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Equation (B-12) enables us to compute the
perturbation in image corresponding to a given perturbation in the
velocity field, that is, to migrate the scattered field. The operation
adjoint to migration, back-projection, can be derived from the same
equation using the adjoint state system:
| |
(32) |

where
- is the back-projected perturbation in the
velocity field obtained from the perturbation in the image.

Therefore, the back-projected perturbation in velocity () is derived from the perturbation in the reflectivity image
() using the following expression:

| |
(33) |

Equations (B-12) and (B-14) comprise
a pair of adjoint operators that relate the perturbation in
velocity to the perturbation in reflectivity image. We can use these
two operators to invert for velocity from measurable perturbations in
the image.

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Stanford Exploration Project

6/1/1999