# Proof of the ABC refraction equation

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

Title | Problems in Exploration Seismology and their Solutions |

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

Chapter | 11 |

Pages | 415 - 468 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Contents

## Problem 11.4

Prove the ABC refraction equation [equation (11.4a)].

### Background

The ABC equation is often used to calculate the weathering thickness. Assuming reversed profiles as shown in Figure 11.4a and writing , for the traveltimes from the sources to a geophone at and for the traveltime from to , the ABC equation gives the depth as

**(**)

### Solution

Assuming that , , and are coplanar and that elevation corrections have been made, we can write

Thus,

## Continue reading

Previous section | Next section |
---|---|

Effect of a hidden layer | Adachi’s method |

Previous chapter | Next chapter |

Geologic interpretation of reflection data | 3D methods |

## Also in this chapter

- Salt lead time as a function of depth
- Effect of assumptions on refraction interpretation
- Effect of a hidden layer
- Proof of the ABC refraction equation
- Adachi’s method
- Refraction interpretation by stripping
- Proof of a generalized reciprocal method relation
- Delay time
- Barry’s delay-time refraction interpretation method
- Parallelism of half-intercept and delay-time curves
- Wyrobek’s refraction interpretation method
- Properties of a coincident-time curve
- Interpretation by the plus-minus method
- Comparison of refraction interpretation methods
- Feasibility of mapping a horizon using head waves
- Refraction blind spot
- Interpreting marine refraction data