Fourier transform input data over time-axis Loop over frequency { Initialize wave at z=0 Factor wave equation for this w/v Recursively divide input data by factor Fourier Transform back to time-domain Sum into output }Incorporating this code into the

Figure compares the results of the new extrapolation procedure with the conventional Crank-Nicolson solution to the 45 equation. The new approach has little dispersion since I use a rational approximation (the `one-sixth trick') to the Laplacian on the vertical and horizontal axes. In addition, the new factorization retains accuracy up to 90. The high dip, evanescent energy in the 45 movie, propagates correctly in the new approach.

vs45
Comparison of the 45 wave equation
(left) with the helical factorization of the Helmholtz equation
(right).
Figure 3 |

Figure compares different value of the `one-sixth' parameter, . For this application, the optimal value seems to be .

Figure 4

Figure compares different finite-difference Laplacian operators. In all cases the finite-difference Laplacian was given by the linear sum of 5-point filters,

(33) |

Figure 5

5/27/2001