Hongchuan Sun and Gerard T. Schuster
3-D prestack Kirchhoff migration (KM) is too 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 an alternative, we show that the stationary phase approximation to the KM integral restricts the smearing of the time sample along a small Fresnel zone portion of the quasi-ellipsoid. This is equivalent to smearing the time samples in a trace along 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, WM has a computational count of N^5.5 compared to KM which has a computational count of N^7, where N is the number of grid points along one side of a cubic velocity model. Our results with poststack synthetic and poststack field data show that WM provides an image that is in some places less in quality than KM. However, the computation time of WM is less than 1/3 that of KM.