Measuring image focusing for velocity analysis

Discussion and conclusions

Using image focusing and unfocusing for velocity estimation has been for long time an elusive goal in reflection seismology. The main challenge is the ambiguity between image focusing and reflectors' curvature. Consequently, previously published methods had to rely on strong assumptions on reflectors' curvature, such as assuming that reflections were generated by point diffractors; that is, by infinite-curvature reflectors. I present a method that does not rely on this assumption because it explicitly takes into account of reflectors' curvature when measuring image focusing.

The synthetic-data example I present in the third section and the field-data example I present in the fourth section show that the method may provide higher resolution and more robust velocity information than conventional methods based on measuring image coherency only along the aperture-angle axes (or the offset axes when constant-offset migration is performed.) Furthermore, the proposed method extract image-focusing information from prestack data that is consistent with the velocity information that we routinely extract by measuring image coherency along the aperture-angle axes.

The two zero-offset synthetic-data examples I show in the last section suggest that useful velocity information can be extracted from zero-offset data. Images that were migrated with approximately the correct velocity have no crossing events and thus the local dip information measured from these images is consistent with the focusing information measured by the image-focusing semblance functional. When the migration velocity is far from the correct one, the migrated images have a lot of crossing events. The local-dips information measured from these images is unreliable and inconsistent with the focusing information measured by the image-focusing semblance functional. These results suggest that it might be useful to estimate the reflectors' curvature by local curvature estimators (Al-Dossary and Marfurt, 2006) and use this information to further constrain the velocity estimates obtained by applying the image-focusing semblance proposed in this paper.

Measuring image focusing for velocity analysis