# Plotting raypaths for primary and multiple reflections

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 4.7

A well encounters a horizon at a depth of 2.7 km with a dip of . Sources are located 2 km downdip from the well and a geophone is placed at depths of 1000 and 2600 m. Plot the raypaths and calculate the traveltimes for the primary reflection from the 3-km horizon and its first multiple. Assume km/s.

### Background

Image points were used in Figures 4.1a and 4.2a to find travel paths in constant velocity situations. Figure 4.7a illustrates their use for the more complicated situation of multiples. The image point gives the raypaths for the wave after reflection at the dipping horizon. When the wave is then reflected at the surface is equivalent to a new source, so the image point is located on the perpendicular from to the surface as far above the surface as is below. If this multiple is reflected a second time at the horizon, the image point is located on the perpendicular to the horizon as far below the horizon as is above it.

### Solution

With the origin at the source, the vertical depth of the reflector beneath the source is m. The perpendicular from the source to the reflector meets the reflector at , , i.e., at , and the source image for the primary is at , . The image for the surface multiple (reflected at the reflector and then at the surface) is at .

The arrival time of the primary reflection at the phone 1000 m deep is

and the surface multiple arrives at

The arrival time of the primary at the phone 2600 m deep is

and the multiple arrives at

The source and geophone stations in the well are drawn to scale but displaced to the right in Figure 4.7b. The raypath to the 2600 m phone for the primary (the solid line) and for the surface multiple (the dashed line) are shown. The reflection point moves updip as the distance between the phone and the reflector increases, i.e., as the phone becomes shallower. The reflection points for the multiples lie still further updip.

Traveltimes | |||
---|---|---|---|

Depth | Primary | Multiple | |

1000 m | 1.475 s | 2.139 s | |

266 | 0.946 | 2.671 |

The traveltimes for intermediate depths are calculated in the same way. The results are tabulated in Table 4.7a.

## Continue reading

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

Calculation of reflector depths and dips | Effect of migration on plotted reflector locations |

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