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Forward interpolation plays only a supplementary role in this paper,
but it has many applications of its own in the seismic processing
practice. It is sufficient to mention such applications as trace
resampling, NMO, Kirchoff and Stolt migrations, log-stretch, radial
transform, etc. Two simple examples appear at the end of this section.
The general form of a linear forward interpolation operator is

| |
(1) |

where *n* is a point on a given regular grid *N*, *x* is a point in
the continuum, *f*(*x*) is the reconstructed continuous function, and
*W*(*x*,*n*) is a linear weight. Although in the discussion that follows, I refer
to only the one-dimensional theory, a generalization to many
dimensions is straightforward.

** Next:** Nearest neighbor and beyond
** Up:** Fomel: Inverse interpolation
** Previous:** Introduction
Stanford Exploration Project

9/5/2000