# Appendix B: Exercises

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

Title | Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing |

Author | Enders A. Robinson and Sven Treitel |

Chapter | 2 |

DOI | http://dx.doi.org/10.1190/1.9781560801610 |

ISBN | 9781560801481 |

Store | SEG Online Store |

1. Show that (in the case of two dimensions *x*, *y*) if the velocity is then the rays are brought to a common focus (both time and distance) with common emergence distance and common emergence time . This exercise represents the traditional case of diving waves.

2. In the case when velocity increases linearly with depth, we first found by integration that . Show that depth *y* can be found without integration by simply using Snell’s law in the velocity equation .

3. Let the velocity (in the case of two dimensions *x*,*y*) be . Show that the equation for the raypath with initial angle to the vertical is

which is a parabola. Find the vertex of the parabola. Show that the ray is progressively bent toward the normal if *a* is positive and away from the normal if *a* is negative.

4. Let velocity (in the case of two dimensions *x*,*y*) be the exponential . Show that

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Wave Motion | Visualization |

## Also in this chapter

- Reflection seismology
- Digital processing
- Signal enhancement
- Migration
- Interpretation
- Rays
- The unit tangent vector
- Traveltime
- The gradient
- The directional derivative
- The principle of least time
- The eikonal equation
- Snell’s law
- Ray equation
- Ray equation for velocity linear with depth
- Raypath for velocity linear with depth
- Traveltime for velocity linear with depth
- Point of maximum depth
- Wavefront for velocity linear with depth
- Two orthogonal sets of circles
- Migration in the case of constant velocity
- Implementation of migration