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The analysis above ignores the *v*(*z*) true-amplitude
WKBJ Green's functions Stolt and Benson (1986) discussed in
section .
It also ignores the effect the imaging condition has on dipping
events. Sava et al. (2001) discuss this in more detail; but
the Jacobian associated with the transformation from temporal
frequency to vertical wavenumber causes the slight attenuation of
dipping events visible in Figure .
Both of these effects, however, are well-understood, and they
can be compensated for in a true-amplitude migration operator,
.
Such a true-amplitude migration operator will no longer be the true
adjoint of the forward modeling operator;
but we can still build and solve the system of normal equations,

| |
(89) |

Since replaces , the
solution to this system will not be equivalent to the solution
that minimizes the residual error in fitting goal,
| |
(90) |

However, if a pair of invertible operators ( and ) exist, such that
then the solution to equation () will be the same as
the solution that minimizes the residual error in fitting goal,
| |
(91) |

The solution will also converge faster under an iterative inversion
scheme since
.

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** Up:** Compensating for irregular shot
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Stanford Exploration Project

5/27/2001