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In a 2-D rectangular coordinate frame the wave equation in the time
domain is given by,

When this equation is Fourier transformed over time and *x* we obtain,
or,
If we assume a solution of the form,
*P*(*z*) = *P*(*z*_{0}) *e*^{ i kz ( z- z0 ) },

we find
| |
(1) |

Given a solution at one depth level *P*(*z*) we can extrapolate it to a new depth
level using a pure phase shift .The positive square root is chosen for positive frequencies in order to select
waves that propagate downwards as time increases.
Using this method we can propagate an initial condition specified at
*z*=0 to any depth by applying suitable phase shifts at each depth level.

** Next:** Initial conditions in rectangular
** Up:** Nichols: Modeling in polar
** Previous:** Introduction
Stanford Exploration Project

11/17/1997