Integral operator quality from low order interpolation or Sometimes nearest neighbor beats linear interpolation

Discussion and conclusions

We have clearly seen a significant difference between slant stacking (or NMO stacking) and migration in how interpolation affects the result. This is a reflection (no pun intended) on the fact that the former is adding signals in phase while the latter is relying on massive destructive interference to suppress those data that shouldn't contribute to the output. (See, e.g., Levin (2004).) The constructive interference in the 3D poststack migration example is over a fairly small patch and has led to some unwanted noise and other artifacts. However full prestack Kirchhoff migration suppresses the noise and confirms the original conclusion that it is the average case, not the worst case, of interpolation that should be the focus of integral operator system analysis.