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

(18) |

It is clearly impossible to divide the system by
or any of it's constituent parts (in particular - the velocity) without changing the value of the diagonal weight. If the velocity is variable, this will result in a different set of finite-difference weights at various lines of the linear system in (17), requiring a different set of spectrally factorized coefficients wherever the velocity changes.

The option of using a ``filter bank'' for different parts of the wavefield according to the local velocity has already been discussed in Rickett et al. (1998), for wave propagation in the frequency-wavenumber domain. This may also be applicable to propagation in the time-space domain, but I have not yet tested it. It was my hope that this would be unecessary, and that a single set of filter coefficients could be utilized for the entire wavefield irrespective of velocity. This would make the propagation algorithm simpler, and more amenable to future parallelization schemes.

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

2010-05-19