need one point on each curve and then use the refraction-curve slope to the right of . For the first type, we find the coordinates of :

For the second type we find coordinates of :

## Problem 6.16c

What happens when the reflector dips to the left and the refractor to the left?

### Solution

A summary of the detailed graphical solution is as follows. The traveltime curves are shown in Figure 6.16b labeled (c). The various angles in Figure 6.16d are

The refraction curve is a straight line though and :

The incident angle at is , which is less than the critical angle, so that no refraction will be generated there, only a reflection. However, the refraction that starts at will give rise to upgoing rays which will be reflected, giving a reflected refraction, such as the ray that ends at . The traveltime curve is parallel to the refraction curve and exists beyond whose coordinates are

## Continue reading

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Reflections/diffractions from refractor terminations | Destructive and constructive interference for a wedge |

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