Figure compares the impulse responses of the 45 equation obtained with the x-y splitting approximation [panel (a)] and the helical factorization methodology described in this chapter [panel (b)]. Implicit migration with the full Laplacian, instead of a splitting approximation, produces an impulse response that is azimuthally isotropic without the need for any phase corrections.
Figure shows the effects of the different boundary conditions on the two spatial axes. The fast spatial axis (top and bottom of Figure) have helical boundary conditions, and show wrap-around. The slow spatial axis (left and right of Figure) has a zero-value boundary condition, and hence is reflective.
For the examples in this chapter, we set the `one-sixth' parameter Claerbout (1985), , and used the isotropic nine-point Laplacian from equation () that corresponds to in equation ().
Figure 3 Depth-slice of offset impulse response corresponding to a dip of 45. Note the helical boundary conditions on the fast spatial axis.