The approximation that is most detrimental to sub-salt imaging is caused by downward-continuing the offset plane waves separately. In lateral varying media, wave-propagation theory predicts that plane-wave components should mix at every depth step. It is difficult to study analytically the effects of this approximation. But the imaging results show a consistent deterioration of sub-salt image quality when plane-wave components were not allowed to mix during the downward-continuation process.

The effects of setting the cross-line offset ray parameter to zero can be studied analytically, at least under the simplifying assumption of constant migration velocity. The fundamental insight for the theoretical analysis is provided by the decomposition of the dispersion relations used for common-azimuth migration and offset plane wave migration in the cascades of two dispersion relations. This decomposition yields to a straightforward evaluation of the equivalent constant-velocity migration operators.

The imaging results confirm the predictions of the theoretical analysis that the shallow reflectors dipping at 45 degrees with respect to the acquisition axes are the most affected by this approximation. On the contrary, this approximation does not seem to have affected the imaging results of the deeper reflectors. However, my theoretical analysis predicts that the errors introduced by this approximation increase with offsets, and the synthetic data set used for this study has a shorter maximum offset (2.4 km) than data sets routinely recorded for sub-salt imaging (4-6 km). Therefore, the results presented in this paper are not conclusive to determine whether the imaging of deeper reflectors would be satisfactory with real data.

Offset plane-wave migration has some potential computational advantages with respect to common-azimuth migration. Therefore, the results presented in this paper indicate it could be a cost-effective migration method to produce full-volume images of deep targets below relatively mild velocity functions. Though more expensive, common-azimuth migration should produce better images below complex overburden (e.g. below salt bodies) and when shallow dipping reflectors are important to the overall interpretation.

10/25/1999