# Reflector dip in terms of traveltimes squared

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

Title | Problems in Exploration Seismology and their Solutions |

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

Chapter | 4 |

Pages | 79 - 140 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 4.4a

Using the dip-moveout equation (4.2b) and the result of problem 4.3, verify that

**where , , traveltime for path , traveltime to receiver at (Figure 4.4a).**

### Solution

Since in problem 4.3 equals here, we have

From equation (4.2b) we get

## Problem 4.4b

Using equation (4.2a), show that

### Solution

Equation (4.2a) gives

## Problem 4.4c

Under what circumstances is the result for part (b) the same as equation (4.2b) and also consistent with part (a)?

### Solution

The result in part (b) can be written

The expression in the first curly brackets is the same as the right-hand side of equation (4.2b). Hence, for the above to be the same as equation (4.2b), we must have that is,

In part (a) we got by finding and . The expression for involves no approximation, so the only approximation is that used in the derivation of equation (4.2b) to get . Thus, results in (a) and (c) are consistent provided we take .

## Continue reading

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Relationship for a dipping bed | Second approximation for dip moveout |

Previous chapter | Next chapter |

Partitioning at an interface | Seismic velocity |

## Also in this chapter

- Accuracy of normal-moveout calculations
- Dip, cross-dip, and angle of approach
- Relationship for a dipping bed
- Reflector dip in terms of traveltimes squared
- Second approximation for dip moveout
- Calculation of reflector depths and dips
- Plotting raypaths for primary and multiple reflections
- Effect of migration on plotted reflector locations
- Resolution of cross-dip
- Cross-dip
- Variation of reflection point with offset
- Functional fits for velocity-depth data
- Relation between average and rms velocities
- Vertical depth calculations using velocity functions
- Depth and dip calculations using velocity functions
- Weathering corrections and dip/depth calculations
- Using a velocity function linear with depth
- Head waves (refractions) and effect of hidden layer
- Interpretation of sonobuoy data
- Diving waves
- Linear increase in velocity above a refractor
- Time-distance curves for various situations
- Locating the bottom of a borehole
- Two-layer refraction problem