# Difference between revisions of "Destructive and constructive interference for a wedge"

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− | == Problem == | + | == Problem 6.17 == |

Figures 6.17a show three reflections, where the second and third reflections are from the top and bottom of wedges that converge to the right. Explain why waves in Figure 6.17a(i) interfere destructively and in Figure 6.17a(ii) constructively when the wedge thickness is <math>\frac{1}{4} \lambda</math>. | Figures 6.17a show three reflections, where the second and third reflections are from the top and bottom of wedges that converge to the right. Explain why waves in Figure 6.17a(i) interfere destructively and in Figure 6.17a(ii) constructively when the wedge thickness is <math>\frac{1}{4} \lambda</math>. | ||

=== Solution === | === Solution === | ||

In Figure 6.17a(i) both reflections from the wedge have the same polarity. As the reflectors converge, at a thickness of <math>\frac{1}{4}\lambda</math> (2-way distance <math>\frac{1}{4}\lambda</math>) one half-cycle of the wavelet reflected from the base interferes destructively with the next half-cycle from the top. In Figure 6.17a(ii), where a phase reversal occurs on reflection at one surface but not at the other surface, the reflections from the top and base of the wedge interfere constructively at <math>\frac{1}{4}\lambda</math> thickness (before they undergo destructive interference as they converge further). Note that timing the peaks or troughs does not give the correct traveltimes to the respective interfaces where the thickness is <math><\frac{1}{4} \lambda</math> (about 8 ms in Figure 6.17a). | In Figure 6.17a(i) both reflections from the wedge have the same polarity. As the reflectors converge, at a thickness of <math>\frac{1}{4}\lambda</math> (2-way distance <math>\frac{1}{4}\lambda</math>) one half-cycle of the wavelet reflected from the base interferes destructively with the next half-cycle from the top. In Figure 6.17a(ii), where a phase reversal occurs on reflection at one surface but not at the other surface, the reflections from the top and base of the wedge interfere constructively at <math>\frac{1}{4}\lambda</math> thickness (before they undergo destructive interference as they converge further). Note that timing the peaks or troughs does not give the correct traveltimes to the respective interfaces where the thickness is <math><\frac{1}{4} \lambda</math> (about 8 ms in Figure 6.17a). | ||

+ | |||

+ | [[file:Ch06_fig6-17a.png|thumb|center|{{figure number|6.17a.}} Reflections where the second and third reflectors converge; zero-phase wavelet.]] | ||

== Continue reading == | == Continue reading == |

## Latest revision as of 15:28, 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 |

## Problem 6.17

Figures 6.17a show three reflections, where the second and third reflections are from the top and bottom of wedges that converge to the right. Explain why waves in Figure 6.17a(i) interfere destructively and in Figure 6.17a(ii) constructively when the wedge thickness is **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4} \lambda}**
.

### Solution

In Figure 6.17a(i) both reflections from the wedge have the same polarity. As the reflectors converge, at a thickness of **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}\lambda}**
(2-way distance **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}\lambda}**
) one half-cycle of the wavelet reflected from the base interferes destructively with the next half-cycle from the top. In Figure 6.17a(ii), where a phase reversal occurs on reflection at one surface but not at the other surface, the reflections from the top and base of the wedge interfere constructively at **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}\lambda}**
thickness (before they undergo destructive interference as they converge further). Note that timing the peaks or troughs does not give the correct traveltimes to the respective interfaces where the thickness is **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle <\frac{1}{4} \lambda}**
(about 8 ms in Figure 6.17a).

## Continue reading

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Refractions and refraction multiples | Dependence of resolvable limit on frequency |

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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