Common-azimuth migration was first introduced by Biondi and Palacharla 1994. It is a

3-D depth imaging method based on a recursive downward continuation of prestack data, and allows a robust and accurate depth migration since it is derived directly from the full wave equation. As opposed to Kirchhoff methods, common-azimuth migration is not derived from asymptotic approximations, and thus it represents a potentially robust alternative to Kirchhoff methods for 3-D prestack migration.

The implementation of wave-equation methods presents several difficulties. Whereas Kirchhoff methods handle irregular geometries relatively easily, the downward-continuation process needs data with a regular geometry in order to correctly propagate the wavefield. Additionally, full volume 3-D wave equation migration still has a high computational cost. The challenge for such a recursive algorithm is to extrapolate the wavefield in a 5-D space: time, in-line and cross-line midpoint coordinates, and in-line and cross-line offsets, (*t*,*m*_{x},*m*_{y},*h*_{x},*h*_{y}). This computation is still beyond the reach of current computer technology. We can address this problem by only downward continuing common-azimuth data for which *h*_{y}=0. In this way, the data space is reduced to 4-D. Common-azimuth data are obtained through azimuth moveout (AMO), which rotates and modifies the offset of 3-D prestack data Biondi et al. (1998). AMO is used as a preprocessing step to regularize the 3-D data acquisition, and organize it in sets of constant cross-line offset. The first section discusses the original method, and the second one presents its new extension.

4/20/1999