This section presents a brief physical interpretation of the various members of relation (17).

Consider that we have recorded two wavefields at the top and bottom
of a depth slab:
*W _{0}*, the wavefield at the top of the slab which has not propagated
through the anomalous region;

We can imagine that the linearized process can be thought of as a succession of four steps.

- 1.
- Continuation of
*W*and_{0}*W*to a level inside the slab where we can compare the two wavefields. This level can be either at the top, bottom or anywhere in between:_{1}(37) *k*_{z}represents the depth wavenumber and is a function of the arbitrary slowness inside any given depth slab, and is a scalar which defines where inside the slab we continue the two wavefields. - 2.
- Linearization of
*W*and_{0}*W*with respect to the slowness perturbation:_{1}(38) - 3.
- Datuming of the linearized wavefields to the bottom of
the slab:
(39) (40) - 4.
- Subtraction of the wavefield propagated through the
perturbed medium from the wavefield propagated through the
background medium:
(41)

All three cases in Equation (14) can be derived from Equation (41) as follows:

(42) | ||

(43) | ||

(44) |

6/7/2002