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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) |

This equation corresponds to the analytical solution of the ordinary
differential equation
| |
(2) |

where the ' sign represents a derivative with respect to the
depth *z*.
We can consider that the depth wavenumber () depends linearly,
through a Taylor series expansion, on its value in the reference
medium () and the laterally varying slowness in the depth
interval from *z* to ,

| |
(3) |

where *s*_{r} represents the constant slowness associated with the
depth slab between the two depth intervals, and represents the
derivative of the depth wavenumber with respect to the reference
slowness and which can be implemented in many different ways
Sava (2000).
The wavefield downward-continued through the *background* slowness
can, therefore, be written as
| |
(4) |

from which we obtain that the full wavefield depends on the
background wavefield through the relation
| |
(5) |

where represents the difference between the
true and background slownesses .

** Next:** Born wave-equation MVA
** Up:** Sava and Fomel: WEMVA
** Previous:** Introduction
Stanford Exploration Project

6/7/2002