# Magnitude

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 3.10

Using equation (1,8) in Table 2.2a, show that the fractional change is not necessarily small when , , and are all small.

### Solution

Equation (1,8) in Table 2.2a is

Because does not enter into this equation, it has no effect upon . The fractions , , and are of the form which suggests that we use logs [since . Taking logs of both sides of the above equation, we get

.

Differentiation gives

Thus,

Since , the product of the two -factors varies between (when ) and (when ). Therefore, even though is small (being the difference between two small quantities), the right-hand side can be large.

## Continue reading

Previous section | Next section |
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Diffraction from a half-plane | Reflection/refraction at a solid/solid interface and displacement of a free surface |

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
- Reinforcement depth in marine recording
- Complex coefficient of reflection
- Reflection and transmission coefficients
- Amplitude/energy of reflections and multiples
- Reflection/transmission coefficients at small angles and magnitude
- AVO versus AVA and effect of velocity gradient
- Variation of reflectivity with angle (AVA)