Including causality and viscosity in the definition of R=ikz (equation 12) it is possible to preserve the energy content for any arbitrary value.
Figure 7 presents the modeling-migration results, using the model of synthetic data set in Figure 6, with equations (2) and (12) for two different values of .Figure 8 shows the respective frequency spectrum.
We can assure the stability of the R definition presented in equation (12) based on the results of Figures 7 and 8; besides, this R definition is valid for all values of and kx.
We also perform the phase-shift migration over a real data set, we present the results on Figures 9 and 10. These results show a comparison between phase-shift migration without considering the damping factor [R definition in equation (1)] and considering the damping factor [R definition in equation (12)].
The image that we obtain with the damping factor is much cleaner than the image without the damping factor; therefore, the events definition and the faults are more clear.