Numerical examples

 Although the instability in Figure  is not catastrophic, the instability can cause amplitudes to explode and contaminate the entire model. For example, migration with the raw (unsmoothed) SEG/EAGE velocity model does become unstable, producing no useful output. Figure  shows another example: the results of imaging the zero-offset wavefield from the Marmousi dataset Bourgeois et al. (1991) with a velocity model that contains a sharp discontinuity. This example is similar to the model that Etgen (1994) showed caused instability for explicit operators.

 

marmstab
Figure 4 Instability in 2-D helical factorization of implicit 2-D system.