Common azimuth migration for elliptical and VTI media

Satyakee Sen and Biondo Biondi

ssen@sep.stanford.edu, biondo@sep.stanford.edu

ABSTRACT

We derive the Commom Azimuth downward continuation operator for elliptically anisotropic and VTI media. For elliptically anisotropic media, the Common Azimuth downward continuation operator derived by a stationary phase approximation of the full 3-D downward continuation operator is exact and it agrees with the constraint imposed by the Common Azimuth approximation on the propagation direction of the source and receiver rays. For VTI media, the dispersion relationship is much more complicated and results in a quartic equation for the stationary path. We introduce a bounded form of Common Azimuth migration for this kind of media, which allows us to develop closed-form analytical solutions without directly solving the quartic equation. Error analysis indicates that the derived analytical solution has similar accuracy as that obtained by solving the full quartic equation. 3-D impulse responses of the anisotropic Common Azimuth downward continuation operator also show significant differences compared to the isotropic operator even at moderate propagation angles.