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We use finite-difference methods to propagate waves in heterogeneous media,
so the spatial and temporal grid sizes are determined by the range of velocities
in the model and the frequency content of the waves we wish to propagate.
The maximum frequency and the minimum velocity combine with the accuracy of our scheme to limit the maximum spatial grid size
that can be used.
Then, given the spatial grid sizes, the maximum velocity in the model sets the maximum time step size that we can use for stability reasons.
Because of all this, each model (each unique combination of and )
will have it's own set of optimum coefficients.
In practice I just compute a table of coefficients for the case at hand and build precomputed
"updating stencils". This wastes memory somewhat (maybe more than somewhat), but in principle can lead to a highly efficient code.