Steeply Faulted Regions, Artifacts, and Stability in the 45-Degree Omega-Finite Difference Algorithm
, by Heloise Bloxom and Einar Kjartansson
To test the hypothesis that possible artifacts ("reflections," coherent amplitude or phase lineups,
etc.) were generated by steep interfaces or severe velocity contrasts in the 45-degree finite difference
program, a series of test cases were migrated. Random number inputs with a severe (1:2) velocity contrast
across a 90-degree (or near 90-degree) interface result in unstable migrations. No instability is detectable
on random number migrations with dipping interfaces of 45 degrees or less (1:2 velocity contrast). The
instability is greatly reduced by an ad hoc modification of the Crank-Nicolson equation that results in
symmetric matrices. Artifcats are generated on real datasets when an interface dips more steeply than 45
degreees, even when the velocity contrast is small (6%).
STANFORD