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# Helical factorization of paraxial
extrapolators

Implicit wavefield extrapolation has several potential advantages over
other depth migration algorithms. For example, as an domain method, it naturally handles both finite-frequency effects
and lateral velocity variations. Also as implicit method, it has the
potential for unconditional stability.
However, the simple 3-D extension of conventional 2-D wavefield
extrapolation by implicit finite-differencing requires the
inversion of a 2-D convolution matrix which is computationally
difficult.
In this chapter, I solve the 45 paraxial wave equation with
helical boundary conditions on one of the spatial axes, and study the
impulse response of the corresponding migration operators.

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Stanford Exploration Project

5/27/2001