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Given the kinematic equivalence between the water-bottom multiple and a primary
from a reflector dipping at twice the dip angle, we can express the image space
coordinates of the water-bottom multiple in terms of the data space coordinates
by solving the system of equations presented by Fomel and Prucha
1999:
| |
(13) |

| (14) |

| (15) |

where are the image space coordinates of the
primary that is kinematically equivalent to the first order water-bottom multiple as
mentioned n the previous section and . The formal solution of
these equations, for the image space coordinates is:
| |
(16) |

| (17) |

| (18) |

These equations allow the computation of the impulse response of the
water-bottom multiples in image space as a function of the aperture angle. More
importantly, they are the starting
point for understanding the kinematics of the data in 3D ADCIGs Tisserant and Biondi (2004),
still a subject of research.

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Stanford Exploration Project

5/3/2005