Physical interpretation

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

Consider that we have recorded two wavefields at the top and bottom of a depth slab: W₀, the wavefield at the top of the slab which has not propagated through the anomalous region; W₁, the wavefield at the bottom of the slab which incorporates scattering effects caused by the slowness anomaly inside the slab. The goal of WEMVA is to extract the slowness perturbation 141#141 from W₀ and W₁.

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

1.

Continuation of W₀ and W₁ 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:

203#203 (88)

k_z represents the depth wavenumber and is a function of the arbitrary slowness inside any given depth slab, and 160#160 is a scalar which defines where inside the slab we continue the two wavefields.

2.

Linearization of W₀ and W₁ with respect to the slowness perturbation:

204#204 (89)

where 205#205 is the function defined in Equation ().

3.

Datuming of the linearized wavefields to the bottom of the slab:

206#206 (90) (91)

4.

Subtraction of the wavefield propagated through the perturbed medium from the wavefield propagated through the background medium:  

 207#207 (92)

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

208#208 (93) (94) (95)