Relative phase shift across aperture angles ($\gamma$)

 

azim-gamma-all Figure 8 Image as function of the reflection azimuth at constant aperture angle: a) $\gamma=4^\circ$,b) $\gamma=20^\circ$, and c) $\gamma=35^\circ$.

A close examination of both Figure  and Figure  reveals that the smaller aperture angles ( $\gamma\leq 8$)have a slight phase shift with respect to the rest of the aperture angles. A ``frowning'' artifact that is related to this phase shift is also visible in the gathers. This artifact is attenuated by limiting the azimuthal range of the summation, as described in the next section. Comparison of Figures - with Figure a also suggests that the phase shift is caused by the stacking over azimuths, since it is absent in the gather shown in Figure a.

The phase shift is indeed related to the summation over azimuth and it is easily explained by the analysis of the image as a function of the reflection azimuth $\phi$and at constant aperture angle $\gamma$.The three panels in Figure  show such sections for three different aperture angles: a) $\gamma=4^\circ$,b) $\gamma=20^\circ$, and c) $\gamma=35^\circ$.The curvature of the reflectors as a function of the azimuth is different in Figure a from both Figure b and Figure c. These differences in the curvature of the reflector cause the relative phase shift of the stacked gathers shown in Figures -. In other words, the phase shift at large aperture angles ( $\gamma\gt 8$) is caused by the interference of the flanks of the hyperbolic curves shown in Figures - with the correct summation of the flat spots of the same hyperbolic curves.

Fortunately, both the phase shift and the ``frowning'' artifact are related to the illumination of the reflectors by the data (common-azimuth acquisition geometry) and they are not caused by the methodology employed to image the data. As the azimuthal range of the data increases, the flat spots at the top of the hyperbolic curves shown in Figures - should widen. Consequently, when stacking over azimuths the influence of the flanks should decrease relative to the influence of the flat spot, and the phase shift should disappear. It would be interesting to confirm this hypothesis with a real data example from a marine data set.