The main feature of applying finite difference to the Eikonal equation, as opposed to the wave equation,
is the efficiency gained in calculating traveltimes
and computing synthetic sections. A major reason for the cost difference
between using the wave equation and Eikonal
equation is the difference in the dimensionality of the problem. Using the Eikonal equation we solve for
, whereas by using the wave equation we solve for the time-varying
wavefield, *W*(*x*,*y*,*z*,*t*). Add to that, the fine grid necessary to solve
the wave equation to avoid dispersion. However the eikonal equation is a
high frequency asymptotic approximation
that would only provide traveltime information for the fastest arrival Vidale (1990).
In complex media, the fastest arrival is not
necessary the most energetic, and as a result, traveltime solutions obtained
by applying the finite difference
scheme on the eikonal equation might result in less sufficient solutions.

10/9/1997