Linearized downward continuation preserves the FEAVO effects

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 ). Figure 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 the propagation was done with linearized downward continuation [the complexified local Born-Fourier method (), as described by ()], 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 , especially in time, they are clearly distinguishable.

 

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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 - 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.