Factoring the wave equation for fast, implicit numerical solutions

Michael P. Lamoureux, RJ Vestrum

Numerical solutions to the wave equations that arise in seismic imaging have been richly developed over the last 70+ years, and typically depend on explicit time-stepping or Fourier techniques for fast, accurate solutions. The counterpart to explicit methods are implicit methods which have enjoy features such as unconditional stability, but typically are computationally prohibitive in two and three spatial dimensions. We demonstrate here a fast, stable implicit time-stepping numerical method for solving the wave equation in two dimensions and higher, that makes use of novel operator factorization in a grid algebra. Several computational demonstrations of the method are presented as well.