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Levin and Shah (1977) show that for a flat subsea reflector and dipping
seabed, the moveout equation of the ``S102G''
(source-seabed-surface-reflector-receiver) pegleg multiple is:
| |
(5) |

where and are the dip angle (in radians) of the seabed and subsea
reflector, respectively. For small dip angles (i.e., less than 5 degrees), we can
make the small angle approximation for angles , , and to update equation (5) accordingly:
| |
(6) |

Multiplying out the squares in equation (6) and collecting
terms gives:
| |
(7) |

The and terms are negligible for small angles, so we can
ignore these terms and further simplify equation (7):
| |
(8) |

Notice that equation (8) is equivalent to the previously
derived equation (1) for a first-order pegleg, with the addition
of an offset-dependent correction term for the dipping layers.
Although explicit seabed and subsea reflector dip angles, and ,are contained in equation (14), they were introduced only to
show equivalence to equation (8). Locally-planar
reflectors are not required to implement equation (3).

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** Up:** Acknowledgment
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Stanford Exploration Project

7/8/2003