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In migration by downward continuation, the wavefield at depth
() is obtained by phase-shift from the wavefield at
depth *z* ()

| |
(1) |

where the depth wavenumber depends linearly
through a Taylor series expansion
on its value in the reference medium () and
the slowness in the depth interval from *z* to ,
and :
| |
(2) |

where, by definition, .
If we denote the wavefield downward continued through the
reference velocity as

| |
(3) |

we obtain
| |
(4) |

The Born approximation linearizes the phase-shift exponential
, such that we can write

| |
(5) |

Therefore, at any particular depth level,
the wavefield perturbation is
| |
(6) |

which we can also write as
| |
(7) |

The image perturbation is simply obtained from the wavefield
perturbation by summation over frequencies:
| |
(8) |

** Next:** Image perturbation by residual
** Up:** Sava and Biondi: Image
** Previous:** Introduction
Stanford Exploration Project

9/18/2001