Helical factorization of paraxial extrapolators

  Implicit wavefield extrapolation has several potential advantages over other depth migration algorithms. For example, as an $(\omega,x)$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$^\circ$ paraxial wave equation with helical boundary conditions on one of the spatial axes, and study the impulse response of the corresponding migration operators.