# Prestack partial migration

Series | Investigations in Geophysics |
---|---|

Author | Öz Yilmaz |

DOI | http://dx.doi.org/10.1190/1.9781560801580 |

ISBN | ISBN 978-1-56080-094-1 |

Store | SEG Online Store |

While conventional normal-moveout correction involves only a time shift given by equation (**7b**), dip-moveout correction involves mapping both in time and space given by equations (**8b**) and (**9b**), respectively. This means that dip-moveout correction, strictly speaking, is not a moveout correction in conventional terms; rather, it is a process of *partial migration before stack* applied to common-offset data. We therefore may speak of a *dip-moveout operator* with a specific impulse response as for the migration process itself. Following this partial migration to map nonzero-offset data to the plane of zero-offset, each common-offset section is then *fully migrated* using a zero-offset migration operator.

A dip-moveout operator maps amplitudes on a moveout-corrected trace of a common-offset section along its impulse response trajectory. Before we derive the expression for its impulse response, we shall first make some inferences about the DMO process based on equations (**8b**) and (**9b**). Tables 5-1, 5-2, and 5-3 show horizontal (Δ*y _{DMO}*) and vertical (Δ

*t*) displacements associated with dip-moveout correction described by equations (

_{DMO}**8b**) and (

**9b**), respectively. Combined with equations (

**8b**) and (

**9b**), we make the following observations:

- Set
*ϕ*= 0 in equations (**8b**) and (**10b**), and note that Δ*y*= 0 and Δ_{DMO}*t*= 0. Hence, the DMO operator has no effect on a flat reflector, irrespective of the offset. The steeper the dip, the larger the DMO correction._{DMO} - Note from Table 5-1 that the horizontal displacement Δ
*y*and the vertical displacement Δ_{DMO}*t*with time_{DMO}decrease*t*. This means that the spatial aperture of the dip-moveout operator, in contrast with a migration operator, actually decreases with event time._{n} - Substitute equation (
**5**) into equation (**8b**) and note that, in the limit*t*= 0, Δ_{n}*y*. This means that the largest spatial extent of the DMO operator equals the offset 2_{DMO}= h*h*associated with the moveout-corrected trace at*t*= 0._{n} - Compare the values for Δ
*y*and Δ_{DMO}*t*in Tables 5-1 and 5-2, and note that the lower the velocity, the larger the DMO correction. This also implies that the shallower the event, the more significant the DMO term, since lower velocities generally are found in shallow parts of the seismic data._{DMO} - For a specific reflector dip
*ϕ*, compare the values for Δ*y*and Δ_{DMO}*t*in Tables 5-2 and 5-3, and note that the larger the offset 2_{DMO}*h*, the more the DMO correction. Whatever the reflector dip, DMO correction has no effect on zero-offset data with*h*= 0. - Finally, note from Tables 5-1, 5-2 and 5-3 that the reflection point smear Δ given by equation (
**10**) decreases in time and for small offsets.

t (s)_{n} |
v (m/s) |
Δy (m)_{DMO} |
Δt (s)_{DMO} |
Δ (m) |

0.5 | 2400 | 1,170 | 0.188 | 1,013 |

1.0 | 2400 | 793 | 0.152 | 687 |

1.5 | 2400 | 575 | 0.115 | 497 |

2.0 | 2400 | 446 | 0.090 | 386 |

2.5 | 2400 | 363 | 0.075 | 314 |

3.0 | 2400 | 305 | 0.063 | 264 |

4.0 | 2400 | 230 | 0.008 | 199 |

t (s)_{n} |
v (m/s) |
Δy (m)_{DMO} |
Δt (s)_{DMO} |
Δ (m) |

0.5 | 1800 | 1,284 | 0.243 | 1,111 |

1.0 | 2000 | 900 | 0.200 | 779 |

1.5 | 2200 | 620 | 0.135 | 536 |

2.0 | 2400 | 446 | 0.090 | 386 |

2.5 | 2700 | 324 | 0.060 | 280 |

3.0 | 3000 | 246 | 0.036 | 213 |

4.0 | 4000 | 140 | 0.016 | 121 |

t (s)_{n} |
v (m/s) |
Δy (m)_{DMO} |
Δt (s)_{DMO} |
Δ (m) |

0.5 | 1800 | 241 | 0.064 | 209 |

1.0 | 2000 | 121 | 0.030 | 105 |

1.5 | 2200 | 74 | 0.015 | 64 |

2.0 | 2400 | 51 | 0.010 | 44 |

2.5 | 2700 | 37 | 0.008 | 32 |

3.0 | 3000 | 27 | 0.004 | 23 |

4.0 | 4000 | 15 | 0.000 | 13 |

## Equations

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## See also

- Frequency-wavenumber DMO correction
- Log-stretch DMO correction
- Integral DMO correction
- Velocity errors
- Variable velocity
- Turning-wave migration