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Given a vertically upcoming plane wave
at the earth's surface,
say ,and an assumption that the earth's velocity is
vertically stratified, i.e. *v*=*v*(*z*),
we can presume that the upcoming wave down in the earth
is simply time-shifted from what we see on the surface.
(This assumes no multiple reflections.)
Time shifting can be represented as a linear operator in the time domain
by representing it as convolution with an impulse function.
In the frequency domain, time shifting is simply multiplying
by a complex exponential.
This is expressed as
| |
(3) |

| (4) |

Sign conventions must be attended to,
and that is explained more fully in chapter .

** Next:** Continuation of a dipping
** Up:** Downward continuation
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Stanford Exploration Project

12/26/2000