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The third WEMVA step relies on inverting a linearized
downward continuation operator in order to obtain the velocity
perturbation from the image perturbation.
This means the linearization must not destroy
the FEAVO anomalies.
One way to check
this is to actually do WEMVA for a synthetic case. A smarter, less
time-consuming way is to see whether the non-inverted
operator correctly propagates a wavefield through a velocity anomaly
to create a FEAVO effect.
A good comparison case can be provided by the
waveform modeling of deep FEAVO anomalies (Figure
6). Figure 5 represents the results of
an equivalent experiment - propagating a shot (20Hz Ricker wavelet,
laterally smoothed a bit) from the surface to a line of receivers 6 km
deep. The difference is that in Figure 5 the
propagation was done with linearized downward continuation [the
complexified local Born-Fourier method de Hoop et al. (2000), as
described by Sava (2000)], instead of pseudospectral
waveform modeling. Details about the operator and the way the image
was constructed are in Appendix B. The FEAVO effects are easily
recognizable in amplitudes and the dispersion is missing. Even if they are less
powerful than in Figure 6, especially in time, they are clearly distinguishable.

**popic
**

Figure 5 **Left, from top to bottom:**
1. Wavefield recorded 6 km deep after propagation through constant
velocity (background wavefield); 2. Linearly scattered wavefield
(physically equivalent to the difference between the wavefield
propagated through the velocity model containing the slab - panel 6 of
Figure 6 - and the background wavefield); **Right, from
top to bottom:** 3. Ratio between the maximum amplitudes in panel (1+2) and
panel 1, for each x location; 4. Difference between the times of the
maximum amplitudes in 1 and (1+2), for each x location. The wavefield was
propagated by linearized downward continuation (complexified local
Born-Fourier method) instead of pseudospectral waveform modeling.

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Stanford Exploration Project

11/11/2002