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

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.

- Introduction

- Explicit finite difference in 2D using spectral factorization and helical coordinates
- Explicit Vs. Implicit Finite difference approximation of the 2-way acoustic wave equation
- Formulation for 1 dimension
- Application of spectral factorization and the helix operator
- Formulation for 2 dimensions
- Validity tests of derived coefficients

- Standard implicit propagation Vs. helical implicit propagation

- Conclusion and future work
- Acknowledgments
- Bibliography
- About this document ...

2010-05-19