In the downward-propagation finite-difference scheme, the numerical errors
get large
if , which occurs when rays travel almost
horizontally.
This numerical noise can be reduced by decreasing the stepsize in *z* when
rays have large propagation angles at the current depth level, and increasing
it when the propagation angles get smaller.
If greater accuracy is still required, an other alternative is to use
higher-order finite difference
schemes.

Since the method does not calculate ray paths, it is only of limited use in tomographic methods. It is possible, however, to calculate ray directions on the grid from the traveltime gradient. One component of the slowness vector, , is already available as , the other one, , is calculated using .

1/13/1998