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Claerbout (1998b) describes the isomorphic process by which
multi-dimensional functions can be mapped into equivalent
one-dimensional functions.
The process depends on the concept of the helical boundary conditions,
and is best illustrated by Figure , which shows a small
five-point filter on a two-dimensional space, being mapped into an
equivalent one-dimensional filter.
**helix
**

Figure 1 Illustration of helical boundary
conditions mapping a two-dimensional function (a) onto a helix (b),
and then unwrapping the helix (c) into an equivalent one-dimensional
function (d). Figure by Sergey Fomel.

Under such a transformation, the concepts of causality and
minimum-phase become clear. One-dimensional spectral factorization
algorithms can be directly applied to the multi-dimensional helical
functions.

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** Up:** Spectral factorization
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Stanford Exploration Project

5/27/2001