Wavefield extrapolation in pseudodepth domain |

For homogeneous velocity and regularly spaced grids, the stability condition is often studied by Von Neumann analysis (Trefethen, 1994). Consider -D second-order wave equation,

approximated by central difference in space and time

where superscripts indicate time index and subscripts indicate space index. Substitute ansatz into Equation H-2 yields

(36) |

where amplification factor characterizes the growth of the numerical solution during iteration. Stability of the numerical solution requires for all wavenumbers . It can be shown that in order for the quadratic equation

(37) |

to have bounded roots , it is necessary that . This is equivalent to

(38) |

thus yields the well-known CFL condition

In domain, the -D problem can be extracted from the vertical component of Equation 19

Following the same analysis for H-2, we can obtain domain CFL condition

Wavefield extrapolation in pseudodepth domain |

2013-04-02