Recall the migration differencing schemes in chapter . We did the time differencing in the same way that we did the depth differencing. The bad news is that there does not seem to exist a representation of causal differentiation that is any more accurate than the Crank-Nicolson representation. Thus the sample intervals of and must be reduced considerably from the Nyquist criterion. The practical picture may not be as bleak as the one I am painting.
Many people are pleased with both the speed and accuracy of time-domain migrations at milliseconds.
Stolt shows how dropping causality at the known depth level while retaining it at the next level allows stable finite differencing. With the depth z -axis we are stuck with causal derivatives, although Fourier methods could be used for discrete layers. Such simulations enable us to compare the accuracy of various migration methods.