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The original finite difference traveltime calculations implemented after
Van Trier and Symes (1990) did not have an adaptive step determination.
As a result,
numerical instabilities appeared in unpredictable cases, for example
the simple constant gradient velocity model in Figure 2.
Such instability does not present a problem for research algorithms
because numerical
instabilities can be controlled by decreasing the grid spacing.
However, for production programs this is impractical
as users may not have complete control of each step of the finite
difference calculation.

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Stanford Exploration Project

12/18/1997