Two-parameters residual-moveout analysis for wave-equation migration velocity analysis

Local convergence analysis

To gain an insight whether using a two-parameter RMO provides more accurate gradients starting from a CIG that is already close to be flat, we can zoom into the previous correlation plots around the location of the maximum. The correlation function in these smaller windows is related to ``local convergence'' of velocity estimation methods based on the selected RMO functions.

Figure 10 shows the zooms into the plots shown in Figure 5; that is, comparing the correlation function for the first CIG (velocity anomaly) obtained using the ``Taylor'' RMO function (Figure 10a) and the conventional one-parameter RMO function (Figure 10b). I set the width of the close up windows to be equal to the distance of the maximum from the starting CIG; that is, the difference between the minimum and the maximum value of the $\rho$ parameter is $\Delta \rho=\left(\widehat{\rho}-1\right)$ and the difference between the minimum and the maximum value of the $\lambda_T$ parameter is $\Delta \lambda_T=\left(\widehat{\lambda_T}-1\right)$ . The two plots shown in Figure 10 are almost identical, indicating that in this case there would be a negligible advantage to be gained by employing a two-parameter RMO function.

Figure 11 analyze the application of the ``Orthogonal'' RMO function to the same CIG as the previous figure. It shows the zooms into the plots shown in Figure 7b and Figure 6b, respectively. I set the window width following the same criterion described above for the ``Taylor'' RMO function. In this case, the one-parameter RMO function seems to provide better local convergence than the two-parameter RMO function.

The last two figures, Figure 12 and Figure 13, show similar analysis as the previous two, but applied to the CIG that suffers from the effects of anisotropy. For these CIG the two-parameters RMO function provides a better local convergence than the one-parameter function. The improvements look more substantial for the ``Orthogonal'' RMO function than for the ``Taylor'' RMO function.

Zoom-CorrShift-TP Figure 10. Zooms into the correlation functions shown in Figure 5.

Zoom-CorrShift-OP-narrow Figure 11. Zooms into the correlation functions shown in Figure 7b and Figure 6b, respectively.

Zoom-CorrShift-TP-aniso Figure 12. Zooms into the correlation functions shown in Figure 8.

Zoom-CorrShift-OP-aniso Figure 13. Zooms into the correlation functions shown in Figure 9.

Two-parameters residual-moveout analysis for wave-equation migration velocity analysis