Impulse Responses

Figure 1 shows the impulse response of the three residual prestack migration operators [equations (3), (5), (6)].

 

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Figure 1 Impulse response for the residual prestack migration operators. From top to bottom, a) equation (3) for $\rho_p=1.2$, $\rho_s=1.2$, $\gamma_0=2$; b) equation (5) for $\rho_p=1.2$, $\gamma=2$;c) equation (6) for $\rho_p=1.2$, $\rho_s=1.2$.

Figure 1a presents the impulse response for equation (3), with $\rho_p=1.2$, $\rho_s=1.2$ and $\gamma_0=2$.Figure 1b presents the impulse response for equation (5), with $\rho_p=1.2$ and $\gamma=2$.As expected from the theory discussed in the previous section, Figure 1a and Figure 1b are identical because $\gamma=\gamma_0$.

Figure 1c presents the impulse response for equation (6), with $\rho_p=1.2$, $\rho_s=1.2$. It is possible to observe the difference with respect to figures 1a and 1b. The difference is due to the approximation in the transformation kernel.

Figure 2 demonstrates the differences between equations (3) and (5). Figure 2a shows the impulse response for equation (3) with, $\rho_p =0.9$, $\rho_s =1.4$ and $\gamma_0=2$.Figure 2b shows the impulse response for equation (5) with, $\rho_p =0.9$ and $\gamma=2$.It is easy to observe the difference between the impulse responses due to the approximation in the transformation kernel.

 

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Figure 2 Impulse response for the residual prestack migration operators. From top to bottom, a) equation (3) for $\rho_p=1.2$, $\rho_s =1.4$, $\gamma_0=2$; b) equation (5) for $\rho_p=1.2$, $\gamma=2$.