The nice thing about a vertically incident source of
plane waves *p*=0 in a horizontally stratified medium
is that the ensuing wavefield is laterally invariant.
In other words, an observation or a theory for a wavefield would
in this case be of
the form .Snell waves for any particular nonzero *p*-value are also laterally invariant.
That is, with

(27) | ||

(28) |

(29) |

The coordinate system (27) and (28) is a retarded coordinate system, not a moving coordinate system. Moving coordinate systems work out badly in solid-earth geophysics. The velocity function is never time-variable in the earth, but it becomes time-variable in a moving coordinate system. This adds a whole dimension to computational complexity.

The goal is to create images from data using a
*model*
velocity that is a function of all space dimensions.
But the coordinate system used will have a
*reference*
velocity that is a function of depth only.

10/31/1997