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Helical boundary conditions allow the critical 2-D inverse-filtering
step in FFD migration to be recast as 1-D inverse-filtering. A
spectral factorization algorithm can then factor this 1-D filter into
a (minimum-phase) causal component and a (maximum-phase) anti-causal
component.
This factorization provides an *LU* decomposition of the matrix,
which can then be inverted directly by back-substitution.
The cost of this approximate inversion remains *O*(*N*) where *N* is the
size of the matrix.
I demonstrate this alternative factorization retains azimuthal
isotropy without the need for additional correction terms, and apply
the migration algorithm to the 3-D SEG/EAGE salt dome synthetic
dataset.

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Stanford Exploration Project

4/27/2000