MODELING COUPLED WAVE PROPAGATION

Modeling of coupled wave propagation represents a special problem for certain algorithms. Examining Equation 18 we expect the eigenvalues of the system to be grouped into two categories for the two propagating wave types; one in the range of speed of light in the material, the other in the range of seismic wave speeds. This grouping of eigenvalues establishes a scale difference between elastic and electromagnetic wavetypes. This discrepancy poses a problem if we want to propagate both coupled wavetypes at the same time. We basically have to propagate the wavetypes with the higher speed on a grid which is orders of magnitude smaller than the one we use for the slower speed wavetypes. Obviously a finite difference algorithm would be costly and inefficient when propagating the coupled waves on a common space-time grid. A phase shift related algorithm is much more effective, but is restricted to horizontal layers. However, in my opinion, a phase shift algorithm can easily be extended to model or migrate coupled waves in arbitrary anisotropic media. This is a promising future application. In this case the disadvantage of being restricted to horizontal layers is outweighed by the possibility of calculating coupled material constants using the group theoretical approach of Schoenberg and Muir.