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One solution of (10) is:
| |
(23) |

| (24) |

We implemented (24) with the split-step method
Stoffa et al. (1990). To implement (23) we take a Taylor expansion of
the term:
| |
(25) |

Equation (23) becomes:
| |
(26) |

The last exponentials cannot be computed in a single step because
the velocity terms and the horizontal wavenumber do not belong
to the same domain. One solution consists of
expanding the exponentials in a Taylor series and keeping only the terms of
order smaller or equal to 4 in *k*_{x}:
| |
(27) |

The correction is:
| |
(28) |

We give an algorithm of the mixed-domain implementation in Appendix B.

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Stanford Exploration Project

7/8/2003