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In 2-D, the offset-to-angle transformation is done with the relation
| |
(1) |

where is the aperture angle of the reflection,
*k*_{h} is the offset wavenumber associated with the
subsurface horizontal offset, and
*k*_{z} is the vertical wavenumber.
Tisserant and Biondi (2003) presented a 3-D generalization
of Equation 1:
| |
(2) |

| (3) |

where and **bold**k_h are the midpoint and offset vector
wavenumber, respectively, and where the reflection azimuth, ,
is introduced through
| |
(4) |

| (5) |

| (6) |

| (7) |

The offset-to-angle transforms a
(*k*_{z},*k*_{mx},*k*_{my},*k*_{hx},*k*_{hy}) five dimensions cube into
another 5-D one .Figure is the measured
aperture-azimuth
distribution for the configuration displayed in Figure
obtained with ray-tracing.
We set the lower boundary in because of an increased
incertitude in the estimation of as gets close to .
The upper boundary in is reached when one of the two rays
begins to overturn.
We now present a more complex 3-D extension: the one addressing
the 3-D full prestack migration with a wrong migration velocity.

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Stanford Exploration Project

10/14/2003