Implementing implicit finite-difference in the time-space domain using spectral factorization and helical deconvolution |

The increased dispersion of the implicit finite-difference scheme in comparison to an explicit scheme is an attribute of the scheme itself. This is not a fundamental problem, since some of this dispersion can be alleviated simply by using a higher order approximation. However, the causes of the instability of the wavefield beyond a certain time step size remained unclear. In order to understand the reasons behind the instability, I tested several hypotheses for its causes. These were:

- The implicit finite-difference approximation itself.
- The precision of the floating point representation of the filter coefficients.
- The number of filter coefficients.
- The spectral factorization method.

First I will review the method by which wave propagation can be done by deconvolutions with spectrally factorized filters of a finite-difference approximation, and then I will go over the various tests I carried out to try and determine the causes for the instability problem.

Implementing implicit finite-difference in the time-space domain using spectral factorization and helical deconvolution |

2010-11-26