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The initiation of migration based on equation (4) requires the specification of
both *P* and on the surface. Since only one
of these fields is recorded in practice, the remaining field must be
generated from mathematical assumptions.
In a region in which the acoustic velocity c is constant, the acoustic
wave equation can be doubly transformed in x and t to give
| |
(20) |

where P is the two dimensionally transformed pressure and *k*_{x} is the
horizontal wavenumber. The solution to equation (20) are given by
| |
(21) |

the solution (21) includes only upgoing waves under the convention that z
increases with depth.
The doubly transformed pressure gradients can be obtained from equation (21)
by differentiation
| |
(22) |

The generated vertical pressure gradient on the surface are obtained from
equation (22) by setting *z*=0 and by an inverse Fourier transformation with
respect to x.

** Next:** ELIMINATION OF EVANESCENT ENERGY
** Up:** Ji: generalized phase-shift method
** Previous:** Tal-Ezer Method
Stanford Exploration Project

1/13/1998