# Migration of PS data

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 |

We learned in migration principles that migration of the stacked *PP* data can be performed by summation of amplitudes (equation 4-5) along a hyperbolic traveltime trajectory (equation 4-4) associated with a coincident source-receiver pair at the surface and a point diffractor at the subsurface. The amplitude from the resulting summation is placed at the apex time of the diffraction hyperbola. Prior to summation (equation 4-5), amplitude and phase factors inferred by the Kirchhoff integral solution to the scalar wave equation are applied to the stacked data (migration principles).

Similarly, migration of the stacked *PS* data can be conceptualized as a summation along a traveltime trajectory associated with a coincident source-receiver pair at the surface and a point diffractor at the subsurface. The difference between the zero-offset *PP* and the *PS* diffraction summation trajectories is in the velocities. Set *x* = 0 in equation (**76**) to get the traveltime equation for the zero-offset *PS* diffraction summation trajectory as

**(**)

**(**)

**(**)

where *t* is the time associated with the unmigrated *PS*-stack, and *t*_{0} is the time associated with the migrated *PS*-stack given by equation (**75**).

Equation (**81**) is of the same form as equation (4-4) that describes the zero-offset *PP* diffraction summation trajectory. In fact, setting *γ* = 1 in equation (**81**) yields equation (4-4) for the case of constant velocity. Note from equation (**81**) that the migration velocity for the *PS* data is given by *α*/(*γ* + 1), which is neither the *P*-wave velocity *α* nor the *S*-wave velocity *β*. The *PS*-velocity *α*/(*γ* + 1) can be obtained from the *PP*-velocity *α* and the velocity ratio *γ*, both estimated from the velocity analysis described earlier in this section. Once the velocity field is estimated, the *PS*-stack can, in principle, be migrated using any of the algorithms described in migration.

## See also

- 4-C seismic method
- Recording of 4-C seismic data
- Gaiser’s coupling analysis of geophone data
- Processing of PP data
- Rotation of horizontal geophone components
- Common-conversion-point binning
- Velocity analysis of PS data
- Dip-moveout correction of PS data