Figure 7 Left panel shows the wavenumber energy for a migrated flat reflector when using sources at every tenth receiver location. On the left, and all source locations.
From this simple example, we can see that the anti-aliasing restriction required for the decimated migration are sloped lines to remove energy from the upper-right and lower-left quadrants. In general, any of the four corners may experience aliased replications depending on the inequality between receiver and source sampling during acquisition. The form of the imaging condition in the Fourier domain as shown in equation 7 provides important insight into how to implement anti-aliasing criteria for shot-profile migration.
Limiting the image by neither constant kx nor kh will appropriately remove the aliased energy of Figure . Instead, one should limit the maximum bandwidth of both the and wavefields. Table 1 provides a convenient display of this fact. This will maintain the center diamond of appropriate energy. If the anti-aliasing bandlimit is applied to the image space instead of the two wavefields used to calculate it, there are two important conclusions: 1) the bandlimit should be the same for both the offset and location axes, and 2) the limit is a diamond shaped, not circular, filter on the kx-kh plane.