2-D wavepath migration

Prestack Kirchhoff migration (KM) is computationally intensive for iterative velocity analysis. This is partly because each time sample in a trace must be smeared along a quasi-ellipsoid in the model. As a less costly alternative, we use the stationary phase approximation to the KM integral so that the time sample is smeared along a small Fresnel zone portion of the quasi-ellipsoid. This is equivalent to smearing the time samples in a trace over a 1.5-D fat ray (i.e., wavepath), so we call this "wavepath migration" (WM). This compares to standard KM, which smears the energy in a trace along a 3-D volume of quasi-concentric ellipsoids. In principle, single trace migration with WM has a computational count of O(N^1.5) compared to KM, which has a computational count of O(N³), where N is the number of grid points along one side of a cubic velocity model. Our results with poststack data show that WM produces an image that in some places contains fewer migration artifacts and is about as well resolved as the KM image. For a 2-D poststack migration example, the computation time of WM is less than one-third that of KM. Our results with prestack data show that WM images contain fewer migration artifacts and can define the complex structure more accurately. It is also shown that WM can be significantly faster than KM if a slant stack technique is used in the migration. The drawback with WM is that it is sometimes less robust than KM because of its sensitivity to errors in estimating the incidence angles of the reflections.