Conclusions

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.