Implicit finite difference in time-space domain with the helix transform

Abstract:

Spectral factorization is a method of creating causal filters which have causal inverses. I use spectral factorization of an implicit finite-difference stencil of the two-way wave equation approximation in order to model wave propagation by a sequence of deconvolutions. I deconvolve this filter's coefficients with the wavefield propagating in a constant velocity medium using the helix approach. In comparison with explicit approximations, implicit approximations have unconditional stability, enabling the use of larger time steps during the modeling process. The advantages are both in reduced computation time, and in the extension and scalability to multiple dimensions enabled by the helix operator.