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A perturbation of the wavefield at some depth level can
be derived from the background wavefield
by a simple application of the chain rule to
Equation (1):
| |
(5) |

This is also a recursive equation which can be written in
matrix form as
or in a more compact notation as:
| |
(6) |

where the operator stands for a
perturbation of the extrapolation operator .
Biondi and Sava (1999) show that, at every depth
level, we can write the operator as a chain of
the extrapolation operator and a scattering operator applied to the slowness perturbation :

| |
(7) |

The expression for the wavefield perturbation becomes

| |
(8) |

which is also a recursive relation that can be written in matrix
form as
or in a more compact notation as:
| |
(9) |

The vector stands for the slowness perturbation.
If we introduce the notation

| |
(10) |

we obtain a relation between a slowness perturbation
and the corresponding wavefield perturbation:
| |
(11) |

** Next:** Image transformation
** Up:** Theory of wave-equation MVA
** Previous:** Imaging by wavefield extrapolation
Stanford Exploration Project

11/11/2002