Wavefield extrapolation in pseudodepth domain |

A geometrical description of the domain isotropic wavefield can be achieved by looking at its eikonal. A dispersion relation associated with the domain wave equation 15 is obtained by taking Fourier transform of this equation in space and time, specifically, do the substitution and , the result is

Note here and has units of , while has the angular frequency unit of .

We then relate slowness vector with wavenumber vector by , thus the domain isotropic eikonal equation is

where is the component of slowness vector in the direction, is traveltime. Similarly, while and has slowness units , is dimensionless. Alternatively, Equation G-2 can be derived by applying chain rule 9 to the Cartesian domain eikonal .

Wavefield extrapolation in pseudodepth domain |

2013-04-02