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Things are different, however, for the amplitude correction which is
applied during the propagation. Equation 28 of
Vlad et al. (2003) states that the correction to be applied
at each downward continuation step is
| |
(5) |

Counting a possible linearization of the exponential in front and the
presence of *v*_{z}, this is an expression of degree 5 in
velocity. Moreover, at each depth step this has to be multiplied with
the first-order-in-slowness propagation step in Equation
2 . The result would be a expression of at least
degree 6. Discarding terms of order higher than 1 would result in losing an
important amount accuracy in the propagation step itself, since a part
of it will be multiplied with higher-order amplitude correction terms. We conclude
that the propagation operator amplitude correction is not applicable
to linearized downward continuation because of compounding
linearization errors that will affect both the kinematics and the amplitudes.

** Next:** Conclusions
** Up:** Application to linearized downward
** Previous:** The boundary condition correction
Stanford Exploration Project

5/23/2004