Numerical Examples

Figure 4 compares the PP-AMO impulses response obtained with the filter in both equation (10) (top) and equation (11) (bottom). Both are obtained with a value of $\gamma=1$ for the two cases. Both impulse responses are kinematicly equal. However, the dynamically behavior is different, the amplitudes distribution with the filter in equation (11) is more accurate. The impulse response with the filter in equation (11) and $\gamma=1$ is exactly the same as Vlad and Biondi (2001).

Figure 5 presents a similar comparison to Figure 4, for the case of converted waves. Here, we use $\gamma=1.2$ and v_p=2.0Km/s. As in the previous case, the same kinematic behavior occurs in both operators, but the response with the filter in equation (11) is dynamically correct.

Figure 6 shows the comparison between the PP-AMO impulse response and the PS-AMO impulse response. The PS-AMO not only has the same saddle shape as the PP-AMO operator, but it also exhibits a lateral movement. This lateral displacement correspond to the asymmetry of the raypaths or the CCP transformation. The displacement is toward the lower-left part of the cube.

 

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Figure 4 PP-AMO impulse response comparison, filter in equation (10) (top) and filter in equation (11) (bottom), with $\gamma=1$.

 

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Figure 5 PS-AMO impulse response comparison, filter in equation (10) (top) and filter in equation (11) (bottom), with $\gamma=1.2$ and v_p=2.0km/s.

 

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Figure 6 PP-AMO (top) vs. PS-AMO (bottom) impulse response comparison

A variation of the PS-AMO impulse response with respect to depth is also observable in Figure 7. This behavior is due to the dependence of the operator on $\frac{v_p}{v_s}$ ratio It is possible to observe how the impulses responses movement toward the left is stronger for shallower events. It is also possible to detect how the response change along the crossline coordinate.

 

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Figure 7 PS-AMO impulses response variation with $\tau$