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20
We define .Equation 20 can be written:
| |
(30) |

or
| |
(31) |

We apply the finite difference method:
| |
(32) |

| (33) |

| (34) |

After some little rearrangements, equation 31 can be written:
| |
(35) |

where
| |
(36) |

For downward continuing the receiver (upgoing) wavefield, we choose
the positive sign in the relation above; for downward continuation of
the source (downgoing) wavefield we take the sign in to be
negative. To solve the equation, . For the
equation, , and for the
equation, Lee and Suh (1985). In our implementation, we have used the equation with the `` trick''
Claerbout (1985) for improving the accuracy of the second
derivative. This changes (31) and (36) into
| |
(37) |

| (38) |

where we took *s* = 8.13 Fomel and Claerbout (1997). Equation
(35) with the new gives a tridiagonal system for each
frequency and depth.

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Stanford Exploration Project

7/8/2003