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The wavefield constructed by downward continuation from the
surface to depth *z*, is
| |
(1) |

where is the data at the surface and
is the complex phase shift at one depth level.
We can write the phase at every depth level
as a Taylor expansion
around a reference medium of slowness *s*_{o}
| |
(2) |

| (3) |

If we plug equation (2) in equation (1) we can write
the following expression for the wavefield :

| |
(4) |

where corresponds to the background slowness *s*_{o},
and corresponds to an arbitrary spatially varying
slowness .
We can define a wavefield perturbation at depth *z*
by the expression

| |
(5) |

| (6) |

or, if we use the notation
| |
(7) |

In general, we can compute a wavefield perturbation by applying a non-linear operator which depends on
the background wavefield
to a slowness perturbation , according
to equation (7):

| |
(8) |