Spatial aliasing and scale invariance

INTERPOLATION BEYOND ALIASING

A traditional method of data interpolation on a regular mesh is a four-step procedure: (1) Set zero values at the points to be interpolated; (2) Fourier transform; (3) Set to zero the high frequencies; and (4) Inverse transform. This is a fine method and is suitable for many applications in both one dimension and higher dimensions. However, this method fails to take advantage of our prior knowledge that seismic data has abundant fragments of plane waves that link an axis that is not aliased (time) to axes that often are (space).