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In this Appendix I derive equations 5 and 6.
From equation 3 we have:
| |
(51) |

and, from the condition that the sum of the traveltime of the
extrapolated rays at the image point has to be equal to the traveltime
of the multiple we have
| |
(52) |

Solving those two equations for and we get
| |
(53) |

| (54) |

It is interesting to check these equations in two particular cases.
For a non-diffracted flat water-bottom multiple, we have ,, *t*_{s1}=*t*_{s2}=*t*_{r2}=*t*_{r1} and therefore we get
and as the geometry of the
problem requires. Notice that this is true for any . The second case
is for a non-diffracted water-bottom multiple migrated with water velocity.
In that case, and . Furthermore, since
the multiple behaves as a primary,
and we again
get and .B

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Stanford Exploration Project

11/1/2005