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The present drawback to the Van Trier and Symes algorithm is
that for a given grid size the algorithm is
numerically unstable. The problem is that presently one cannot
determine a priori a stable grid spacing.
The program will execute without any evidence of numerical
instability. Only by examining the results one can
determine if numerical instability has occurred.
By reducing the grid spacing one can resolve this
problem. Further work is necessary to
detect automatically numerical instability
or determine the stability conditions as a
function of the velocity model and grid spacing.
Detecting numerical instability and
correcting it at run-time will be an important improvement.
In 3-D the instability problem is more serious compared to 2-D.
The velocity models I tested need to have smooth velocity
variations in order to run in the presently available computer
memory without presenting numerical instability.

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Stanford Exploration Project

12/18/1997