# Difference between revisions of "Reinforcement depth in marine recording"

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== Problem 3.5a == | == Problem 3.5a == | ||

− | + | For a source at a depth <math>h</math>, show that the maximum amplitude of a downgoing incident wave and its reflection at the surface of the sea occurs at the depth <math>\lambda /\left(4\cos \theta\right)</math>, where <math>\theta</math> is the angle of incidence, by expressing the pressure <math>P</math> in the form used in equations (3.1b,d) and applying appropriate boundary conditions. | |

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

## Latest revision as of 17:07, 7 November 2019

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

Title | Problems in Exploration Seismology and their Solutions |

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

Chapter | 3 |

Pages | 47 - 77 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 3.5a

For a source at a depth , show that the maximum amplitude of a downgoing incident wave and its reflection at the surface of the sea occurs at the depth , where is the angle of incidence, by expressing the pressure in the form used in equations (3.1b,d) and applying appropriate boundary conditions.

### Solution

Since the interface is liquid/vacuum, only two waves exist, the incident and reflected P-waves. Taking the *z*-axis positive downward, we take in the form

There is only one boundary condition, namely that at . This gives Using Euler’s formulas (see Sheriff and Geldart, 1995, problem 15.12a), we get

upon inserting the time factor. The amplitude of the combined incident and reflected waves is

It is a maximum when , that is, when

## Continue reading

Previous section | Next section |
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Zoeppritz’s equations for incident SV- and SH-waves | Complex coefficient of reflection |

Previous chapter | Next chapter |

Theory of Seismic Waves | Geometry of seismic waves |

## Also in this chapter

- General form of Snell’s law
- Reflection/refraction at a solid/solid interface and displacement of a free surface
- Reflection/refraction at a liquid/solid interface
- Zoeppritz’s equations for incident SV- and SH-waves
- Complex coefficient of reflection
- Reflection and transmission coefficients
- Amplitude/energy of reflections and multiples
- Reflection/transmission coefficients at small angles and magnitude
- Magnitude
- AVO versus AVA and effect of velocity gradient
- Variation of reflectivity with angle (AVA)