# Translations:Mathematical foundation of 3-D migration/37/en

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In summary, to implement separation or splitting, the inline and crossline terms of the 3-D migration operator need to be decoupled. This can be achieved by making rational approximations (equation **G-9** or **G-12**) to the square root in equation (**G-3**). Separation works for 90-degree, constant-velocity (i.e., Stolt migration) or 15-degree, slowly varying *v*(*z*) cases. When there are large vertical velocity gradients or strong lateral velocity variations, splitting must be used. The algorithm for a one-pass implicit frequency-space 3-D poststack migration that uses the splitting method is identical to the 2-D algorithm outlined in Figure 4.1-23, except for the additional application of the diffraction term in the crossline direction (Figure G-1).